10-MatrixChainMultiplicationDP.js

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));