From 5af6d723ab21f6ab7b47eeeb97e9464403a89f63 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 12 Mar 2016 16:28:55 -0300
Subject: [PATCH 01/33] added bucket and counting sort

---
 chapter10/01-SortingSearchingAlgorithms.js | 82 +++++++++++++++++++---
 1 file changed, 73 insertions(+), 9 deletions(-)

diff --git a/chapter10/01-SortingSearchingAlgorithms.js b/chapter10/01-SortingSearchingAlgorithms.js
index b4081024..77a95497 100755
--- a/chapter10/01-SortingSearchingAlgorithms.js
+++ b/chapter10/01-SortingSearchingAlgorithms.js
@@ -6,10 +6,12 @@ function ArrayList(){
         array.push(item);
     };
 
-    var swap = function(index1, index2){
+    var swap = function(array, index1, index2){
         var aux = array[index1];
         array[index1] = array[index2];
         array[index2] = aux;
+        //ES2015 swap - Firefox only, for other browser, uncomment code above and coment line below
+        //[array[index1], array[index2]] = [array[index2], array[index1]];
     };
 
     this.toString= function(){
@@ -25,7 +27,7 @@ function ArrayList(){
                 console.log('compare ' + array[j] + ' with ' + array[j+1]);
                 if (array[j] > array[j+1]){
                     console.log('swap ' + array[j] + ' with ' + array[j+1]);
-                    swap(j, j+1);
+                    swap(array, j, j+1);
                 }
             }
         }
@@ -84,6 +86,20 @@ function ArrayList(){
         }
     };
 
+    var insertionSort_ = function(array){
+        var length = array.length,
+            j, temp;
+        for (var i=1; i<length; i++){
+            j = i;
+            temp = array[i];
+            while (j>0 && array[j-1] > temp){
+                array[j] = array[j-1];
+                j--;
+            }
+            array[j] = temp;
+        }
+    };
+
     this.mergeSort = function(){
         array = mergeSortRec(array);
     };
@@ -156,7 +172,7 @@ function ArrayList(){
 
             if (i <= j) {
                 console.log('swap ' + array[i] + ' with ' + array[j]);
-                swapQuickStort(array, i, j);
+                swap(array, i, j);
                 i++;
                 j--;
             }
@@ -165,12 +181,6 @@ function ArrayList(){
         return i;
     };
 
-    var swapQuickStort = function(array, index1, index2){
-        var aux = array[index1];
-        array[index1] = array[index2];
-        array[index2] = aux;
-    };
-
     var quick = function(array, left, right){
 
         var index;
@@ -190,6 +200,60 @@ function ArrayList(){
         return array;
     };
 
+    this.countingSort = function(){
+
+        var i,
+            maxValue = this.findMaxValue(),
+            sortedIndex = 0,
+            counts = new Array(maxValue + 1);
+
+        for (i = 0; i < array.length; i++) {
+            if (!counts[array[i]]) {
+                counts[array[i]] = 0;
+            }
+            counts[array[i]]++;
+        }
+
+        console.log('Frequencies: ' + counts.join());
+
+        for (i = 0; i < counts.length; i++) {
+            while (counts[i] > 0) {
+                array[sortedIndex++] = i;
+                counts[i]--;
+            }
+        }
+    };
+
+    this.bucketSort = function(bucketSize){
+
+        var i,
+            minValue = this.findMinValue(),
+            maxValue = this.findMaxValue(),
+            BUCKET_SIZE = 10;
+
+        bucketSize = bucketSize || BUCKET_SIZE;
+        var bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;
+        var buckets = new Array(bucketCount);
+        for (i = 0; i < buckets.length; i++) {
+            buckets[i] = [];
+        }
+
+        for (i = 0; i < array.length; i++) {
+            buckets[Math.floor((array[i] - minValue) / bucketSize)].push(array[i]);
+        }
+
+        array = [];
+        for (i = 0; i < buckets.length; i++) {
+            insertionSort_(buckets[i]);
+
+            console.log('bucket ' + i + ': ' + buckets[i].join());
+
+            for (var j = 0; j < buckets[i].length; j++) {
+                array.push(buckets[i][j]);
+            }
+        }
+    };
+
     this.sequentialSearch = function(item){
 
         for (var i=0; i<array.length; i++){

From 22a6af63183b661fca1944bfa55ca0bf1228838e Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sun, 13 Mar 2016 10:59:41 -0300
Subject: [PATCH 02/33] added heap sort

---
 chapter10/01-SortingSearchingAlgorithms.js | 50 +++++++++++++++++++++-
 1 file changed, 48 insertions(+), 2 deletions(-)

diff --git a/chapter10/01-SortingSearchingAlgorithms.js b/chapter10/01-SortingSearchingAlgorithms.js
index 77a95497..ad23c9d9 100755
--- a/chapter10/01-SortingSearchingAlgorithms.js
+++ b/chapter10/01-SortingSearchingAlgorithms.js
@@ -200,6 +200,47 @@ function ArrayList(){
         return array;
     };
 
+    this.heapSort = function(){
+        var heapSize = array.length;
+
+        buildHeap(array);
+
+        while (heapSize > 1) {
+            heapSize--;
+            swap(array, 0, heapSize);
+            heapify(array, heapSize, 0);
+        }
+    };
+
+    var buildHeap = function(array){
+        var heapSize = array.length;
+        for (var i = Math.floor(array.length / 2); i >= 0; i--) {
+            heapify(array, heapSize, i);
+        }
+    };
+
+    var heapify = function(array, heapSize, i){
+        var left = i * 2 + 1,
+            right = i * 2 + 2,
+            largest = i;
+
+        if (left < heapSize && array[left] > array[largest]) {
+            largest = left;
+        }
+
+        if (right < heapSize && array[right] > array[largest]) {
+            largest = right;
+        }
+
+        console.log('Heap Index = '+ i + ' and Heap Size = ' + heapSize);
+
+        if (largest !== i) {
+            console.log('swap index ' + i + ' with ' + largest + ' (' + + array[i] + ',' + array[largest] + ')');
+            swap(array, i, largest);
+            heapify(array, heapSize, largest);
+        }
+    };
+
     this.countingSort = function(){
 
         var i,
@@ -229,24 +270,29 @@ function ArrayList(){
         var i,
             minValue = this.findMinValue(),
             maxValue = this.findMaxValue(),
-            BUCKET_SIZE = 10;
+            BUCKET_SIZE = 5;
+
+        console.log('minValue ' + minValue);
+        console.log('maxValue ' + maxValue);
 
         bucketSize = bucketSize || BUCKET_SIZE;
         var bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;
         var buckets = new Array(bucketCount);
+        console.log('bucketSize = ' + bucketCount);
         for (i = 0; i < buckets.length; i++) {
             buckets[i] = [];
         }
 
         for (i = 0; i < array.length; i++) {
             buckets[Math.floor((array[i] - minValue) / bucketSize)].push(array[i]);
+            console.log('pushing item ' + array[i] + ' to bucket index ' + Math.floor((array[i] - minValue) / bucketSize));
         }
 
         array = [];
         for (i = 0; i < buckets.length; i++) {
             insertionSort_(buckets[i]);
 
-            console.log('bucket ' + i + ': ' + buckets[i].join());
+            console.log('bucket sorted ' + i + ': ' + buckets[i].join());
 
             for (var j = 0; j < buckets[i].length; j++) {
                 array.push(buckets[i][j]);

From c317e60ed08ad36b046b108155b06917a2b98971 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sun, 13 Mar 2016 10:59:58 -0300
Subject: [PATCH 03/33] added bucket, count, heap sort examples

