algorithmpool/src/algopool/sets/matrixChainMultiplication.js

A pool of algorithms and data-structures for geeks

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(')');
    }
}

export const matrixChainOrder = (p) => {
    const n = p.length;
    const m = [];
    const s = [];
    for (let i = 1; i <= n; i++) {
        m[i] = [];
        m[i][i] = 0;
    }
    for (let i = 0; i <= n; i++) {
        // to help printing the optimal solution
        s[i] = []; // auxiliary
        for (let j = 0; j <= n; j++) {
            s[i][j] = 0;
        }
    }
    for (let l = 2; l < n; l++) {
        for (let i = 1; i <= (n - l) + 1; i++) {
            const j = (i + l) - 1;
            m[i][j] = Number.MAX_SAFE_INTEGER;
            for (let k = i; k <= j - 1; k++) {
                // q = cost/scalar multiplications
                const 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];
}