Given a positive integer n, find the least number of perfect square numbers (for example, 1,
4, 9, 16, ...
) which sum to n.
For example, given n = 12
, return 3
because 12
= 4 + 4 + 4
; given n = 13
, return 2
because 13
= 4 + 9
.
int numSquares(int n) {
if (n <= 1) return 1;
int logn = sqrt(n);
int *res = (int*)malloc((n + 1) * sizeof(int));
memset(res, 0, (n + 1) * sizeof(int));
for (int i = 0; i <= logn; ++i) res[i * i] = 1;
for (int i = 2; i <= n; ++i)
{
if (res[i] != 0) continue;
int tmp = res[i - 1] + 1;
int logi = sqrt(i);
for (int j = 2; j <= logi; ++j) {
if (tmp > res[i - j * j] + 1) tmp = res[i - j * j] + 1;
}
res[i] = tmp;
}
return res[n];
}