---
 chapter10/02-UsingSortingAlgorithms.js | 81 ++++++++++++++++----------
 1 file changed, 50 insertions(+), 31 deletions(-)

diff --git a/chapter10/02-UsingSortingAlgorithms.js b/chapter10/02-UsingSortingAlgorithms.js
index e09c3e33..3b38c037 100755
--- a/chapter10/02-UsingSortingAlgorithms.js
+++ b/chapter10/02-UsingSortingAlgorithms.js
@@ -14,77 +14,96 @@ function createRandomNonSortedArray(){
     array.insert(3);
     array.insert(5);
     array.insert(1);
+    array.insert(6);
     array.insert(4);
+    array.insert(7);
     array.insert(2);
 
     return array;
 }
 
-console.log('********** Bubble Sort **********');
+function printArray(array){
+    console.log(array.toString());
+}
 
-var array = createNonSortedArray(5);
+function createNonSortedArrayAndPrint(size){
+    var array = createNonSortedArray(size);
+    printArray(array);
+
+    return array;
+}
+
+console.log('********** Bubble Sort **********');
 
-console.log(array.toString());
+var array = createNonSortedArrayAndPrint(5);
 
 array.bubbleSort();
 
-console.log(array.toString());
+printArray(array);
 
 console.log('********** Modified Bubble Sort **********');
 
-array = createNonSortedArray(5);
-
-console.log(array.toString());
+array = createNonSortedArrayAndPrint(5);
 
 array.modifiedBubbleSort();
 
-console.log(array.toString());
+printArray(array);
 
 console.log('********** Selection Sort **********');
 
-array = createNonSortedArray(5);
-
-console.log(array.toString());
+array = createNonSortedArrayAndPrint(5);
 
 array.selectionSort();
 
-console.log(array.toString());
+printArray(array);
 
 console.log('********** Insertion Sort **********');
 
-array = createRandomNonSortedArray();
-
-console.log(array.toString());
+array = createNonSortedArrayAndPrint();
 
 array.insertionSort();
 
-console.log(array.toString());
+printArray(array);
 
 console.log('********** Merge Sort **********');
 
-array = createNonSortedArray(8);
-
-console.log(array.toString());
+array = createNonSortedArrayAndPrint(8);
 
 array.mergeSort();
 
-console.log(array.toString());
+printArray(array);
 
 console.log('********** Quick Sort **********');
-array = new ArrayList();
-
-array.insert(3);
-array.insert(5);
-array.insert(1);
-array.insert(6);
-array.insert(4);
-array.insert(7);
-array.insert(2);
+array = createRandomNonSortedArray();
 
-console.log(array.toString());
+printArray(array);
 
 array.quickSort();
 
-console.log(array.toString());
+printArray(array);
+
+console.log('********** Heap Sort **********');
+array = createRandomNonSortedArray();
+
+printArray(array);
+
+array.heapSort();
+
+printArray(array);
+
+
+console.log('********** Counting Sort **********');
+
+array = createNonSortedArrayAndPrint(8);
+
+array.countingSort();
+
+printArray(array);
+
+console.log('********** Bucket Sort **********');
+
+array = createNonSortedArrayAndPrint(8);
 
+array.bucketSort(3);
 
+printArray(array);

From 05ca4cb4ec4e5e7e598214f7e28942f6d24ddd7e Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sun, 13 Mar 2016 11:49:51 -0300
Subject: [PATCH 04/33] added radix sort

---
 chapter10/01-SortingSearchingAlgorithms.js | 51 ++++++++++++++++++++++
 chapter10/02-UsingSortingAlgorithms.js     | 17 ++++++++
 2 files changed, 68 insertions(+)

diff --git a/chapter10/01-SortingSearchingAlgorithms.js b/chapter10/01-SortingSearchingAlgorithms.js
index ad23c9d9..9746795e 100755
--- a/chapter10/01-SortingSearchingAlgorithms.js
+++ b/chapter10/01-SortingSearchingAlgorithms.js
@@ -18,6 +18,10 @@ function ArrayList(){
         return array.join();
     };
 
+    this.array= function(){
+        return array;
+    };
+
     this.bubbleSort = function(){
         var length = array.length;
 
@@ -300,6 +304,53 @@ function ArrayList(){
         }
     };
 
+    this.radixSort = function(radixBase){
+
+        var i,
+            minValue = this.findMinValue(),
+            maxValue = this.findMaxValue(),
+            radixBase = radixBase || 10;
+
+        // Perform counting sort for each significant digit), starting at 1
+        var significantDigit = 1;
+        while (((maxValue - minValue) / significantDigit) >= 1) {
+            console.log('radix sort for digit ' + significantDigit);
+            array = countingSortForRadix(array, radixBase, significantDigit, minValue);
+            console.log(array.join());
+            significantDigit *= radixBase;
+        }
+    };
+
+    var countingSortForRadix = function(array, radixBase, significantDigit, minValue){
+        var i, countsIndex,
+            counts = new Array(radixBase),
+            aux = new Array(radixBase);
+
+        for (i = 0; i < radixBase; i++) {
+            counts[i] = 0;
+        }
+
+        for (i = 0; i < array.length; i++) {
+            countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
+            counts[countsIndex]++;
+        }
+
+        for (i = 1; i < radixBase; i++) {
+            counts[i] += counts[i - 1];
+        }
+
+        for (i = array.length - 1; i >= 0; i--) {
+            countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
+            aux[--counts[countsIndex]] = array[i];
+        }
+
+        for (i = 0; i < array.length; i++) {
+            array[i] = aux[i];
+        }
+
+        return array;
+    };
+
     this.sequentialSearch = function(item){
 
         for (var i=0; i<array.length; i++){
diff --git a/chapter10/02-UsingSortingAlgorithms.js b/chapter10/02-UsingSortingAlgorithms.js
index 3b38c037..fcdf6dc3 100755
--- a/chapter10/02-UsingSortingAlgorithms.js
+++ b/chapter10/02-UsingSortingAlgorithms.js
@@ -107,3 +107,20 @@ array = createNonSortedArrayAndPrint(8);
 array.bucketSort(3);
 
 printArray(array);
+
+console.log('********** Radix Sort **********');
+
+var array = new ArrayList();
+
+array.insert(30);
+array.insert(52);
+array.insert(13);
+array.insert(25);
+array.insert(31);
+array.insert(23);
+array.insert(2);
+
+array.radixSort();
+
+console.log('Result: ');
+printArray(array);

From b12f757e7f89716615b1410323d443142cf73f65 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Tue, 15 Mar 2016 20:16:59 -0300
Subject: [PATCH 05/33] added heap sort algorithm

---
 chapter10/01-SortingSearchingAlgorithms.js | 7 ++++++-
 chapter10/02-UsingSortingAlgorithms.js     | 2 +-
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/chapter10/01-SortingSearchingAlgorithms.js b/chapter10/01-SortingSearchingAlgorithms.js
index 9746795e..916e7403 100755
--- a/chapter10/01-SortingSearchingAlgorithms.js
+++ b/chapter10/01-SortingSearchingAlgorithms.js
@@ -211,16 +211,20 @@ function ArrayList(){
 
         while (heapSize > 1) {
             heapSize--;
+            console.log('swap (' + + array[0] + ',' + array[heapSize] + ')');
             swap(array, 0, heapSize);
+            console.log('heapify ' + array.join());
             heapify(array, heapSize, 0);
         }
     };
 
     var buildHeap = function(array){
+        console.log('building heap');
         var heapSize = array.length;
         for (var i = Math.floor(array.length / 2); i >= 0; i--) {
             heapify(array, heapSize, i);
         }
+        console.log('heap created: ' + array.join());
     };
 
     var heapify = function(array, heapSize, i){
@@ -236,11 +240,12 @@ function ArrayList(){
             largest = right;
         }
 
-        console.log('Heap Index = '+ i + ' and Heap Size = ' + heapSize);
+        console.log('Heapify Index = '+ i + ' and Heap Size = ' + heapSize);
 
         if (largest !== i) {
             console.log('swap index ' + i + ' with ' + largest + ' (' + + array[i] + ',' + array[largest] + ')');
             swap(array, i, largest);
+            console.log('heapify ' + array.join());
             heapify(array, heapSize, largest);
         }
     };
diff --git a/chapter10/02-UsingSortingAlgorithms.js b/chapter10/02-UsingSortingAlgorithms.js
index fcdf6dc3..92b63e8f 100755
--- a/chapter10/02-UsingSortingAlgorithms.js
+++ b/chapter10/02-UsingSortingAlgorithms.js
@@ -59,7 +59,7 @@ printArray(array);
 
 console.log('********** Insertion Sort **********');
 
