题目描述

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.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

分析

动态规划，求解最优化问题，自底向上。

代码

    public int numSquares(int n) {

        int[] dp = new int[n + 1];

        Arrays.fill(dp, Integer.MAX_VALUE);

        // 将所有平方数置1
        for (int i = 0; i * i <= n; i++) {
            dp[i * i] = 1;
        }

        for (int a = 1; a <= n; a++) {
            for (int b = 1; a + b * b <= n; b++) {
                // 取较小值，a + b * b也可能是平方数
                dp[a + b * b] = Math.min(dp[a] + 1, dp[a + b * b]);
            }
        }

        return dp[n];
    }