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// 1690. Stone Game VII
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
/*
* alice and bob take turns playing a game, with alice starting first. there are
* 'n' stones arranged in a row. on each player's turn, they can remove either
* the leftmost stone or the rightmost stone from the row and receive points
* equal to the sum of the remaining stones' values in the row. the winner is
* the one with the higher score when there are no stones left to remove. bob
* found that he will always lose this game (poor bob, he always loses), so he
* decided to minimise the socre's difference. alice'goal is to maximise the
* difference in score. given an array of integers 'stones' where 'stones[i]'
* represents the value of the i'th stone from the left, return the difference
* in alice and bob's score if they both play optimally.
*/
int stoneGameVII(int *stones, int stones_size) {
int n = stones_size;
bool even = !n % 2 ? true : false;
int **dp = malloc(n * sizeof(int *));
for (int i = 0; i < n; i++) {
dp[i] = malloc(n * sizeof(int));
dp[i][i] = 0;
}
int *sum = malloc((n + 1) * sizeof(int));
sum[0] = 0;
for (int i = 1; i <= n; i++)
sum[i] = sum[i - 1] + stones[i - 1];
for (int k = 2; k <= n; k++)
for (int i = 0; i <= n - k; i++) {
int j = i + k - 1;
if (even && !k % 2 || !even && k % 2)
dp[i][j] = fmax(dp[i + 1][j] + sum[j + 1] - sum[i + 1],
dp[i][j - 1] + sum[j] - sum[i]);
else
dp[i][j] = fmin(dp[i + 1][j] - (sum[j + 1] - sum[i + 1]),
dp[i][j - 1] - (sum[j] - sum[i]));
}
int ans = dp[0][n - 1];
for (int i = 0; i < n; i++)
free(dp[i]);
free(dp), free(sum);
return ans;
}
int main() {
int s1[] = {5, 3, 1, 4, 2}, s2[] = {7, 90, 5, 1, 100, 10, 10, 2};
printf("%d\n", stoneGameVII(s1, 5)); // expect: 6
printf("%d\n", stoneGameVII(s2, 8)); // expect: 122
}
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