Create painter’s partition problem.cpp

Author: IffatAzam

C++/Algorithms/Divide-and-Conquer/painter’s partition problem.cpp

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+// A DP based CPP program for painter's partition problem 
+#include <climits> 
+#include <iostream> 
+using namespace std; 
+
+// function to calculate sum between two indices 
+// in array 
+int sum(int arr[], int from, int to) 
+{ 
+int total = 0; 
+for (int i = from; i <= to; i++) 
+total += arr[i]; 
+return total; 
+} 
+
+// bottom up tabular dp 
+int findMax(int arr[], int n, int k) 
+{ 
+// initialize table 
+int dp[k + 1][n + 1] = { 0 }; 
+
+// base cases 
+// k=1 
+for (int i = 1; i <= n; i++) 
+dp[1][i] = sum(arr, 0, i - 1); 
+
+// n=1 
+for (int i = 1; i <= k; i++) 
+dp[i][1] = arr[0]; 
+
+// 2 to k partitions 
+for (int i = 2; i <= k; i++) { // 2 to n boards 
+for (int j = 2; j <= n; j++) { 
+
+// track minimum 
+int best = INT_MAX; 
+
+// i-1 th separator before position arr[p=1..j] 
+for (int p = 1; p <= j; p++) 
+best = min(best, max(dp[i - 1][p], 
+sum(arr, p, j - 1))); 
+
+dp[i][j] = best; 
+} 
+} 
+
+// required 
+return dp[k][n]; 
+} 
+
+// driver function 
+int main() 
+{ 
+int arr[] = { 10, 20, 60, 50, 30, 40 }; 
+int n = sizeof(arr) / sizeof(arr[0]); 
+int k = 3; 
+cout << findMax(arr, n, k) << endl; 
+return 0; 
+}