-array = createNonSortedArrayAndPrint();
+array = createNonSortedArrayAndPrint(5);
 
 array.insertionSort();
 

From 9c9b0e771296ee1076b28ac885bc6d7e5ff373bf Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Tue, 15 Mar 2016 20:17:09 -0300
Subject: [PATCH 06/33] updated read

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 48f5d487..f2762892 100644
--- a/README.md
+++ b/README.md
@@ -29,7 +29,7 @@ Book link - second edition:
 * 07: [Dictionaries and Hashes](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter07)
 * 08: [Trees](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter08)
 * 09: [Graphs](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter09)
-* 10: Sorting and searching algorithms
+* 10: [Sorting and searching algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter10)
 * 11: Pattern of algorithms
 * 12: More about algorithms
 * 13: Functional programming and data structures

From e5e3d664f4795207c4aeaa6db51695e6c2c24559 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:39:47 -0300
Subject: [PATCH 07/33] removed unnecessary code

---
 chapter11/03-MinCoinChangeDP.js                      |  2 --
 chapter11/07-LongestCommonSubsequenceDP.html         | 10 ++++++++++
 chapter11/08-LongestCommonSubsequenceRecursive.html  | 10 ++++++++++
 chapter11/09-MatrixChainMultiplicationDP.html        | 10 ++++++++++
 chapter11/10-MatrixChainMultiplicationRecursive.html | 10 ++++++++++
 5 files changed, 40 insertions(+), 2 deletions(-)
 create mode 100644 chapter11/07-LongestCommonSubsequenceDP.html
 create mode 100644 chapter11/08-LongestCommonSubsequenceRecursive.html
 create mode 100644 chapter11/09-MatrixChainMultiplicationDP.html
 create mode 100644 chapter11/10-MatrixChainMultiplicationRecursive.html

diff --git a/chapter11/03-MinCoinChangeDP.js b/chapter11/03-MinCoinChangeDP.js
index 75d0bfd2..90a4a541 100644
--- a/chapter11/03-MinCoinChangeDP.js
+++ b/chapter11/03-MinCoinChangeDP.js
@@ -1,7 +1,5 @@
 function MinCoinChange(coins){
 
-    var coins = coins;
-
     var cache = {};
 
     this.makeChange = function(amount) {
diff --git a/chapter11/07-LongestCommonSubsequenceDP.html b/chapter11/07-LongestCommonSubsequenceDP.html
new file mode 100644
index 00000000..d538fea6
--- /dev/null
+++ b/chapter11/07-LongestCommonSubsequenceDP.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/08-LongestCommonSubsequenceRecursive.html b/chapter11/08-LongestCommonSubsequenceRecursive.html
new file mode 100644
index 00000000..d538fea6
--- /dev/null
+++ b/chapter11/08-LongestCommonSubsequenceRecursive.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/09-MatrixChainMultiplicationDP.html b/chapter11/09-MatrixChainMultiplicationDP.html
new file mode 100644
index 00000000..d538fea6
--- /dev/null
+++ b/chapter11/09-MatrixChainMultiplicationDP.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/10-MatrixChainMultiplicationRecursive.html b/chapter11/10-MatrixChainMultiplicationRecursive.html
new file mode 100644
index 00000000..d538fea6
--- /dev/null
+++ b/chapter11/10-MatrixChainMultiplicationRecursive.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+
+</body>
+</html>
\ No newline at end of file

From e7ebf9c9b8dfbd2b73189423362e70af50eff6c2 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:40:07 -0300
Subject: [PATCH 08/33] removed unnecessary code

---
 chapter11/04-MinCoinChangeGreedy.js | 1 -
 1 file changed, 1 deletion(-)

diff --git a/chapter11/04-MinCoinChangeGreedy.js b/chapter11/04-MinCoinChangeGreedy.js
index a935c16b..3050f7ed 100644
--- a/chapter11/04-MinCoinChangeGreedy.js
+++ b/chapter11/04-MinCoinChangeGreedy.js
@@ -18,7 +18,6 @@ function MinCoinChange(coins){
     };
 }
 
-
 var minCoinChange = new MinCoinChange([1, 5, 10, 25]);
 console.log(minCoinChange.makeChange(36));
 

From 5a3807565caba9f2f9445e5feeaa40f8aa3b4ae8 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:40:41 -0300
Subject: [PATCH 09/33] updated read

---
 README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/README.md b/README.md
index f2762892..8b256af7 100644
--- a/README.md
+++ b/README.md
@@ -30,9 +30,8 @@ Book link - second edition:
 * 08: [Trees](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter08)
 * 09: [Graphs](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter09)
 * 10: [Sorting and searching algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter10)
-* 11: Pattern of algorithms
+* 11: [Pattern of algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter11)
 * 12: More about algorithms
-* 13: Functional programming and data structures
 
 ### First Edition source code:
 

From 5261d58c421da24994e99e42843db987d5ae0991 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:41:12 -0300
Subject: [PATCH 10/33] knapSack dp

---
 chapter11/05-KnapsackProblemDP.js | 53 +++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 chapter11/05-KnapsackProblemDP.js

diff --git a/chapter11/05-KnapsackProblemDP.js b/chapter11/05-KnapsackProblemDP.js
new file mode 100644
index 00000000..fb6adbe7
--- /dev/null
+++ b/chapter11/05-KnapsackProblemDP.js
@@ -0,0 +1,53 @@
+function knapSack(capacity, weights, values, n) {
+
+    var i, w, a, b, kS = [];
+
+    for (i = 0; i <= n; i++) {
+        kS[i] = [];
+    }
+
+    for (i = 0; i <= n; i++){
+        for (w = 0; w <= capacity; w++){
+            if (i == 0 || w == 0){
+                kS[i][w] = 0;
+
+            } else if (weights[i-1] <= w){
+                a = values[i-1] + kS[i-1][w-weights[i-1]];
+                b = kS[i-1][w];
+                kS[i][w] = (a > b) ? a : b; //max(a,b)
+                console.log(a + ' can be part of the solution');
+            } else{
+                kS[i][w] = kS[i-1][w];
+            }
+        }
+        console.log(kS[i].join());
+    }
+
+    //extra algorithm to find the items that are part of the solution
+    findValues(n, capacity, kS, values, weights);
+
+    return kS[n][capacity];
+}
+
+function findValues(n, capacity, kS, weights, values){
+    var i=n, k=capacity;
+
+    console.log('Items that are part of the solution:');
+
+    while (i>0 && k>0){
+        if (kS[i][k] !== kS[i-1][k]){
+            console.log('item '+i+' can be part of solution w,v: ' + weights[i-1] + ',' + values[i-1]);
+            i--;
+            k = k - kS[i][k];
+        } else {
+            i--;
+        }
+    }
+}
+
+var values = [3,4,5],
+    weights = [2,3,4],
+    capacity = 5,
+    n = values.length;
+
+console.log('Total value that can be carried: ' + knapSack(capacity, weights, values, n));
\ No newline at end of file

From fd0f1d3b9fbdd36c9e12c609d8c295c82dd0c64b Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:41:23 -0300
Subject: [PATCH 11/33] knapSack recursice

