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// 996. Number of Squareful Arrays
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
/*
* an array is squareful if the sum of every pair of adjacent elements is a
* perfect square. given an intger array nums, return the number of permutations
* of 'nums' that are squareful. two permutations 'perm1' and 'perm2' are
* different if there is some index 'i' such that 'perm1[i] != perm2[i]'.
*/
int cmp(const void *a, const void *b) { return *(int *)a - *(int *)b; }
void process(int *idx, int *data, int pos, int *nums, int nums_size,
int *nums_cnt, int n) {
if (pos == n) {
(*idx)++;
return;
}
for (int i = 0; i < nums_size; i++) {
if (nums_cnt[i])
if (pos) {
int sum = data[pos - 1] + nums[i];
int sq = (int)sqrt(sum);
if (sum != sq * sq)
continue;
}
data[pos] = nums[i];
pos++;
nums_cnt[i]--;
process(idx, data, pos, nums, nums_size, nums_cnt, n);
pos--;
nums_cnt[i]++;
}
}
int numSquarefulPerms(int *nums, int nums_size) {
qsort(nums, nums_size, sizeof(int), cmp);
int *new_nums = malloc(nums_size * sizeof(int));
int *nums_cnt = malloc(nums_size * sizeof(int));
new_nums[0] = nums[0];
nums_cnt[0] = 1;
int new_nums_size = 1;
for (int i = 1; i < nums_size; i++) {
if (nums[i] == nums[i - 1])
nums_cnt[new_nums_size - 1]++;
else {
new_nums[new_nums_size] = nums[i];
nums_cnt[new_nums_size] = 1;
new_nums_size++;
}
}
new_nums = realloc(new_nums, sizeof(int) * new_nums_size);
nums_cnt = realloc(nums_cnt, new_nums_size * sizeof(int));
int *idx = calloc(1, sizeof(int));
int *data = malloc(nums_size * sizeof(int));
process(idx, data, 0, new_nums, new_nums_size, nums_cnt, nums_size);
int ans = *idx;
free(idx), free(data), free(new_nums), free(nums_cnt);
return ans;
}
int main() {
int n1[] = {1, 17, 8}, n2[] = {2, 2, 2};
printf("%d\n", numSquarefulPerms(n1, 3)); // expect: 2
printf("%d\n", numSquarefulPerms(n2, 3)); // expect: 1
}
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