Adds playground for Longest Common Subsequence

Author: pedrovereza

Longest Common Subsequence/LongestCommonSubsequence.playground/Contents.swift

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+extension String {
+    func longestCommonSubsequence(other:String) -> String {
+        
+        func lcsLength(other: String) -> [[Int]] {
+            var matrix = [[Int]](count:self.characters.count+1, repeatedValue:[Int](count:other.characters.count+1, repeatedValue:0))
+            
+            for (i, selfChar) in self.characters.enumerate() {
+                for (j, otherChar) in other.characters.enumerate() {
+                    if (otherChar == selfChar) {
+                        matrix[i+1][j+1] = (matrix[i][j]) + 1
+                    }
+                    else {
+                        matrix[i+1][j+1] = max(matrix[i][j+1], matrix[i+1][j])
+                    }
+                }
+            }
+            
+            return matrix;
+        }
+        
+        func backtrack(matrix: [[Int]]) -> String {
+            var i = self.characters.count
+            var j = other.characters.count
+            var charInSequence = self.endIndex
+            
+            var lcs = String()
+            
+            while (i >= 1 && j >= 1) {
+                if (matrix[i][j] == matrix[i][j - 1]) {
+                    j = j - 1
+                }
+                else if (matrix[i][j] == matrix[i - 1][j]) {
+                    i = i - 1
+                    charInSequence = charInSequence.predecessor()
+                }
+                else {
+                    i = i - 1
+                    j = j - 1
+                    charInSequence = charInSequence.predecessor()
+                    
+                    lcs.append(self[charInSequence])
+                }
+            }
+            
+            return String(lcs.characters.reverse());
+        }
+        
+        return backtrack(lcsLength(other))
+    }
+}
+
+// Examples
+
+let a = "ABCBX"
+let b = "ABDCAB"
+let c = "KLMK"
+
+a.longestCommonSubsequence(c) //""
+a.longestCommonSubsequence("") //""
+a.longestCommonSubsequence(b) //"ABCB"
+b.longestCommonSubsequence(a) //"ABCB"
+a.longestCommonSubsequence(a) // "ABCBX"

Longest Common Subsequence/LongestCommonSubsequence.playground/contents.xcplayground

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

Longest Common Subsequence/LongestCommonSubsequence.playground/timeline.xctimeline

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+<?xml version="1.0" encoding="UTF-8"?>
+<Timeline
+   version = "3.0">
+   <TimelineItems>
+   </TimelineItems>
+</Timeline>