---
 ....html => 06-KnapSackProblemRecursive.html} |  2 +-
 chapter11/06-KnapSackProblemRecursive.js      | 22 +++++++++++++++++++
 2 files changed, 23 insertions(+), 1 deletion(-)
 rename chapter11/{08-LongestCommonSubsequenceRecursive.html => 06-KnapSackProblemRecursive.html} (68%)
 create mode 100644 chapter11/06-KnapSackProblemRecursive.js

diff --git a/chapter11/08-LongestCommonSubsequenceRecursive.html b/chapter11/06-KnapSackProblemRecursive.html
similarity index 68%
rename from chapter11/08-LongestCommonSubsequenceRecursive.html
rename to chapter11/06-KnapSackProblemRecursive.html
index d538fea6..cc000756 100644
--- a/chapter11/08-LongestCommonSubsequenceRecursive.html
+++ b/chapter11/06-KnapSackProblemRecursive.html
@@ -5,6 +5,6 @@
     <title></title>
 </head>
 <body>
-
+<script src="06-KnapSackProblemRecursive.js"></script>
 </body>
 </html>
\ No newline at end of file
diff --git a/chapter11/06-KnapSackProblemRecursive.js b/chapter11/06-KnapSackProblemRecursive.js
new file mode 100644
index 00000000..583092e1
--- /dev/null
+++ b/chapter11/06-KnapSackProblemRecursive.js
@@ -0,0 +1,22 @@
+function knapSack(capacity, weights, values, n) {
+
+    if (n == 0 || capacity == 0){
+        return 0;
+    }
+
+    if (weights[n-1] > capacity){
+        return knapSack(capacity, weights, values, n-1);
+
+    } else {
+        var a = values[n-1] + knapSack(capacity-weights[n-1], weights, values, n-1),
+            b = knapSack(capacity, weights, values, n-1);
+        return (a > b) ? a : b;
+    }
+}
+
+var values = [3,4,5],
+    weights = [2,3,4],
+    capacity = 5,
+    n = values.length;
+
+console.log(knapSack(capacity, weights, values, n));
\ No newline at end of file

From aef7f9294c7d019fa9ff2752f6f6154f2a514f47 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:41:40 -0300
Subject: [PATCH 12/33] knapSack greedy

---
 ...nDP.html => 07-KnapSackProblemGreedy.html} |  2 +-
 chapter11/07-KnapSackProblemGreedy.js         | 28 +++++++++++++++++++
 2 files changed, 29 insertions(+), 1 deletion(-)
 rename chapter11/{09-MatrixChainMultiplicationDP.html => 07-KnapSackProblemGreedy.html} (69%)
 create mode 100644 chapter11/07-KnapSackProblemGreedy.js

diff --git a/chapter11/09-MatrixChainMultiplicationDP.html b/chapter11/07-KnapSackProblemGreedy.html
similarity index 69%
rename from chapter11/09-MatrixChainMultiplicationDP.html
rename to chapter11/07-KnapSackProblemGreedy.html
index d538fea6..227d7b4b 100644
--- a/chapter11/09-MatrixChainMultiplicationDP.html
+++ b/chapter11/07-KnapSackProblemGreedy.html
@@ -5,6 +5,6 @@
     <title></title>
 </head>
 <body>
-
+<script src="07-KnapSackProblemGreedy.js"></script>
 </body>
 </html>
\ No newline at end of file
diff --git a/chapter11/07-KnapSackProblemGreedy.js b/chapter11/07-KnapSackProblemGreedy.js
new file mode 100644
index 00000000..4c12e1a6
--- /dev/null
+++ b/chapter11/07-KnapSackProblemGreedy.js
@@ -0,0 +1,28 @@
+function knapSack(capacity, values, weights) {
+    var n = values.length,
+        load = 0,
+        i = 0,
+        val = 0;
+
+    for (i=0; i<n && load < capacity; i++) {
+
+        if (weights[i] <= (capacity-load)) {
+            val += values[i];
+            load += weights[i];
+            console.log('using item ' + (i+1) + ' for the solution');
+
+        } else {
+            var r = (capacity-load)/weights[i];
+            val += r * values[i];
+            load += weights[i];
+            console.log('using ratio of ' + r + ' for item ' + (i+1) + ' for the solution');
+        }
+    }
+    return val;
+}
+
+var values = [3,4,5],
+    weights = [2,3,4],
+    capacity = 6,
+    n = values.length;
+console.log(knapSack(capacity, values, weights));
\ No newline at end of file

From 425552957e58586f45f98fc61d8ce0fcd0b6f081 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:41:48 -0300
Subject: [PATCH 13/33] knapSack dp

---
 ...ongestCommonSubsequenceDP.html => 05-KnapsackProblemDP.html} | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename chapter11/{07-LongestCommonSubsequenceDP.html => 05-KnapsackProblemDP.html} (70%)

diff --git a/chapter11/07-LongestCommonSubsequenceDP.html b/chapter11/05-KnapsackProblemDP.html
similarity index 70%
rename from chapter11/07-LongestCommonSubsequenceDP.html
rename to chapter11/05-KnapsackProblemDP.html
index d538fea6..316f9722 100644
--- a/chapter11/07-LongestCommonSubsequenceDP.html
+++ b/chapter11/05-KnapsackProblemDP.html
@@ -5,6 +5,6 @@
     <title></title>
 </head>
 <body>
-
+<script src="05-KnapsackProblemDP.js"></script>
 </body>
 </html>
\ No newline at end of file

From f8527d259700bc647cb164b66a3afd07da0d8e1d Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:41:59 -0300
Subject: [PATCH 14/33] lcs dp

---
 ...tml => 08-LongestCommonSubsequenceDP.html} |   2 +-
 chapter11/08-LongestCommonSubsequenceDP.js    | 105 ++++++++++++++++++
 2 files changed, 106 insertions(+), 1 deletion(-)
 rename chapter11/{10-MatrixChainMultiplicationRecursive.html => 08-LongestCommonSubsequenceDP.html} (67%)
 create mode 100644 chapter11/08-LongestCommonSubsequenceDP.js

diff --git a/chapter11/10-MatrixChainMultiplicationRecursive.html b/chapter11/08-LongestCommonSubsequenceDP.html
similarity index 67%
rename from chapter11/10-MatrixChainMultiplicationRecursive.html
rename to chapter11/08-LongestCommonSubsequenceDP.html
index d538fea6..dc63ccce 100644
--- a/chapter11/10-MatrixChainMultiplicationRecursive.html
+++ b/chapter11/08-LongestCommonSubsequenceDP.html
@@ -5,6 +5,6 @@
     <title></title>
 </head>
 <body>
-
+<script src="08-LongestCommonSubsequenceDP.js"></script>
 </body>
 </html>
\ No newline at end of file
diff --git a/chapter11/08-LongestCommonSubsequenceDP.js b/chapter11/08-LongestCommonSubsequenceDP.js
new file mode 100644
index 00000000..b5eaf3f1
--- /dev/null
+++ b/chapter11/08-LongestCommonSubsequenceDP.js
@@ -0,0 +1,105 @@
+function lcs(wordX, wordY) {
+
+    var m = wordX.length,
+        n = wordY.length,
+        l = [],
+        i, j, a, b;
+
+    for (i = 0; i <= m; ++i) {
+        l[i] = [];
+        for (j = 0; j <= n; ++j) {
+            l[i][j] = 0;
+        }
+    }
+
+    for (i=0; i<=m; i++) {
+        for (j=0; j<=n; j++) {
+            if (i == 0 || j == 0){
+                l[i][j] = 0;
+
+            } else if (wordX[i-1] == wordY[j-1]) {
+                l[i][j] = l[i-1][j-1] + 1;
+
+            } else {
+                a = l[i-1][j];
+                b = l[i][j-1];
+                l[i][j] = (a > b) ? a : b; //max(a,b)
+            }
+        }
+        console.log(l[i].join());
+    }
+
+    return l[m][n];
+}
+
+//complete algorithm that prints the LCS as well
+
+function lcs2(wordX, wordY) {
+
+    var m = wordX.length,
+        n = wordY.length,
+        l = [],
+        solution = [],
+        i, j, a, b;
+
+    for (i = 0; i <= m; ++i) {
+        l[i] = [];
+        solution[i] = [];
+        for (j = 0; j <= n; ++j) {
+            l[i][j] = 0;
+            solution[i][j] = '0';
+        }
+    }
+
+    for (i=0; i<=m; i++) {
+        for (j=0; j<=n; j++) {
+            if (i == 0 || j == 0){
+                l[i][j] = 0;
+
+            } else if (wordX[i-1] == wordY[j-1]) {
+                l[i][j] = l[i-1][j-1] + 1;
+                solution[i][j] = 'diagonal';
+
+            } else {
+                a = l[i-1][j];
+                b = l[i][j-1];
+                l[i][j] = (a > b) ? a : b; //max(a,b)
+
+                solution[i][j] = (l[i][j] == l[i - 1][j]) ? 'top' : 'left';
+            }
+        }
+        console.log(l[i].join());
+        console.log(solution[i].join());
+    }
+
+    printSolution(solution, l, wordX, wordY, m, n);
+
+    return l[m][n];
+}
+
+function printSolution(solution, l, wordX, wordY, m, n){
+
+    var a = m, b = n, i, j,
+        x = solution[a][b],
+        answer = '';
+
+    while (x !== '0') {
+        if (solution[a][b] === 'diagonal') {
+            answer = wordX[a - 1] + answer;
+            a--;
+            b--;
+        } else if (solution[a][b] === 'left') {
+            b--;
+        } else if (solution[a][b] === 'top') {
+            a--;
+        }
+        x = solution[a][b];
+    }
+
+    console.log('lcs: '+ answer);
+}
+
+var wordX = 'acbaed',
+    wordY = 'abcadf';
+
+console.log(lcs2(wordX, wordY));
\ No newline at end of file

