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）

public class T279 {
    public int numSquares(int n) {
        List<Integer> squareList = getSquareArray(n);
        Queue<Integer> que = new LinkedList<>();
        que.add(n);
        boolean[] visited = new boolean[n];
        int level = 0;
        while (!que.isEmpty()) {
            int size = que.size();
            level++;
            while (size-- > 0) {
                int num = que.poll();
                for (int square : squareList) {
                    int left = num - square;
                    if (left == 0) {
                        return level;
                    }
                    if (left < 0) {
                        break;
                    }
                    if (visited[left]) {
                        continue;
                    }
                    visited[left] = true;
                    que.add(left);
                }

            }
        }
        return level;
    }

    private ArrayList<Integer> getSquareArray(int n) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 1; i <= n; i++) {
            int num = i * i;
            if (num <= n) {
                list.add(num);
            } else {
                break;
            }
        }
        return list;
    }
}

 方法二：dp

public class T279 {
    public int numSquares(int n) {
        List<Integer> squareList = getSquareArray(n);
        int[] dp = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            int min = Integer.MAX_VALUE;
            for (int num : squareList) {
                if (num <= i) {
                    min = Math.min(dp[i - num] + 1, min);
                }
            }
            dp[i] = min;
        }
        return dp[n];
    }

    private ArrayList<Integer> getSquareArray(int n) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 1; i <= n; i++) {
            int num = i * i;
            if (num <= n) {
                list.add(num);
            } else {
                break;
            }
        }
        return list;
    }
}