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Painter Partition Problem (C++)

Ayesha
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Painter Partition Problem (C++)

Problem Statement​

You are given an array boards[] where boards[i] represents the length of the i-th board. You have k painters and each painter takes 1 unit of time to paint 1 unit length of the board. Each painter can only paint continuous sections of boards. Your task is to minimize the time taken to paint all the boards.

Video Explanation​

Approach​

This problem can be solved using Binary Search on the time range and a Greedy approach to allocate boards to painters.

  • Use Binary Search to find the minimal maximum time (mid) a painter can take to paint the boards.
  • Use a greedy method to count the number of painters required for each time guess (mid).
  • The goal is to minimize the maximum time required.

Solution in C++​

#include <bits/stdc++.h>
using namespace std;

// Function to count the number of painters required to paint all boards in "time"
int countPainters(vector<int> &boards, int time) {
int n = boards.size(); // Size of the array
int painters = 1; // Start with 1 painter
long long boardsPainter = 0;

for (int i = 0; i < n; i++) {
if (boardsPainter + boards[i] <= time) {
// Allocate board to the current painter
boardsPainter += boards[i];
} else {
// Allocate board to the next painter
painters++;
boardsPainter = boards[i];
}
}

return painters;
}

// Function to find the largest minimum distance
int findLargestMinDistance(vector<int> &boards, int k) {
// Find the search space for binary search
int low = *max_element(boards.begin(), boards.end());
int high = accumulate(boards.begin(), boards.end(), 0);

// Apply binary search:
while (low <= high) {
int mid = (low + high) / 2;
int painters = countPainters(boards, mid);

if (painters > k) {
low = mid + 1;
} else {
high = mid - 1;
}
}

return low; // Minimum possible maximum time
}

int main() {
vector<int> boards = {10, 20, 30, 40};
int k = 2; // Number of painters

int ans = findLargestMinDistance(boards, k);
cout << "The answer is: " << ans << "\n";

return 0;
}

Key Concepts​

  • Binary Search: Used to find the minimum maximum time required to paint all the boards.
  • Greedy Approach: The helper function countPainters assigns boards to painters ensuring the total time doesn’t exceed the given limit for that iteration.

Mathematical Representation​

The problem can be thought of in terms of minimizing the largest workload:

Minimize max⁡(time taken by any painter)\text{Minimize } \max(\text{time taken by any painter})

Mermaid Diagram​

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