From 39243c9ca92b79f52650bb537a4be3bdd3a5d120 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:42:06 -0300
Subject: [PATCH 15/33] lcs recursive

---
 .../09-LongestCommonSubsequenceRecursive.html | 10 ++++++++++
 .../09-LongestCommonSubsequenceRecursive.js   | 19 +++++++++++++++++++
 2 files changed, 29 insertions(+)
 create mode 100644 chapter11/09-LongestCommonSubsequenceRecursive.html
 create mode 100644 chapter11/09-LongestCommonSubsequenceRecursive.js

diff --git a/chapter11/09-LongestCommonSubsequenceRecursive.html b/chapter11/09-LongestCommonSubsequenceRecursive.html
new file mode 100644
index 00000000..59573751
--- /dev/null
+++ b/chapter11/09-LongestCommonSubsequenceRecursive.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+<script src="09-LongestCommonSubsequenceRecursive.js"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/09-LongestCommonSubsequenceRecursive.js b/chapter11/09-LongestCommonSubsequenceRecursive.js
new file mode 100644
index 00000000..1c96fab1
--- /dev/null
+++ b/chapter11/09-LongestCommonSubsequenceRecursive.js
@@ -0,0 +1,19 @@
+function lcs(wordwordX, wordwordY, m, n) {
+    
+    if (m == 0 || n == 0){
+        return 0;
+    }
+
+    if (wordwordX[m-1] == wordY[n-1]){
+        return 1 + lcs(wordX, wordY, m-1, n-1);
+    } else {
+        var a = lcs(wordX, wordY, m, n-1),
+            b = lcs(wordX, wordY, m-1, n);
+        return (a > b) ? a : b;
+    }
+}
+
+var wordX = 'acbaed',
+    wordY = 'abcadf';
+
+console.log(lcs(wordX, wordY, wordX.length, wordY.length));
\ No newline at end of file

From 49c5cc773011d0fac3a572531e9e22a361cf8b2f Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:42:22 -0300
Subject: [PATCH 16/33] matrixChainOrder dp

---
 chapter11/10-MatrixChainMultiplicationDP.html | 10 ++++
 chapter11/10-MatrixChainMultiplicationDP.js   | 56 +++++++++++++++++++
 2 files changed, 66 insertions(+)
 create mode 100644 chapter11/10-MatrixChainMultiplicationDP.html
 create mode 100644 chapter11/10-MatrixChainMultiplicationDP.js

diff --git a/chapter11/10-MatrixChainMultiplicationDP.html b/chapter11/10-MatrixChainMultiplicationDP.html
new file mode 100644
index 00000000..2108a100
--- /dev/null
+++ b/chapter11/10-MatrixChainMultiplicationDP.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+<script src="10-MatrixChainMultiplicationDP.js"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/10-MatrixChainMultiplicationDP.js b/chapter11/10-MatrixChainMultiplicationDP.js
new file mode 100644
index 00000000..e335b3cc
--- /dev/null
+++ b/chapter11/10-MatrixChainMultiplicationDP.js
@@ -0,0 +1,56 @@
+function matrixChainOrder(p, n) {
+
+    var i, j, k, l, q,
+        m = [], s=[];
+
+    for (i = 1; i <= n; i++){
+        m[i] = [];
+        m[i][i] = 0;
+
+    }
+
+    for (i = 0; i <= n; i++){ //to help printing the optimal solution
+        s[i] = []; //auxiliary
+        for (j=0; j<=n; j++){
+            s[i][j] = 0;
+        }
+    }
+
+    for (l=2; l<n; l++) {
+        for (i=1; i<=n-l+1; i++) {
+            j = i+l-1;
+            m[i][j] = Number.MAX_SAFE_INTEGER;
+            for (k=i; k<=j-1; k++) {
+                // q = cost/scalar multiplications
+                q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
+                if (q < m[i][j]){
+                    m[i][j] = q;
+                    s[i][j]=k; // s[i,j] = Second auxiliary table that stores k
+                }
+            }
+        }
+    }
+
+    console.log(m);
+    console.log(s);
+
+    printOptimalParenthesis(s, 1, n-1);
+
+    return m[1][n-1];
+}
+
+function printOptimalParenthesis(s, i, j){
+    if(i == j) {
+        console.log("A[" + i + "]");
+    } else {
+        console.log("(");
+        printOptimalParenthesis(s, i, s[i][j]);
+        printOptimalParenthesis(s, s[i][j] + 1, j);
+        console.log(")");
+    }
+}
+
+// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
+var p = [10, 100, 5, 50, 1],
+    n = p.length;
+console.log(matrixChainOrder(p, n));
\ No newline at end of file

From 4828b9f7f9a4399ed2edb7a1d3d4310ec60085cb Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 26 Mar 2016 15:42:27 -0300
Subject: [PATCH 17/33] matrixChainOrder recursive

---
 ...11-MatrixChainMultiplicationRecursive.html | 10 +++++++
 .../11-MatrixChainMultiplicationRecursive.js  | 26 +++++++++++++++++++
 2 files changed, 36 insertions(+)
 create mode 100644 chapter11/11-MatrixChainMultiplicationRecursive.html
 create mode 100644 chapter11/11-MatrixChainMultiplicationRecursive.js

diff --git a/chapter11/11-MatrixChainMultiplicationRecursive.html b/chapter11/11-MatrixChainMultiplicationRecursive.html
new file mode 100644
index 00000000..bb627d51
--- /dev/null
+++ b/chapter11/11-MatrixChainMultiplicationRecursive.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+<script src="11-MatrixChainMultiplicationRecursive.js"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/11-MatrixChainMultiplicationRecursive.js b/chapter11/11-MatrixChainMultiplicationRecursive.js
new file mode 100644
index 00000000..0b327524
--- /dev/null
+++ b/chapter11/11-MatrixChainMultiplicationRecursive.js
@@ -0,0 +1,26 @@
+function matrixChainOrder(p, i, j){
+
+    if(i == j) {
+        return 0;
+    }
+
+    var k, count,
+       min = Number.MAX_SAFE_INTEGER;
+
+    for (k = i; k <j; k++) {
+        count = matrixChainOrder(p, i, k) +
+            matrixChainOrder(p, k+1, j) +
+            p[i-1]*p[k]*p[j];
+
+        if (count < min){
+            min = count;
+        }
+    }
+
+    return min;
+}
+
+var p = [10, 100, 5, 50, 1],
+    n = p.length;
+
+console.log(matrixChainOrder(p, 1, n-1));
\ No newline at end of file

