matrixChainOrder dp

loiane · loiane · commit 49c5cc773011 · 2016-03-26T15:42:22.000-03:00
diff --git a/chapter11/10-MatrixChainMultiplicationDP.html b/chapter11/10-MatrixChainMultiplicationDP.html
@@ -0,0 +1,10 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title></title>
+</head>
+<body>
+<script src="10-MatrixChainMultiplicationDP.js"></script>
+</body>
+</html>
diff --git a/chapter11/10-MatrixChainMultiplicationDP.js b/chapter11/10-MatrixChainMultiplicationDP.js
@@ -0,0 +1,56 @@
+function matrixChainOrder(p, n) {
+
+    var i, j, k, l, q,
+        m = [], s=[];
+
+    for (i = 1; i <= n; i++){
+        m[i] = [];
+        m[i][i] = 0;
+
+    }
+
+    for (i = 0; i <= n; i++){ //to help printing the optimal solution
+        s[i] = []; //auxiliary
+        for (j=0; j<=n; j++){
+            s[i][j] = 0;
+        }
+    }
+
+    for (l=2; l<n; l++) {
+        for (i=1; i<=n-l+1; i++) {
+            j = i+l-1;
+            m[i][j] = Number.MAX_SAFE_INTEGER;
+            for (k=i; k<=j-1; k++) {
+                // q = cost/scalar multiplications
+                q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
+                if (q < m[i][j]){
+                    m[i][j] = q;
+                    s[i][j]=k; // s[i,j] = Second auxiliary table that stores k
+                }
+            }
+        }
+    }
+
+    console.log(m);
+    console.log(s);
+
+    printOptimalParenthesis(s, 1, n-1);
+
+    return m[1][n-1];
+}
+
+function printOptimalParenthesis(s, i, j){
+    if(i == j) {
+        console.log("A[" + i + "]");
+    } else {
+        console.log("(");
+        printOptimalParenthesis(s, i, s[i][j]);
+        printOptimalParenthesis(s, s[i][j] + 1, j);
+        console.log(")");
+    }
+}
+
+// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
+var p = [10, 100, 5, 50, 1],
+    n = p.length;
+console.log(matrixChainOrder(p, n));
