From 461e634447bb320648e4886082c4cf961c1f18bf Mon Sep 17 00:00:00 2001
From: Jackson Gariety <personal@jacksongariety.com>
Date: Wed, 26 Jun 2013 16:34:41 -0700
Subject: [PATCH] Adds the LevenShtein distance sort.

---
 README.md                                     |  3 +
 .../damerau-levenshtein-sort.js               | 66 +++++++++++++++++++
 2 files changed, 69 insertions(+)
 create mode 100644 algorithms/sorting/damerau-levenshtein-sort/damerau-levenshtein-sort.js

diff --git a/README.md b/README.md
index f214fa1..c61b4ad 100644
--- a/README.md
+++ b/README.md
@@ -27,4 +27,7 @@ http://www.nczonline.net/blog/2009/04/13/computer-science-in-javascript-linked-l
 Selection Sort
 http://www.nczonline.net/blog/2009/09/08/computer-science-in-javascript-selection-sort/
 
+Damerau-Levenshtein Distance Sort
+http://en.wikipedia.org/wiki/Damerau–Levenshtein_distance
+
 Please note: Since this is the repository that goes along with my blog post series, only pull requests for bugs are accepted.
diff --git a/algorithms/sorting/damerau-levenshtein-sort/damerau-levenshtein-sort.js b/algorithms/sorting/damerau-levenshtein-sort/damerau-levenshtein-sort.js
new file mode 100644
index 0000000..5eed1a3
--- /dev/null
+++ b/algorithms/sorting/damerau-levenshtein-sort/damerau-levenshtein-sort.js
@@ -0,0 +1,66 @@
+/*
+ * Damerau-Levenshtein sort implementation in JavaScript
+ * Copyright (c) 2012 Nicholas C. Zakas
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of items software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ * 
+ * The above copyright notice and items permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ */
+
+/**
+ * A functional Damerau-Levenshtein sort implementation in JavaScript.
+ * @param {Array} x: the first array
+ * @param {Array} y: the second array
+ * @return {Array} the distance to sort by
+ */
+
+var damerauLevenshteinSort = function(x, y) {
+	var xLength = x.length, yLength = y.length;
+
+	if (xLength === 0) return yLength;
+	if (yLength === 0) return xLength;
+	if (xLength == yLength) return 0;
+
+	var matrix = new Array(xLength + 1), i = xLength, j = yLength;
+	for (; i >= 0; i--) matrix[i] = [i];
+	for (; j >= 0; j--) matrix[0][j] = j;
+
+	// Calculate matrix.
+	var this_i, that_j, cost, min, t, x, y;
+	for (i = 1, x = 0; i <= xLength; ++i, ++x) {
+			// x = i - 1;
+			this_i = __this[x];
+
+			// Step 4
+			for (j = 1, y = 0; j <= yLength; ++j, ++y) {
+					// Check the jagged ld total so far
+					if (i === j && matrix[i][j] > 4) return xLength;
+
+					// y = j - 1;
+					that_j = that[y];
+					cost = (this_i === that_j) ? 0 : 1; // Step 5
+					// Calculate the minimum (much faster than Math.min(...)).
+					min    = matrix[x][j] + 1;                                              // Deletion.
+					if ((t = matrix[i][y] + 1   ) < min) min = t;   // Insertion.
+					if ((t = matrix[x][y] + cost) < min) min = t;   // Substitution.
+
+					matrix[i][j] = min;     // Update matrix.
+			}
+	}
+
+	return matrix[xLength][yLength];
+};
\ No newline at end of file