给定一个正整数求最少由几个数的平方和组成

//  5.21
//  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.

tips：也就是说任意一个正整数都可以由若干个正整数的平方和组合而成，具体原理不知

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