Merge b1ea461 into 2211ce9

algorithms/string/longest_common_subsequence.js

@@ -28,8 +28,7 @@ var longestCommonSubsequence = function (s1, s2) {
   for (i = 1; i < s1.length + 1; i++) {
     for (j = 1; j < s2.length + 1; j++) {
       if (s1[i - 1] == s2[j - 1]) {
-        var newValue = cache[i - 1][j - 1] + 1;
-        cache[i][j] = newValue;
+        cache[i][j] = cache[i - 1][j - 1] + 1;
       }
       else {
         cache[i][j] = Math.max(cache[i][j - 1], cache[i - 1][j]);
@@ -44,7 +43,7 @@ var longestCommonSubsequence = function (s1, s2) {
 
   while (cache[i][j] !== 0) {
     if (s1[i - 1] === s2[j - 1]) {
-      lcs += s1[i - 1];
+      lcs = s1[i - 1] + lcs;
       i--;
       j--;
     }
@@ -58,8 +57,7 @@ var longestCommonSubsequence = function (s1, s2) {
     }
   }
 
-  // LCS is built in reverse, return reversed string
-  return lcs.split('').reverse().join('');
+  return lcs;
 };
 
 module.exports = longestCommonSubsequence;

algorithms/string/longest_common_substring.js

@@ -0,0 +1,71 @@
+/**
+ * Implementation of longest common substring
+ *
+ * @author Joshua Curl <curljosh@msu.edu>
+ */
+
+'use strict';
+
+/**
+ * Implementation via dynamic programming
+ */
+var longestCommonSubstring = function (s1, s2) {
+  // Multidimensional array for dynamic programming algorithm
+  var cache = [];
+
+  var i, j;
+
+  // First column and row are initialized with zeroes
+  for (i = 0; i < s1.length + 1; i++) {
+    cache[i] = [];
+    cache[i][0] = 0;
+  }
+  for (i = 0; i < s2.length + 1; i++) {
+    cache[0][i] = 0;
+  }
+
+  var lcsPosition = {};
+  var commonSubstringFound = false;
+
+  // Fill in the cache
+  for (i = 1; i < s1.length + 1; i++) {
+    for (j = 1; j < s2.length + 1; j++) {
+      if (s1[i - 1] == s2[j - 1]) {
+        cache[i][j] = cache[i - 1][j - 1] + 1;
+        if (commonSubstringFound) {
+          if (cache[i][j] > cache[lcsPosition.i][lcsPosition.j]) {
+            lcsPosition.i = i;
+            lcsPosition.j = j;
+          }
+        }
+        else {
+          lcsPosition.i = i;
+          lcsPosition.j = j;
+          commonSubstringFound = true;
+        }
+      }
+      else {
+        cache[i][j] = 0;
+      }
+    }
+  }
+
+  if (!commonSubstringFound) {
+    return '';
+  }
+
+  // Build LCS from cache
+  i = lcsPosition.i;
+  j = lcsPosition.j;
+  var lcs = '';
+
+  while (cache[i][j] !== 0) {
+    lcs = s1[i - 1] + lcs;
+    i--;
+    j--;
+  }
+
+  return lcs;
+};
+
+module.exports = longestCommonSubstring;

test/algorithms/string/longest_common_subseqence.js

@@ -2,11 +2,12 @@
 
 var directory = '../../../algorithms/string/';
 var filename = 'longest_common_subsequence';
-var longestCommonSubsequence = require([directory, filename].join('')),
+var longestCommonSubsequence = require(directory + filename),
     assert = require('assert');
 
 describe('Longest common subsequence', function () {
-  it('should return the proper longest common subsequence', function () {
+  it('should return the longest common subsequence of ' +
+    'two strings', function () {
     assert.equal('', longestCommonSubsequence('', ''));
     assert.equal('', longestCommonSubsequence('', 'aaa'));
     assert.equal('', longestCommonSubsequence('aaa', ''));

test/algorithms/string/longest_common_substring.js

@@ -0,0 +1,18 @@
+'use strict';
+
+var directory = '../../../algorithms/string/';
+var filename = 'longest_common_substring';
+var longestCommonSubstring = require(directory + filename),
+    assert = require('assert');
+
+describe('Longest common substring', function () {
+  it('should return the longest common substring of two strings', function () {
+    assert.equal('', longestCommonSubstring('', ''));
+    assert.equal('', longestCommonSubstring('', 'aaa'));
+    assert.equal('', longestCommonSubstring('aaa', ''));
+    assert.equal('aaa', longestCommonSubstring('aaa', 'aaa'));
+    assert.equal('xun', longestCommonSubstring('xunmjyauz', 'mzjawxun'));
+    assert.equal('xun', longestCommonSubstring('jyaxunmuz', 'mzjawxun'));
+    assert.equal('xun', longestCommonSubstring('jyamuzxun', 'mzjawxun'));
+  });
+});