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  • LeetCode 526. Beautiful Arrangement

    原题链接在这里:https://leetcode.com/problems/beautiful-arrangement/description/

    题目:

    Suppose you have N integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these N numbers successfully if one of the following is true for the ith position (1 <= i <= N) in this array:

    1. The number at the ith position is divisible by i.
    2. i is divisible by the number at the ith position.

    Now given N, how many beautiful arrangements can you construct?

    Example 1:

    Input: 2
    Output: 2
    Explanation: 
    
    The first beautiful arrangement is [1, 2]:
    Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).
    Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).
    The second beautiful arrangement is [2, 1]:
    Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).
    Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.

    Note:

    1. N is a positive integer and will not exceed 15.

    题解:

    典型的backtracking. 用visited记录用过的位置, 挨个position往后permute. 遇到不合规矩的直接返回, 看能不能走到N.

    Time Complexity: exponential. 每次走到最后才遇到不和规矩的backtrack回来.

    Space: O(N).

    AC Java:

     1 class Solution {
     2     int res = 0;
     3     public int countArrangement(int N) {
     4         if(N <= 0){
     5             return 0;
     6         }
     7         
     8         boolean [] visited = new boolean[N+1];
     9         dfs(visited, 1, N);
    10         return res;
    11     }
    12     
    13     private void dfs(boolean [] visited, int pos, int N){
    14         if(pos > N){
    15             res++;
    16             return;
    17         }
    18         
    19         for(int i = 1; i<=N; i++){
    20             if(!visited[i] && (i%pos==0 || pos%i==0)){
    21                 visited[i] = true;
    22                 dfs(visited, pos+1, N);
    23                 visited[i] = false;
    24             }
    25         }
    26     }
    27 }

    跟上Beautiful Arrangement II.

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  • 原文地址:https://www.cnblogs.com/Dylan-Java-NYC/p/7624929.html
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