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// 1043. Partition Array for Maximum Sum
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
/*
* given an integeer array 'arr', partition the array into contiguous subarrays
* of length at most 'k'. after partitioning, each subarray has their values
* changed to become the maximum value of that subarray. return the largest sum
* of the given array after partitioning. test cases are generated so that
* answer fits in a 32-bit integer
*/
int maxSumAfterPartitioning(int *arr, int arr_size, int k) {
int n = arr_size, *dp = malloc((n + 1) * sizeof(int));
dp[0] = 0;
for (int i = 0; i < n; i++) {
int m = arr[i];
dp[i + 1] = arr[i] + dp[i];
for (int j = i - 1; j >= fmax(0, i - k + 1); j--) {
m = fmax(m, arr[j]);
dp[i + 1] = fmax(dp[i + 1], m * (i - j + 1) + dp[j]);
}
}
int ans = dp[n];
free(dp);
return ans;
}
int main() {
int a1[] = {1, 15, 7, 9, 2, 5, 10}, a2[] = {1, 4, 1, 5, 7, 3, 6, 1, 9, 9, 3},
a3[] = {1};
printf("%d\n", maxSumAfterPartitioning(a1, 7, 3)); // expect: 84
printf("%d\n", maxSumAfterPartitioning(a2, 11, 4)); // expect: 83
printf("%d\n", maxSumAfterPartitioning(a3, 1, 1)); // expect: 1
}
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