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// 1425. Constrained Subsequence Sum
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
/*
* given an integer array 'nums' and an integer 'k', return the maximum sum of a
* non-empty subsequnce of that array for every two consecutive integers in the
* subsequence 'nums[i] and 'nums[j] where 'i < j', the condition 'j - i <= k'
* is satisfied. a subsequence of an array is obtained by deleting some number
* of elements (can be zero) from the array, leaving the remaining elements in
* their original order.
*/
int bfs(int *nums, int n, int val) {
int left = 0, right = n - 1, mid;
while (left < right) {
mid = left + (right - left) / 2;
if (nums[mid] >= val)
left = mid + 1;
else
right = mid;
}
return left;
}
int constrainedSubsetSum(int *nums, int nums_size, int k) {
int n = nums_size, max = INT_MIN, head = 0, tail = 1;
int *queue = malloc((n + 1) * sizeof(int));
int *dp = malloc((n + 1) * sizeof(int));
dp[0] = 0;
queue[head] = 0;
for (int i = 1; i <= k; i++) {
dp[i] = nums[i - 1];
if (queue[head])
dp[i] += queue[head];
max = fmax(max, dp[i]);
if (dp[i] < 0)
continue;
else if (dp[i] > queue[head]) {
queue[head] = dp[i];
tail = head + 1;
} else if (dp[i] <= queue[tail - 1]) {
queue[tail] = dp[i];
tail++;
} else {
int m = bfs(&queue[head], tail - head, dp[i]);
queue[head + m] = dp[i];
tail = head + m + 1;
}
}
for (int i = k + 1; i <= n; i++) {
dp[i] = nums[i - 1];
if (queue[head])
dp[i] += queue[head];
max = fmax(max, dp[i]);
if (queue[head] == dp[i - k] && dp[i - k]) {
head++;
if (head == tail) {
queue[head] = 0;
tail = head + 1;
}
}
if (dp[i] < 0)
continue;
else if (dp[i] > queue[head]) {
queue[head] = dp[i];
tail = head + 1;
} else if (dp[i] <= queue[tail - 1]) {
queue[tail] = dp[i];
tail++;
} else {
int m = bfs(&queue[head], tail - head, dp[i]);
queue[head + m] = dp[i];
tail = head + m + 1;
}
}
return max;
}
int main() {
int n1[] = {10, 2, -10, 5, 20}, n2[] = {-1, -2, -3},
n3[] = {10, -2, -10, -5, 20};
printf("%d\n", constrainedSubsetSum(n1, 5, 2)); // expect: 37
printf("%d\n", constrainedSubsetSum(n2, 3, 1)); // expect: -1
printf("%d\n", constrainedSubsetSum(n3, 5, 2)); // expect: 23
}
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