From 69a833f56ddf25ea83eab88194ad54e0c620c8ed Mon Sep 17 00:00:00 2001
From: dirb <dirbarranco@gmail.com>
Date: Sun, 19 Feb 2017 20:42:30 -0600
Subject: [PATCH 1/2] src/filters/lcs.js: implement backtrack in a iterative
 way

---
 src/filters/lcs.js | 43 +++++++++++++++++++++++--------------------
 1 file changed, 23 insertions(+), 20 deletions(-)

diff --git a/src/filters/lcs.js b/src/filters/lcs.js
index 70d5b349..2e18b0af 100644
--- a/src/filters/lcs.js
+++ b/src/filters/lcs.js
@@ -37,34 +37,37 @@ var lengthMatrix = function(array1, array2, match, context) {
   return matrix;
 };
 
-var backtrack = function(matrix, array1, array2, index1, index2, context) {
-  if (index1 === 0 || index2 === 0) {
-    return {
-      sequence: [],
-      indices1: [],
-      indices2: []
-    };
-  }
+var backtrack = function(matrix, array1, array2, context) {
+  var index1 = array1.length;
+  var index2 = array2.length;
 
-  if (matrix.match(array1, array2, index1 - 1, index2 - 1, context)) {
-    var subsequence = backtrack(matrix, array1, array2, index1 - 1, index2 - 1, context);
-    subsequence.sequence.push(array1[index1 - 1]);
-    subsequence.indices1.push(index1 - 1);
-    subsequence.indices2.push(index2 - 1);
-    return subsequence;
-  }
+  var subsequence = {
+    sequence: [],
+    indices1: [],
+    indices2: []
+  };
 
-  if (matrix[index1][index2 - 1] > matrix[index1 - 1][index2]) {
-    return backtrack(matrix, array1, array2, index1, index2 - 1, context);
-  } else {
-    return backtrack(matrix, array1, array2, index1 - 1, index2, context);
+  while (0 < index1  && 0 < index2) {
+    if (matrix.match(array1, array2, index1-1, index2-1, context)) {
+      subsequence.sequence.push(array1[index1-1]);
+      subsequence.indices1.push(index1-1);
+      subsequence.indices2.push(index2-1);
+      index1--;
+      index2--;
+    } else if (matrix[index1][index2-1] > matrix[index1-1][index2]) {
+      index2--;
+    } else {
+      index1--;
+    }
   }
+
+  return subsequence;
 };
 
 var get = function(array1, array2, match, context) {
   context = context || {};
   var matrix = lengthMatrix(array1, array2, match || defaultMatch, context);
-  var result = backtrack(matrix, array1, array2, array1.length, array2.length, context);
+  var result = backtrack(matrix, array1, array2, context);
   if (typeof array1 === 'string' && typeof array2 === 'string') {
     result.sequence = result.sequence.join('');
   }

From efe391171a5cac63f70d89136462b5cdf90e9a83 Mon Sep 17 00:00:00 2001
From: dirb <dirbarranco@gmail.com>
Date: Sat, 25 Feb 2017 19:24:29 -0600
Subject: [PATCH 2/2] src/filters/lcs.js: optimize by trim off matching items
 at the beginning and the end

---
 src/filters/lcs.js | 55 ++++++++++++++++++++++++++++++++++++----------
 1 file changed, 44 insertions(+), 11 deletions(-)

diff --git a/src/filters/lcs.js b/src/filters/lcs.js
index 2e18b0af..4f88862c 100644
--- a/src/filters/lcs.js
+++ b/src/filters/lcs.js
@@ -11,8 +11,23 @@ var defaultMatch = function(array1, array2, index1, index2) {
 };
 
 var lengthMatrix = function(array1, array2, match, context) {
-  var len1 = array1.length;
-  var len2 = array2.length;
+  var start = 0;
+  var end1 = array1.length;
+  var end2 = array2.length;
+
+  //trim off the matching items at the beginning
+  while (start < end1 && start < end2 && match(array1, array2, start, start, context)) {
+    start++;
+  }
+
+  //trim off the matching items at the end
+  while (start < end1 && start < end2 && match(array1, array2, end1 - 1, end2 - 1, context)) {
+    end1--;
+    end2--;
+  }
+
+  var len1 = end1 - start;
+  var len2 = end2 - start;
   var x, y;
 
   // initialize empty matrix of len1+1 x len2+1
@@ -24,10 +39,13 @@ var lengthMatrix = function(array1, array2, match, context) {
     }
   }
   matrix.match = match;
+  matrix.start = start;
+  matrix.end1 = end1;
+  matrix.end2 = end2;
   // save sequence lengths for each coordinate
   for (x = 1; x < len1 + 1; x++) {
     for (y = 1; y < len2 + 1; y++) {
-      if (match(array1, array2, x - 1, y - 1, context)) {
+      if (match(array1, array2, start + x - 1, start + y - 1, context)) {
         matrix[x][y] = matrix[x - 1][y - 1] + 1;
       } else {
         matrix[x][y] = Math.max(matrix[x - 1][y], matrix[x][y - 1]);
@@ -38,23 +56,38 @@ var lengthMatrix = function(array1, array2, match, context) {
 };
 
 var backtrack = function(matrix, array1, array2, context) {
-  var index1 = array1.length;
-  var index2 = array2.length;
-
   var subsequence = {
     sequence: [],
     indices1: [],
     indices2: []
   };
 
+  var x;
+  //push matching items at the beginning
+  for (x = 0; x < matrix.start; x++) {
+    subsequence.sequence.push(array1[x]);
+    subsequence.indices1.push(x);
+    subsequence.indices2.push(x);
+  }
+
+  //push matching items at the end
+  for (x = matrix.end1; x < array1.length; x++) {
+    subsequence.sequence.push(array1[x]);
+    subsequence.indices1.push(x);
+    subsequence.indices2.push(matrix.end2 + (x - matrix.end1));
+  }
+
+  var index1 = matrix.end1 - matrix.start;
+  var index2 = matrix.end2 - matrix.start;
+
   while (0 < index1  && 0 < index2) {
-    if (matrix.match(array1, array2, index1-1, index2-1, context)) {
-      subsequence.sequence.push(array1[index1-1]);
-      subsequence.indices1.push(index1-1);
-      subsequence.indices2.push(index2-1);
+    if (matrix.match(array1, array2, matrix.start + index1 - 1, matrix.start + index2 - 1, context)) {
+      subsequence.sequence.push(array1[matrix.start + index1 - 1]);
+      subsequence.indices1.push(matrix.start + index1 - 1);
+      subsequence.indices2.push(matrix.start + index2 - 1);
       index1--;
       index2--;
-    } else if (matrix[index1][index2-1] > matrix[index1-1][index2]) {
+    } else if (matrix[index1][index2 - 1] > matrix[index1 - 1][index2]) {
       index2--;
     } else {
       index1--;