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 }
来源：https://www.cnblogs.com/zzytxl/p/12446682.html