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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)
1def minCost(cost, time):
2 n = len(cost)
3 dp = [float('inf')] * (n+1)
4 dp[0] = 0
5
6 for i in range(n):
7 occupied = 0
8 for j in range(i + 1, n + 1):
9 if occupied >= time[i]:
10 dp[j] = min(dp[j], dp[i] + cost[j-1])
11 break
12 occupied += time[i]
13
14 return dp[n]
15
16# Example usage
17cost = [1, 2, 3, 2]
18time = [1, 2, 3, 2]
19print(minCost(cost, time))This Python solution utilizes a list to manage the state of minimum cost to paint up to each wall by assessing which painter to use based on availability and cost-effectiveness.
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)
1#include <iostream>
2#include <vector>
#include <algorithm>
using namespace std;
bool compare(pair<int, int> a, pair<int, int> b) {
return (double)a.first / a.second < (double)b.first / b.second;
}
int minCost(vector<int> &cost, vector<int> &time) {
int n = cost.size();
vector<pair<int, int>> ratio;
for (int i = 0; i < n; i++) {
ratio.push_back(make_pair(cost[i], time[i]));
}
sort(ratio.begin(), ratio.end(), compare);
int totalCost = 0;
int occupiedTime = 0;
for (int i = 0; i < n; i++) {
if (occupiedTime < ratio[i].second) {
totalCost += ratio[i].first;
occupiedTime += ratio[i].second;
}
}
return totalCost;
}
int main() {
vector<int> cost = {1, 2, 3, 2};
vector<int> time = {1, 2, 3, 2};
cout << minCost(cost, time) << endl;
return 0;
}This C++ implementation follows a greedy strategy where pairs of cost and time are sorted based on their ratios. This helps in selecting the most cost-effective walls to paint first, reducing overall expenses.