Leetcode 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

.

Difficulty: Medium

Solution: DP

public class Solution {
public int numSquares(int n) {
int max = (int) Math.sqrt(n);

int[] dp = new int[n+1];
Arrays.fill(dp, Integer.MAX_VALUE);

for(int i=1; i<=n; i++){
for(int j=1; j<=max; j++){
if(i==j*j){
dp[i]=1;
}else if(i>j*j){
dp[i]=Math.min(dp[i], dp[i-j*j] + 1);
}
}
}

return dp
;
}
}