From 7db54bfa32be4923130f9fc341de5770e49e7c72 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sun, 27 Mar 2016 11:14:06 -0300
Subject: [PATCH 18/33] big-o chart code

---
 {chapter11 => chapter12}/05-BigONotation.html | 0
 {chapter11 => chapter12}/05-BigONotation.js   | 0
 {chapter11 => chapter12}/bigOChart/chart.js   | 0
 {chapter11 => chapter12}/bigOChart/index.html | 0
 4 files changed, 0 insertions(+), 0 deletions(-)
 rename {chapter11 => chapter12}/05-BigONotation.html (100%)
 rename {chapter11 => chapter12}/05-BigONotation.js (100%)
 rename {chapter11 => chapter12}/bigOChart/chart.js (100%)
 rename {chapter11 => chapter12}/bigOChart/index.html (100%)

diff --git a/chapter11/05-BigONotation.html b/chapter12/05-BigONotation.html
similarity index 100%
rename from chapter11/05-BigONotation.html
rename to chapter12/05-BigONotation.html
diff --git a/chapter11/05-BigONotation.js b/chapter12/05-BigONotation.js
similarity index 100%
rename from chapter11/05-BigONotation.js
rename to chapter12/05-BigONotation.js
diff --git a/chapter11/bigOChart/chart.js b/chapter12/bigOChart/chart.js
similarity index 100%
rename from chapter11/bigOChart/chart.js
rename to chapter12/bigOChart/chart.js
diff --git a/chapter11/bigOChart/index.html b/chapter12/bigOChart/index.html
similarity index 100%
rename from chapter11/bigOChart/index.html
rename to chapter12/bigOChart/index.html

From 1e2e6711551971feb7768bd5e03dba8014e144b5 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sun, 27 Mar 2016 11:14:40 -0300
Subject: [PATCH 19/33] updated readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 8b256af7..643c6d36 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ Book link - second edition:
 * 09: [Graphs](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter09)
 * 10: [Sorting and searching algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter10)
 * 11: [Pattern of algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter11)
-* 12: More about algorithms
+* 12: [More about algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter12)
 
 ### First Edition source code:
 

From b008a7264913928fa90943647089717d432a8098 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Sat, 2 Apr 2016 12:16:27 -0300
Subject: [PATCH 20/33] js functional programming examples

---
 chapter11/12-IntroFunctionalProgramming.html |  10 ++
 chapter11/12-IntroFunctionalProgramming.js   | 147 +++++++++++++++++++
 2 files changed, 157 insertions(+)
 create mode 100644 chapter11/12-IntroFunctionalProgramming.html
 create mode 100644 chapter11/12-IntroFunctionalProgramming.js

diff --git a/chapter11/12-IntroFunctionalProgramming.html b/chapter11/12-IntroFunctionalProgramming.html
new file mode 100644
index 00000000..422a711b
--- /dev/null
+++ b/chapter11/12-IntroFunctionalProgramming.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+<script src="12-IntroFunctionalProgramming.js"></script>
+</body>
+</html>
\ No newline at end of file
diff --git a/chapter11/12-IntroFunctionalProgramming.js b/chapter11/12-IntroFunctionalProgramming.js
new file mode 100644
index 00000000..47787255
--- /dev/null
+++ b/chapter11/12-IntroFunctionalProgramming.js
@@ -0,0 +1,147 @@
+console.log('Using imperative JS');
+
+var printArray = function(array){
+    for (var i=0; i<array.length; i++){
+        console.log(array[i]);
+    }
+};
+
+printArray([1, 2, 3, 4, 5]);
+
+//how can we abstract the For flow? Can we use a callback for action?
+
+console.log('Using functional JS');
+
+var forEach = function(array, action){
+    for (var i=0; i<array.length; i++){
+        action(array[i]);
+    }
+};
+
+var logItem = function (item) {
+    console.log(item);
+};
+
+forEach([1, 2, 3, 4, 5], logItem);
+
+//how can we abstract the For flow?
+console.log('Finding the min value in an array - imperative');
+
+var findMinArray = function(array){
+    var minValue = array[0];
+    for (var i=1; i<array.length; i++){
+        if (minValue > array[i]){
+            minValue = array[i];
+        }
+    }
+
+    return minValue;
+};
+
+console.log(findMinArray([8,6,4,5,9]));
+
+console.log('Finding the min value in an array - functional ES2015');
+const min_ = function(array){
+    return Math.min(...array)
+};
+
+//simplifying using arrow functions
+const min = arr => Math.min(...arr);
+
+console.log(min_([8,6,4,5,9]));
+console.log(min([8,6,4,5,9]));
+
+//concat + reduce
+console.log('merge arrays - imperative');
+
+var mergeArrays_ = function(arrays){
+    var count = arrays.length,
+        newArray = [],
+        k =0;
+    for (var i=0; i<count; i++){
+        for (var j=0; j<arrays[i].length; j++){
+            newArray[k++] = arrays[i][j];
+        }
+    }
+    return newArray;
+};
+
+console.log(mergeArrays_([[1, 2, 3], [4, 5], [6]]));
+
+console.log('merge arrays - using concat');
+var mergeArraysConcat = function(arrays){
+    return arrays.reduce( function(p,n){
+        return p.concat(n);
+    });
+};
+
+console.log(mergeArraysConcat([[1, 2, 3], [4, 5], [6]]));
+
+console.log('merge arrays - ES2015');
+
+const mergeArrays = (...arrays) => [].concat(...arrays);
+console.log(mergeArrays([1, 2, 3], [4, 5], [6]));
+
+console.log('sum values of arrays - imperative');
+var sumValues = function(array){
+    var total = array[0];
+    for (var i=1; i<array.length; i++){
+        total += array[i];
+    }
+    return total;
+};
+
+console.log(sumValues([1, 2, 3, 4, 5]));
+
+//reduce
+console.log('sum values of arrays - functional');
+var sum_ = function(array){
+    return array.reduce(function(a, b){
+        return a + b;
+    })
+};
+
+console.log(sum_([1, 2, 3, 4, 5]));
+
+console.log('sum values of arrays - ES2015');
+const sum = arr => arr.reduce((a, b) => a + b);
+
+console.log(sum([1, 2, 3, 4, 5]));
+
+//map
+var daysOfWeek = [
+    {name: 'Monday', value: 1},
+    {name: 'Tuesday', value: 2},
+    {name: 'Wednesday', value: 7}
+];
+
+var daysOfWeekValues_ = [];
+for (var i = 0; i < daysOfWeek.length; i++) {
+    daysOfWeekValues_.push(daysOfWeek[i].value);
+}
+
+//to
+var daysOfWeekValues = daysOfWeek.map(function(day) {
+    return day.value;
+});
+console.log(daysOfWeekValues);
+
+
+//filter
+var positiveNumbers_ = function(array){
+    var positive = [];
+    for (var i = 0; i < array.length; i++) {
+        if (array[i] >= 0){
+            positive.push(array[i]);
+        }
+    }
+    return positive;
+}
+console.log(positiveNumbers_([-1,1,2,-2]));
+
+var positiveNumbers = function(array){
+    return array.filter(function(num){
+        return num >= 0;
+    })
+};
+console.log(positiveNumbers([-1,1,2,-2]));
\ No newline at end of file

From 798050597c4e45b614bea3b9890403f0d957235c Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Mon, 18 Apr 2016 20:47:47 -0300
Subject: [PATCH 21/33] fixed chapter name

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 643c6d36..4e9eca37 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ Book link - second edition:
 * 09: [Graphs](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter09)
 * 10: [Sorting and searching algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter10)
 * 11: [Pattern of algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter11)
-* 12: [More about algorithms](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter12)
+* 12: [Algorithm Complexity](https://github.com/loiane/javascript-datastructures-algorithms/tree/second-edition/chapter12)
 
