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// 279. Perfect Squares
#include "leetcode.h"
/*
* given an integer 'n', return the least number of perfect square numbers that
* sum to 'n'. a perfect square is an integer that is the square of an integer;
* in other words, it is the product of some integer with itself. for example,
* 1,4,9,16 are perfect squares while 3 and 11 are not.
*/
int numSquares(int n) {
int *dp = (int *)malloc((n + 1) * sizeof(int));
for (int i = 0; i <= n; i++)
dp[i] = INT_MAX;
dp[0] = INT_MAX;
if (n > 0)
dp[1] = 1;
if (n > 1)
dp[2] = 2;
if (n > 2)
dp[3] = 3;
if (n > 3)
dp[4] = 1;
int k, tmp;
for (int i = 5; i <= n; i++) {
k = sqrt(i);
if (k * k == i) {
dp[i] = 1;
continue;
}
for (int j = 1; j <= k; j++) {
tmp = j * j;
if (dp[tmp] + dp[i - tmp] < dp[i])
dp[i] = dp[tmp] + dp[i - tmp];
}
}
int ans = dp[n];
free(dp);
return ans;
}
int main() {
printf("%d\n", numSquares(12)); // expect: 3
printf("%d\n", numSquares(13)); // expect: 2
}
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