[LeetCode 279] Perfect Squares

最新推荐文章于 2019-11-27 13:09:52 发布

原创最新推荐文章于 2019-11-27 13:09:52 发布 · 3.5k 阅读

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本文探讨了如何找出构成给定正整数n所需的最少完全平方数的数量，并提供了一个使用动态规划解决该问题的Java实现。

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.

solution:

similar to 0/1 knapsack problem, use dp to solve this.

public class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n+1];
        dp[1] = 1;
        for(int i=2;i<=n;i++){
            int min = Integer.MAX_VALUE;
            int j = 1;
            while(j*j<=i) {
                if(j*j == i){
                    min = 1;
                    break;
                }
                min = Math.min(min, dp[i-j*j]+1);
                ++j;
            }
            dp[i] = min;
        }
        return dp[n];
    }
}