leetcode.279. Perfect Squares

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

.

class Solution {
public:
int numSquares(int n) {
// 将所有非平方数的结果置最大，保证之后比较的时候不被选中
vector<int> nums(n + 1, INT_MAX);

// 将所有整平方数的结果置1
for (int i = 0; i*i <= n; ++i)
{
nums[i*i] = 1;
}//for

// 从小到大找任意数a
for (int a = 0; a <= n; ++a)
{
// 从小到大找平方数b*b
for (int b = 0; a + b*b <= n; ++b)
{
// 因为a+b*b可能本身就是平方数，所以我们要取两个中较小的
nums[a + b*b] = min(nums[a] + 1, nums[a + b*b]);
}//for
}//for
return nums
;

}
};