LeetCode-Perfect Squares

Description：
Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, …) which sum to n.

Example 1:

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

Example 2:

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

题意：给定一个正整数$n$，令$n$=a₁+a₂+…a_i+…+a_n，其中a_i为一个完全平方数，计算使上述等式满足的最小个数的a_i；

解法：这道题可以转为一个图的问题，假设此时的$n=8$，那么我们就是要在下图中找到一条最短的路径到达$0$；即图中虚线的那个路径就是最短的；我们利用队列来实现，队列中的元素为，即整数值和已走的步数，每到下一个节点，步数加1，直到到达$n=0$的那个节点；

Java

class Solution {
    public int numSquares(int n) {
        LinkedList> queue = new LinkedList<>();
        boolean[] visited = new boolean[n + 1];
        visited[n] = true;
        queue.addLast(Arrays.asList(n, 0));
        while (!queue.isEmpty()) {
            List list = queue.poll();
            int num = list.get(0);
            int step = list.get(1);
            for (int i = 1; ; i++) {
                int ret = num - i * i;
                if (ret < 0) {
                    break;
                }
                if (ret == 0) {
                    return step + 1;
                }
                if (!visited[ret]) {
                    queue.addLast(Arrays.asList(ret, step + 1));
                    visited[ret] = true;
                }
            }
        }

        throw new RuntimeException("no solution");
    }
}