[LeetCode]Perfect Squares

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.

分析

这种是典型的DP题，类似于硬币凑钱的题目，碰到这种题首先就要往DP想。

复杂度

time: O(n^1.5), space: O(n)

代码

public class Solution {
    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];
    }
}