 ### First Edition source code:
 

From 5d9f8c68dca6c43f4c6a25fc769c7e6af15c4511 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loiane@Loianes-MacBook-Pro.local>
Date: Wed, 1 Jun 2016 00:02:58 -0300
Subject: [PATCH 22/33] reviewed code bundle

---
 chapter04/03-PriorityQueue.js | 2 --
 1 file changed, 2 deletions(-)

diff --git a/chapter04/03-PriorityQueue.js b/chapter04/03-PriorityQueue.js
index f9071ddc..3b029e4d 100644
--- a/chapter04/03-PriorityQueue.js
+++ b/chapter04/03-PriorityQueue.js
@@ -50,7 +50,5 @@ let priorityQueue = new PriorityQueue();
 priorityQueue.enqueue("John", 2);
 priorityQueue.enqueue("Jack", 1);
 priorityQueue.enqueue("Camila", 1);
-priorityQueue.enqueue("Maxwell", 2);
-priorityQueue.enqueue("Ana", 3);
 priorityQueue.print();
 

From b6f84d04665e6f98aed8f1089f3ee6e784aed9b1 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Fri, 10 Jun 2016 15:39:43 -0300
Subject: [PATCH 23/33] Update 14-ES6ParameterHandling.js

---
 chapter01/14-ES6ParameterHandling.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapter01/14-ES6ParameterHandling.js b/chapter01/14-ES6ParameterHandling.js
index 706c2059..4645f2a7 100644
--- a/chapter01/14-ES6ParameterHandling.js
+++ b/chapter01/14-ES6ParameterHandling.js
@@ -30,8 +30,8 @@ function restParamaterFunction (x, y, ...a) {
 console.log(restParamaterFunction(1, 2, "hello", true, 7)); // outputs 9;
 
 //code above is the same as ES5:
-function restParamaterFunction (x, y) {
+function restParamaterFunction2 (x, y) {
     var a = Array.prototype.slice.call(arguments, 2);
     return (x + y) * a.length;
 };
-console.log(restParamaterFunction2(1, 2, "hello", true, 7));
\ No newline at end of file
+console.log(restParamaterFunction2(1, 2, "hello", true, 7));

From 2cb57e826889e02d2bd6578255997fa3e75dd8e1 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Fri, 10 Jun 2016 15:46:08 -0300
Subject: [PATCH 24/33] Update 02-UsingDictionaries.js

---
 chapter07/02-UsingDictionaries.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapter07/02-UsingDictionaries.js b/chapter07/02-UsingDictionaries.js
index 3ec30d4b..dc0bf258 100644
--- a/chapter07/02-UsingDictionaries.js
+++ b/chapter07/02-UsingDictionaries.js
@@ -11,9 +11,9 @@ console.log(dictionary.keys()); //outputs ["Gandalf", "John", "Tyrion"]
 console.log(dictionary.values()); //outputs ["gandalf@email.com", "johnsnow@email.com", "tyrion@email.com"]
 console.log(dictionary.get('Tyrion')); //outputs tyrion@email.com
 
-dictionary.delete(‘John');
+dictionary.delete('John');
 
 console.log(dictionary.keys()); //outputs ["Gandalf", "Tyrion"]
 console.log(dictionary.values()); //outputs ["gandalf@email.com", "tyrion@email.com"]
 
-console.log(dictionary.getItems()); //Object {Gandalf: "gandalf@email.com", Tyrion: "tyrion@email.com"}
\ No newline at end of file
+console.log(dictionary.getItems()); //Object {Gandalf: "gandalf@email.com", Tyrion: "tyrion@email.com"}

From d0ebbf9b87573ceb29240e177c7f69448aacc5b8 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Thu, 25 Aug 2016 09:18:00 -0300
Subject: [PATCH 25/33] removed print tree function (did not exist)

---
 chapter08/02-UsingBinarySearchTree.js | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/chapter08/02-UsingBinarySearchTree.js b/chapter08/02-UsingBinarySearchTree.js
index 41f2c691..eb139837 100644
--- a/chapter08/02-UsingBinarySearchTree.js
+++ b/chapter08/02-UsingBinarySearchTree.js
@@ -50,7 +50,3 @@ tree.inOrderTraverse(printNode);
 
 console.log('********* raw data structure ***********');
 console.log(tree.getRoot());
-
-console.log('********* printing HTML tree ***********');
-var parent = document.getElementsByTagName('body')[0];
-printHTMLTree(tree.getRoot(), parent, 255);
\ No newline at end of file

From 78685366d9fa14d5e1d8c84e359f1336782a1330 Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Thu, 1 Sep 2016 14:10:05 -0300
Subject: [PATCH 26/33] closes #13

---
 chapter07/07-HashCollisionLinearProbing.js | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/chapter07/07-HashCollisionLinearProbing.js b/chapter07/07-HashCollisionLinearProbing.js
index 74fdbac5..38b07c0f 100644
--- a/chapter07/07-HashCollisionLinearProbing.js
+++ b/chapter07/07-HashCollisionLinearProbing.js
@@ -46,10 +46,10 @@ function HashLinearProbing(){
                 return table[position].value;
             } else {
                 var index = ++position;
-                while (table[index] === undefined || table[index].key !== key){
+                while (table[index] !== undefined && (table[index] && table[index].key !== key)){
                     index++;
                 }
-                if (table[index].key === key) {
+                if (table[index] && table[index].key === key) {
                     return table[index].value;
                 }
             }
@@ -82,4 +82,4 @@ function HashLinearProbing(){
             }
         }
     };
-}
\ No newline at end of file
+}

From 2a89e21fc883821c6da1068c8d6f4b659f9f7fb3 Mon Sep 17 00:00:00 2001
From: Victor Wang <2501211450@qq.com>
Date: Sun, 11 Sep 2016 16:19:51 +0800
Subject: [PATCH 27/33] Update 05-CircularLinkedList2.js

fix some errors
---
 chapter05/05-CircularLinkedList2.js | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/chapter05/05-CircularLinkedList2.js b/chapter05/05-CircularLinkedList2.js
index 13f36665..5aab62d0 100644
--- a/chapter05/05-CircularLinkedList2.js
+++ b/chapter05/05-CircularLinkedList2.js
@@ -133,8 +133,8 @@ let CircularLinkedList2 = (function () {
 
         remove(element) {
 
-            let index = indexOf(element);
-            return removeAt(index);
+            let index = this.indexOf(element);
+            return this.removeAt(index);
         }
 
         indexOf(element) {
@@ -198,4 +198,4 @@ let CircularLinkedList2 = (function () {
         }
     }
     return CircularLinkedList2;
-})();
\ No newline at end of file
+})();

From 94b2c6826736363a03443aa905ae051dda030169 Mon Sep 17 00:00:00 2001
From: beizhedenglong <2501211450@qq.com>
Date: Sun, 11 Sep 2016 23:26:57 +0800
Subject: [PATCH 28/33] fix bug in CircularLinkedList

There is a bug in insert function. If you insert an element in an empty
list at the first  position. It will throw a TypeError: Cannot read
property 'next' of null.
---
 chapter05/05-CircularLinkedList.js  | 27 +++++++++++++++++----------
 chapter05/05-CircularLinkedList2.js | 21 ++++++++++++---------
 2 files changed, 29 insertions(+), 19 deletions(-)

diff --git a/chapter05/05-CircularLinkedList.js b/chapter05/05-CircularLinkedList.js
index 5f05e85f..c3151148 100644
--- a/chapter05/05-CircularLinkedList.js
+++ b/chapter05/05-CircularLinkedList.js
@@ -46,16 +46,22 @@ function CircularLinkedList() {
                 index = 0;
 
             if (position === 0){ //add on first position
-
-                node.next = current;
-
-                //update last element
-                while(current.next !== head){ //last element will be head instead of NULL
-                    current = current.next;
+                
+                if(!head){ // if no node  in list
+                    head = node;
+                    node.next = head;
+                }else{
+                    node.next = current;
+
+                    //update last element
+                    while(current.next !== head){ //last element will be head instead of NULL
+                        current = current.next;
+                    }
+
+                    head = node;
+                    current.next = head;
                 }
-
-                head = node;
-                current.next = head;
+                
 
