lcs dp

loiane · loiane · commit f8527d259700 · 2016-03-26T15:41:59.000-03:00
diff --git a/chapter11/08-LongestCommonSubsequenceDP.html b/chapter11/08-LongestCommonSubsequenceDP.html
@@ -5,6 +5,6 @@
     <title></title>
 </head>
 <body>
-
+<script src="08-LongestCommonSubsequenceDP.js"></script>
 </body>
 </html>
diff --git a/chapter11/08-LongestCommonSubsequenceDP.js b/chapter11/08-LongestCommonSubsequenceDP.js
@@ -0,0 +1,105 @@
+function lcs(wordX, wordY) {
+
+    var m = wordX.length,
+        n = wordY.length,
+        l = [],
+        i, j, a, b;
+
+    for (i = 0; i <= m; ++i) {
+        l[i] = [];
+        for (j = 0; j <= n; ++j) {
+            l[i][j] = 0;
+        }
+    }
+
+    for (i=0; i<=m; i++) {
+        for (j=0; j<=n; j++) {
+            if (i == 0 || j == 0){
+                l[i][j] = 0;
+
+            } else if (wordX[i-1] == wordY[j-1]) {
+                l[i][j] = l[i-1][j-1] + 1;
+
+            } else {
+                a = l[i-1][j];
+                b = l[i][j-1];
+                l[i][j] = (a > b) ? a : b; //max(a,b)
+            }
+        }
+        console.log(l[i].join());
+    }
+
+    return l[m][n];
+}
+
+//complete algorithm that prints the LCS as well
+
+function lcs2(wordX, wordY) {
+
+    var m = wordX.length,
+        n = wordY.length,
+        l = [],
+        solution = [],
+        i, j, a, b;
+
+    for (i = 0; i <= m; ++i) {
+        l[i] = [];
+        solution[i] = [];
+        for (j = 0; j <= n; ++j) {
+            l[i][j] = 0;
+            solution[i][j] = '0';
+        }
+    }
+
+    for (i=0; i<=m; i++) {
+        for (j=0; j<=n; j++) {
+            if (i == 0 || j == 0){
+                l[i][j] = 0;
+
+            } else if (wordX[i-1] == wordY[j-1]) {
+                l[i][j] = l[i-1][j-1] + 1;
+                solution[i][j] = 'diagonal';
+
+            } else {
+                a = l[i-1][j];
+                b = l[i][j-1];
+                l[i][j] = (a > b) ? a : b; //max(a,b)
+
+                solution[i][j] = (l[i][j] == l[i - 1][j]) ? 'top' : 'left';
+            }
+        }
+        console.log(l[i].join());
+        console.log(solution[i].join());
+    }
+
+    printSolution(solution, l, wordX, wordY, m, n);
+
+    return l[m][n];
+}
+
+function printSolution(solution, l, wordX, wordY, m, n){
+
+    var a = m, b = n, i, j,
+        x = solution[a][b],
+        answer = '';
+
+    while (x !== '0') {
+        if (solution[a][b] === 'diagonal') {
+            answer = wordX[a - 1] + answer;
+            a--;
+            b--;
+        } else if (solution[a][b] === 'left') {
+            b--;
+        } else if (solution[a][b] === 'top') {
+            a--;
+        }
+        x = solution[a][b];
+    }
+
+    console.log('lcs: '+ answer);
+}
+
+var wordX = 'acbaed',
+    wordY = 'abcadf';
+
+console.log(lcs2(wordX, wordY));
