LeetCode 216. Combination Sum III (组合的和之三)

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.


Example 1:

Input: k = 3, n = 7

Output:

 

[[1,2,4]]

 


Example 2:

Input: k = 3, n = 9

Output:

 

[[1,2,6], [1,3,5], [2,3,4]]

 

 


 

题目标签:Array, Backtracking

  题目给了我们 k 和 n, 让我们找到 从1到9里的 k 个数字组合,没有重复,加起来之和等于 n。这道题目与前面两个版本的基本思路一样,利用 backtracking来做,就是有一些条件不一样而已。这题规定了只能从1 到 9 里选数字,之前两个版本的题目都是给的array;还有就是 这一题 规定了我们 数字的数量要等于 k。所以只要做一些条件的修改就可以了,具体看code。

 

 

Java Solution:

Runtime beats 45.85% 

完成日期:09/06/2017

关键词:Array,Backtracking

关键点:加入数字 -> 递归 -> 去除最后一个数字 来测试所有的组合可能性

 

 1 class Solution 
 2 {
 3     public List<List<Integer>> combinationSum3(int k, int n) 
 4     {
 5         List<List<Integer>> list = new ArrayList<>();
 6         int len = 10; // use only numbers from 1 to 9
 7         backtrack(list, new ArrayList<>(), n, 1, len, k);
 8         
 9         return list;
10     }
11     
12     public boolean backtrack(List<List<Integer>> list, List<Integer> tempList, 
13             int remain, int start, int len, int size)
14     {
15         if(remain < 0 || tempList.size() > size) // if remain less than 0 or number limit exceeds
16             return false;                         // no need to continue 
17         else if(remain == 0 && tempList.size() == size) // only add tempList into list
18         {                                               // when remain = 0 and number limit size matches
19             list.add(new ArrayList<>(tempList));
20             return false;
21         }
22         else
23         {
24             for(int i=start; i<len; i++)
25             {
26                 boolean flag;
27                 tempList.add(i);
28                 flag = backtrack(list, tempList, remain - i, i+1, len, size); // i + 1 because we cannot use same number more than once
29                 tempList.remove(tempList.size() - 1);
30                 
31                 if(!flag) // if find a tempList answer or fail, no need to continue that loop
32                     break; // because 1~9 is sorted and unique, the rest numbers are greater, they'll fail
33             }
34             
35             return true;
36         }
37     }
38 }

参考资料:N/A

 

LeetCode 算法题目列表 - LeetCode Algorithms Questions List

 

posted @ 2017-09-07 05:19  Jimmy_Cheng  阅读(185)  评论(0编辑  收藏  举报