package com.fishercoder.solutions;

/**
 * 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.
 */
public class _279 {

    public int numSquares(int n) {
        int result = n, num = 2;
        while (num * num <= n) {
            int temp1 = n / (num * num), temp2 = n % (num * num);
            result = Math.min(result, temp1 + numSquares(temp2));
            num++;
        }
        return result;
    }

}

package com.fishercoder.solutions;
import java.util.*;
/**
 * 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.
 */
public class _279 {

    public int numSquares(int n) {
        int result = n, num = 2;
        while (num * num <= n) {
            int temp1 = n / (num * num), temp2 = n % (num * num);
            result = Math.min(result, temp1 + numSquares(temp2));
            num++;
        }
        return result;
    }

    //DP solution
    public int numSquaresDP(int n) {
        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        dp[1] = 1;
        for(int i = 1; i <= n; i++) {
            int min = Integer.MAX_VALUE;
            int j = 1;
            while(i -j*j >= 0) {
                min = Math.min(min, dp[i - j*j] + 1);
                j++;
            }
            dp[i] = min;
        }
        return dp[n];
    }

}

edit 279 (#14)