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.
Solution :
use Dynamic programming to find the solution for smaller numbers, and use that to find solution for bigger numbers
public class Solution {
public int numSquares(int n) {
if(n < 4)
return n;
int[] dp = new int[n+1];
dp[0] = 0;
dp[1] = 1;
dp[2] = 2;
dp[3] = 3;
for(int i=4; i<=n; i++){
dp[i] = i;
for(int j=1; j<=i; j++){
int temp = j*j;
if(temp > i)
break;
else{
dp[i] = Math.min(dp[i], dp[i-temp]+1);
}
}
}
return dp[n];
}
}