2742. Painting the Walls

Problem

You are given two 0-indexed integer arrays, cost and time, of size n representing the costs and the time taken to paint n different walls respectively. There are two painters available:

• A paid painter that paints the ith wall in time[i] units of time and takes cost[i] units of money.

• A free painter that paints any wall in 1 unit of time at a cost of 0. But the free painter can only be used if the paid painter is already occupied.

Return **the minimum amount of money required to paint the **n walls.

  Example 1:

Input: cost = [1,2,3,2], time = [1,2,3,2]
Output: 3
Explanation: The walls at index 0 and 1 will be painted by the paid painter, and it will take 3 units of time; meanwhile, the free painter will paint the walls at index 2 and 3, free of cost in 2 units of time. Thus, the total cost is 1 + 2 = 3.

Example 2:

Input: cost = [2,3,4,2], time = [1,1,1,1]
Output: 4
Explanation: The walls at index 0 and 3 will be painted by the paid painter, and it will take 2 units of time; meanwhile, the free painter will paint the walls at index 1 and 2, free of cost in 2 units of time. Thus, the total cost is 2 + 2 = 4.

  Constraints:

• 1 <= cost.length <= 500

• cost.length == time.length

• 1 <= cost[i] <= 106

• 1 <= time[i] <= 500

Solution

/**
 * @param {number[]} cost
 * @param {number[]} time
 * @return {number}
 */
var paintWalls = function(cost, time) {
    var dp = Array(cost.length).fill(0).map(() => Array(cost.length + 1));
    return helper(cost, time, 0, cost.length, dp);
};

var helper = function(cost, time, i, remains, dp) {
    if (remains <= 0) return 0;
    if (i === cost.length) return Number.MAX_SAFE_INTEGER;
    if (dp[i][remains] !== undefined) return dp[i][remains];
    var paintByPaidPainter = cost[i] + helper(cost, time, i + 1, remains - time[i] - 1, dp);
    var paintByFreePainter = helper(cost, time, i + 1, remains, dp);
    dp[i][remains] = Math.min(paintByPaidPainter, paintByFreePainter);
    return dp[i][remains];
};

Explain:

Top down dp.

Complexity:

• Time complexity : O(n ^ 2).
• Space complexity : O(n ^ 2).