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This approach uses a dynamic programming strategy to determine the minimum cost. The idea is to leverage a DP array where dp[i] represents the minimum cost to paint up to the i-th wall. For each wall, we decide whether to use only the paid painter or to also utilize the free painter effectively when paid painter is occupied.
Time Complexity: O(n^2), Space Complexity: O(n)
1function minCost(cost, time) {
2 const n = cost.length;
3 const dp = Array(n + 1).fill(Infinity);
4 dp[0] = 0;
5
6 for (let i = 0; i < n; i++) {
7 let occupied = 0;
8 for (let j = i + 1; j <= n; j++) {
9 if (occupied >= time[i]) {
10 dp[j] = Math.min(dp[j], dp[i] + cost[j - 1]);
11 break;
12 }
13 occupied += time[i];
14 }
15 }
16 return dp[n];
17}
18
19// Example usage:
20const cost = [1, 2, 3, 2];
21const time = [1, 2, 3, 2];
22console.log(minCost(cost, time));In JavaScript, this solution implements a dynamic programming approach with an array to evaluate and update the lowest cost progression while considering the optimal use of available painters.
This approach leverages a greedy strategy, prioritizing the choice that minimizes cost per time unit. By sorting or considering smallest cost per time unit, we attempt to reach a solution that overall minimizes the total cost.
Time Complexity: O(n log n), Space Complexity: O(n)
1using System;
2using System.Collections.Generic;
class Program {
class Pair : IComparable<Pair> {
public int cost, time;
public Pair(int c, int t) {
cost = c;
time = t;
}
public int CompareTo(Pair other) {
return ((double)cost / time).CompareTo((double)other.cost / other.time);
}
}
static int MinCost(int[] cost, int[] time) {
List<Pair> ratios = new List<Pair>();
for (int i = 0; i < cost.Length; i++) {
ratios.Add(new Pair(cost[i], time[i]));
}
ratios.Sort();
int totalCost = 0;
int occupiedTime = 0;
foreach (Pair pair in ratios) {
if (occupiedTime < pair.time) {
totalCost += pair.cost;
occupiedTime += pair.time;
}
}
return totalCost;
}
static void Main() {
int[] cost = {1, 2, 3, 2};
int[] time = {1, 2, 3, 2};
Console.WriteLine(MinCost(cost, time));
}
}This C# solution uses a list of custom Pair objects sorted based on their efficiency (cost/time). This allows painting order to be optimized, achieving a minimum cost solution.