             } else {
                 while (index++ < position){
@@ -180,4 +186,5 @@ function CircularLinkedList() {
     this.print = function(){
         console.log(this.toString());
     };
-}
\ No newline at end of file
+}
+
diff --git a/chapter05/05-CircularLinkedList2.js b/chapter05/05-CircularLinkedList2.js
index 5aab62d0..6f7574ef 100644
--- a/chapter05/05-CircularLinkedList2.js
+++ b/chapter05/05-CircularLinkedList2.js
@@ -58,15 +58,18 @@ let CircularLinkedList2 = (function () {
 
               if (position === 0) { //add on first position
 
-                    node.next = current;
-
-                    //update last element
-                    while (current.next !== this.getHead()) { //last element will be head instead of NULL
-                        current = current.next;
-                    }
-
-                    head.set(this, node);
-                    current.next = this.getHead();
+                  if(!this.getHead()) { // if no node  in list
+                      head.set(this, node);
+                      node.next = this.getHead();
+                  } else {
+                      node.next = current;
+                      //update last element
+                      while(current.next !== this.getHead()) { //last element will be head instead of NULL
+                          current = current.next;
+                      }
+                      head.set(this, node);
+                      current.next = this.getHead();
+                  }
 
                 } else {
                     while (index++ < position) {

From c2eb4acefba97503766ac59158d299c22a56c5f8 Mon Sep 17 00:00:00 2001
From: TerryX <terryxlife@gmail.com>
Date: Wed, 2 Nov 2016 23:21:11 +0800
Subject: [PATCH 29/33] Fix aValues being undefined

---
 chapter02/06-ES6Methods.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapter02/06-ES6Methods.js b/chapter02/06-ES6Methods.js
index 60468aa4..bf4eb36a 100644
--- a/chapter02/06-ES6Methods.js
+++ b/chapter02/06-ES6Methods.js
@@ -40,7 +40,7 @@ console.log(aKeys.next()); // {value: 1, done: false }
 console.log(aKeys.next()); // {value: 2, done: false }
 
 console.log('Array.values');
-//let aValues = numbers.values();
+let aValues = numbers.values();
 console.log(aValues.next()); // {value: 1, done: false } done false means iterator has more values
 console.log(aValues.next()); // {value: 2, done: false }
 console.log(aValues.next()); // {value: 3, done: false }

From a5fc23e474e68f9edbf003271264e447d65310ac Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Mon, 17 Apr 2017 14:26:05 -0300
Subject: [PATCH 30/33] Update README.md

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 4e9eca37..64771d99 100644
--- a/README.md
+++ b/README.md
@@ -5,7 +5,7 @@ Source code of **Learning JavaScript Data Structures and Algorithms** book.
 
 | 1st edition   | 2nd edition   | 
 | ------------- |:-------------:| 
-| ![1st edition](https://d1ldz4te4covpm.cloudfront.net/sites/default/files/imagecache/ppv4_main_book_cover/4874OS_Learning%20JavaScript%20Data%20Structures%20and%20Algorithms.jpg)      | ![2nd edition](https://dz13w8afd47il.cloudfront.net/sites/default/files/imagecache/ppv4_main_book_cover/B05348_MockupCover_Normal.jpg) | 
+| ![1st edition](https://d1ldz4te4covpm.cloudfront.net/sites/default/files/imagecache/ppv4_main_book_cover/4874OS_Learning%20JavaScript%20Data%20Structures%20and%20Algorithms.jpg)      | ![2nd edition](https://d255esdrn735hr.cloudfront.net/sites/default/files/imagecache/ppv4_main_book_cover/5493OS_5348_Learning%20JavaScript%20Data%20Structures%20and%20Algorithms,%20Second%20Edition.jpg) | 
 | [Book link](http://amzn.to/1Y1OWPx)| [Book link](http://amzn.to/1TSkcA1)|
 
 Book link - first edition:
@@ -17,6 +17,7 @@ Book link - first edition:
 Book link - second edition:
  - [Packt](https://www.packtpub.com/web-development/learning-javascript-data-structures-and-algorithms-second-edition)
  - [Amazon](http://amzn.to/1TSkcA1)
+ - [Brazilian Portuguese version](https://novatec.com.br/livros/estruturas-de-dados-algoritmos-em-javascript/)
 
 ### List of Chapters:
   

From c44e74918af79cb45532cc7423bdcb3a853f27fd Mon Sep 17 00:00:00 2001
From: loiane <loianeg@gmail.com>
Date: Mon, 21 Aug 2017 09:57:03 -0300
Subject: [PATCH 31/33] fixes #23

---
 chapter07/07-HashCollisionLinearProbing.js      | 9 +++++++++
 chapter07/08-UsingHashCollisionLinearProbing.js | 8 ++++++++
 2 files changed, 17 insertions(+)

diff --git a/chapter07/07-HashCollisionLinearProbing.js b/chapter07/07-HashCollisionLinearProbing.js
index 38b07c0f..4b1172be 100644
--- a/chapter07/07-HashCollisionLinearProbing.js
+++ b/chapter07/07-HashCollisionLinearProbing.js
@@ -53,6 +53,15 @@ function HashLinearProbing(){
                     return table[index].value;
                 }
             }
+        } else { //search for possible deleted value
+            var index = ++position;
+            while (table[index] == undefined || index == table.length ||
+                (table[index] !== undefined && table[index] && table[index].key !== key)){
+                index++;
+            }
+            if (table[index] && table[index].key === key) {
+                return table[index].value;
+            }
         }
         return undefined;
     };
diff --git a/chapter07/08-UsingHashCollisionLinearProbing.js b/chapter07/08-UsingHashCollisionLinearProbing.js
index 902384ee..36a33e61 100644
--- a/chapter07/08-UsingHashCollisionLinearProbing.js
+++ b/chapter07/08-UsingHashCollisionLinearProbing.js
@@ -26,4 +26,12 @@ console.log('**** Remove **** ');
 
 hashLinearProbing.remove('Gandalf');
 console.log(hashLinearProbing.get('Gandalf'));
+hashLinearProbing.print();
+
+console.log('**** Remove Test 2 **** ');
+console.log('Removing Jonathan', hashLinearProbing.remove('Jonathan'));
+console.log('**** Print **** ');
+hashLinearProbing.print();
+console.log('Get Jamie', hashLinearProbing.get('Jamie'));
+console.log('**** Print **** ');
 hashLinearProbing.print();
\ No newline at end of file

From 10b24fd4a3ec01aa8db5a5bffb29e55559647dae Mon Sep 17 00:00:00 2001
From: loiane <loianeg@gmail.com>
Date: Thu, 7 Sep 2017 09:18:28 -0300
Subject: [PATCH 32/33] gitignore

---
 .gitignore | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/.gitignore b/.gitignore
index 6fee6d3a..2458e8b0 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,4 @@
 .idea/*
-*.log
\ No newline at end of file
+*.log
+node_modules
+coverage

From f06567601501477cb470a8e0b59cfb9f36d8d19d Mon Sep 17 00:00:00 2001
From: Loiane Groner <loianeg@gmail.com>
Date: Mon, 20 Nov 2017 13:09:10 -0200
Subject: [PATCH 33/33] Update 14-ES6ParameterHandling.js

---
 chapter01/14-ES6ParameterHandling.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapter01/14-ES6ParameterHandling.js b/chapter01/14-ES6ParameterHandling.js
index 4645f2a7..af23585c 100644
--- a/chapter01/14-ES6ParameterHandling.js
+++ b/chapter01/14-ES6ParameterHandling.js
@@ -14,7 +14,7 @@ function sum2 (x, y, z) {
         z = 3;
     return x + y + z;
 };
-console.log(sum2(4,2)); //outpus 10
+console.log(sum2(4,2)); //outpus 9
 
 //******* EcmaScript 6: spread operator ('...')
 var params = [3, 4, 5];