Selecting the minimum/maximum value in an array

Author: Chris Pilcher

README.markdown

@@ -33,7 +33,7 @@ If you're new to algorithms and data structures, here are a few good ones to sta
 - [Linear Search](Linear Search/). Find an element in an array.
 - [Binary Search](Binary Search/). Quickly find elements in a sorted array.
 - [Count Occurrences](Count Occurrences/). Count how often a value appears in an array.
-- Select Minimum / Maximum
+- [Select Minimum / Maximum](Select Minimum Maximum). Find the minimum/maximum value in an array.
 - Select k-th Largest Element
 - Selection Sampling
 - Union-Find

Select Minimum Maximum/Maximum.swift

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+/*
+  Finds the maximum value in an array in O(n) time.
+  The array must not be empty.
+*/
+
+func maximum<T: Comparable>(var array: [T]) -> T? {
+  var maximum = array.removeFirst()
+  for element in array {
+    maximum = element > maximum ? element : maximum
+  }
+  return maximum
+}

Select Minimum Maximum/Minimum.swift

@@ -0,0 +1,12 @@
+/*
+  Finds the minimum value in an array in O(n) time.
+  The array must not be empty.
+*/
+
+func minimum<T: Comparable>(var array: [T]) -> T? {
+  var minimum = array.removeFirst()
+  for element in array {
+    minimum = element < minimum ? element : minimum
+  }
+  return minimum
+}

Select Minimum Maximum/README.markdown

@@ -0,0 +1,61 @@
+# Select Minimum / Maximum
+
+Goal: Find the minimum/maximum object in an unsorted array.
+
+We have an array of generic objects and we iterate over all the objects keeping track of the minimum/maximum element so far.
+
+### An example
+
+Let's say the we want to find the maximum value in the unsorted list `[ 8, 3, 9, 4, 6 ]`.
+
+Pick the first number, `8`, and store it as the maximum element so far. 
+
+Pick the next number from the list, `3`, and compare it to the current maximum `8`. `3` is less than `8` so the maximum `8` does not change.
+
+Pick the next number from the list, `9`, and compare it to the current maximum `8`. `9` is greater than `8` so we store `9` as the maximum.
+
+Repeat this process until the all items in the list have been processed.
+
+### The code
+
+Here is a simple implementation in Swift:
+
+```swift
+func minimum<T: Comparable>(var array: [T]) -> T? {
+  var minimum = array.removeFirst()
+  for element in array {
+    minimum = element < minimum ? element : minimum
+  }
+  return minimum
+}
+
+func maximum<T: Comparable>(var array: [T]) -> T? {
+  var maximum = array.removeFirst()
+  for element in array {
+    maximum = element > maximum ? element : maximum
+  }
+  return maximum
+}
+```
+
+Put this code in a playground and test it like so:
+
+```swift
+let array = [ 8, 3, 9, 4, 6 ]
+minimum(array) // This will return 3
+maximum(array) // This will return 9
+```
+
+### Performance
+
+The algorithm runs at **O(n)**. It compares each object in the array with the running minimum/maximum so the time it takes is proportional to the array length.
+
+### Swift library
+
+The Swift library already contains an extension to `SequenceType` that returns the minimum/maximum element in a sequence.
+
+```swift
+let array = [ 8, 3, 9, 4, 6 ]
+array.minElement() // This will return 3
+array.maxElement() // This will return 9
+```

Select Minimum Maximum/SelectMinimumMaximum.playground/Contents.swift

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+func minimum<T: Comparable>(var array: [T]) -> T? {
+  var minimum = array.removeFirst()
+  for element in array {
+    minimum = element < minimum ? element : minimum
+  }
+  return minimum
+}
+
+func maximum<T: Comparable>(var array: [T]) -> T? {
+  var maximum = array.removeFirst()
+  for element in array {
+    maximum = element > maximum ? element : maximum
+  }
+  return maximum
+}
+
+// Simple test minimum and maximum functions
+let array = [ 8, 3, 9, 4, 6 ]
+minimum(array)
+maximum(array)
+
+// Built-in Swift functions
+array.maxElement()
+array.minElement()

Select Minimum Maximum/SelectMinimumMaximum.playground/contents.xcplayground

@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>

Select Minimum Maximum/SelectMinimumMaximum.playground/timeline.xctimeline

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>