You are given two integer arrays, skill and mana, of length n and m, respectively. In a laboratory, n wizards must brew m potions in order. Each potion has a mana capacity mana[j] and must pass through all the wizards sequentially to be brewed prope

minTime.js

/**
 * @param {number[]} skill
 * @param {number[]} mana
 * @return {number}
 */
var minTime = function(skill, mana) {
    let m = mana.length;       // Number of potions
    let n = skill.length;      // Number of wizards

    // done[i] represents the time when wizard i is ready to start the next potion
    // We use n+1 to simplify indexing (done[n] will hold the final result)
    let done = new Array(n + 1).fill(0);

    // Loop through each potion in order
    for (let j = 0; j < m; j++) {
        // Forward pass: compute brewing time for potion j across all wizards
        for (let i = 0; i < n; i++) {
            // Wizard i+1 starts potion j after both:
            // - wizard i finishes potion j
            // - wizard i+1 finishes previous potion
            done[i + 1] = Math.max(done[i], done[i + 1]) + (skill[i] * mana[j]);
        }

        // Backward pass: reset done[i] to represent start time of wizard i for next potion
        // This subtracts the time just added, leaving only the start time
        for (let i = n - 1; i >= 0; i--) {
            done[i] = done[i + 1] - (skill[i] * mana[j]);
        }
    }

    // Final result: time when last wizard finishes last potion
    return done[n];
};