LeetCode279 perfect-squares 完全平方数

题目

Given an integer n, return the least number of perfect square numbers that sum to n.
A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

 Example 1: 
Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.

 Example 2: 
Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

 Constraints: 
 1 <= n <= 10⁴ 

方法

动态规划法（完全背包）

dp[i]表示平方和为i时最少的数字个数

• 时间复杂度：O(n)
• 空间复杂度：O(n)

class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n+1];
        Arrays.fill(dp,n+1);
        dp[0]=0;
        for(int i=1;i*i<=n;i++){
            int num = i*i;
            for (int j=0;j<=n;j++){
                if(j>=num){
                    dp[j] = Math.min(dp[j],dp[j-num]+1);
                }
            }
        }
        return dp[n]>n?-1:dp[n];
    }
}

class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n+1];
        Arrays.fill(dp,n+1);
        dp[0] = 0;
        for(int i=0;i<=n;i++){
            for(int j=1;j*j<=n;j++){ //每回都选一个j*j看看是不是最小的
                int num = j*j;
                if(i>=num){
                    dp[i] = Math.min(dp[i],dp[i-num]+1);
                }
            }
        }
        return dp[n]>n?-1:dp[n];
    }
}