完全平方数

给定正整数 n，找到若干个完全平方数（比如 1, 4, 9, 16, ...）使得它们的和等于 n。你需要让组成和的完全平方数的个数最少。

示例 1:

输入: n = 12
输出: 3
解释: 12 = 4 + 4 + 4.
示例 2:

输入: n = 13
输出: 2
解释: 13 = 4 + 9.

方法1：深度优先（BFS）

 1 public class T279 {
 2     public int numSquares(int n) {
 3         List<Integer> squareList = getSquareArray(n);
 4         Queue<Integer> que = new LinkedList<>();
 5         que.add(n);
 6         boolean[] visited = new boolean[n];
 7         int level = 0;
 8         while (!que.isEmpty()) {
 9             int size = que.size();
10             level++;
11             while (size-- > 0) {
12                 int num = que.poll();
13                 for (int square : squareList) {
14                     int left = num - square;
15                     if (left == 0) {
16                         return level;
17                     }
18                     if (left < 0) {
19                         break;
20                     }
21                     if (visited[left]) {
22                         continue;
23                     }
24                     visited[left] = true;
25                     que.add(left);
26                 }
27 
28             }
29         }
30         return level;
31     }
32 
33     private ArrayList<Integer> getSquareArray(int n) {
34         ArrayList<Integer> list = new ArrayList<>();
35         for (int i = 1; i <= n; i++) {
36             int num = i * i;
37             if (num <= n) {
38                 list.add(num);
39             } else {
40                 break;
41             }
42         }
43         return list;
44     }
45 }

 方法二：dp

 1 public class T279 {
 2     public int numSquares(int n) {
 3         List<Integer> squareList = getSquareArray(n);
 4         int[] dp = new int[n + 1];
 5         for (int i = 1; i <= n; i++) {
 6             int min = Integer.MAX_VALUE;
 7             for (int num : squareList) {
 8                 if (num <= i) {
 9                     min = Math.min(dp[i - num] + 1, min);
10                 }
11             }
12             dp[i] = min;
13         }
14         return dp[n];
15     }
16 
17     private ArrayList<Integer> getSquareArray(int n) {
18         ArrayList<Integer> list = new ArrayList<>();
19         for (int i = 1; i <= n; i++) {
20             int num = i * i;
21             if (num <= n) {
22                 list.add(num);
23             } else {
24                 break;
25             }
26         }
27         return list;
28     }
29 }

 

posted @ 2020-03-09 08:32  海绵爱上星  阅读(346)  评论(0)  编辑  收藏  举报