Perfect Squares完美平方数

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.

解题思路：DP

dp[i]表示正整数i能少能由多个完全平方数组成

public int numSquares(int n) {
    int[] dp = new int[n + 1];
    for (int i = 1; i <= n; i++) {
        dp[i] = i;
        for (int j = 1; j * j <= i; j++) {
            dp[i] = Math.min(dp[i], dp[i - j * j] + 1);
        }
    }
    return dp[n];
}