**一. 题目描述**
Given a set of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.
The same repeated number may be chosen from C unlimited number of times.
Note:
• All numbers (including target) will be positive integers.
• Elements in a combination (a1; a2; … ; ak) must be in non-descending order. (a1<=a2<=…<= ak).
• The solution set must not contain duplicate combinations.
For example, given candidate set 2,3,6,7 and target 7, A solution set is:
~~~
[7]
[2, 2, 3]
~~~
**二. 题目分析**
题目大意是:有一个正整数集合C和一个正整数目标T。现从C中选出一些数,使其累加和恰好等于T(C中的每个数都可以取若干次),求所有不同的取数方案,是一道典型的深度优先搜索题。
题目的一个细节是,正整数集合C可能存在**重复的数**,而这些数用于组合时,会产生重复的排列组合,如下图所示,而题目要求:The solution set must not contain duplicate combinations.
![](https://box.kancloud.cn/2016-01-05_568bb5f11dc9e.jpg)
我的解决方法是对正整数集合C先进行从小到大排序,然后使用vector的erase方法去除集合C的重复元素,然后再进行DFS的相关运算。
**三. 示例代码**
~~~
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
class Solution
{
public:
vector<vector<int> > combinationSum(vector<int> &candidates, int target)
{
vector<int> temp; // 用于存放临时组合
sort(candidates.begin(), candidates.end());
// 结果要求输出的组合不能重复,需要去除candidates中的重复元素
candidates.erase(unique(candidates.begin(), candidates.end()), candidates.end());
combinationDFS(candidates, temp, 0, target);
return result;
}
private:
vector<vector<int> > result;
void combinationDFS(vector<int> &candidates, vector<int> &temp, size_t index, int target)
{
if (target == 0) // 得到满足目标的一组解
{
result.push_back(temp);
return;
}
else
{
for (size_t i = index; i < candidates.size(); ++i)
{
if (candidates[i] > target)
return;
temp.push_back(candidates[i]);
combinationDFS(candidates, temp, i, target - candidates[i]);
temp.pop_back();
}
}
}
};
~~~
![](https://box.kancloud.cn/2016-01-05_568bb5f136576.jpg)
**四. 小结**
该题是一道经典的DFS题目,后续还有Combination Sum II和Combination Sum III,需要深入研究。
- 前言
- 2Sum
- 3Sum
- 4Sum
- 3Sum Closest
- Remove Duplicates from Sorted Array
- Remove Duplicates from Sorted Array II
- Search in Rotated Sorted Array
- Remove Element
- Merge Sorted Array
- Add Binary
- Valid Palindrome
- Permutation Sequence
- Single Number
- Single Number II
- Gray Code(2016腾讯软件开发笔试题)
- Valid Sudoku
- Rotate Image
- Power of two
- Plus One
- Gas Station
- Set Matrix Zeroes
- Count and Say
- Climbing Stairs(斐波那契数列问题)
- Remove Nth Node From End of List
- Linked List Cycle
- Linked List Cycle 2
- Integer to Roman
- Roman to Integer
- Valid Parentheses
- Reorder List
- Path Sum
- Simplify Path
- Trapping Rain Water
- Path Sum II
- Factorial Trailing Zeroes
- Sudoku Solver
- Isomorphic Strings
- String to Integer (atoi)
- Largest Rectangle in Histogram
- Binary Tree Preorder Traversal
- Evaluate Reverse Polish Notation(逆波兰式的计算)
- Maximum Depth of Binary Tree
- Minimum Depth of Binary Tree
- Longest Common Prefix
- Recover Binary Search Tree
- Binary Tree Level Order Traversal
- Binary Tree Level Order Traversal II
- Binary Tree Zigzag Level Order Traversal
- Sum Root to Leaf Numbers
- Anagrams
- Unique Paths
- Unique Paths II
- Triangle
- Maximum Subarray(最大子串和问题)
- House Robber
- House Robber II
- Happy Number
- Interlaving String
- Minimum Path Sum
- Edit Distance
- Best Time to Buy and Sell Stock
- Best Time to Buy and Sell Stock II
- Best Time to Buy and Sell Stock III
- Best Time to Buy and Sell Stock IV
- Decode Ways
- N-Queens
- N-Queens II
- Restore IP Addresses
- Combination Sum
- Combination Sum II
- Combination Sum III
- Construct Binary Tree from Inorder and Postorder Traversal
- Construct Binary Tree from Preorder and Inorder Traversal
- Longest Consecutive Sequence
- Word Search
- Word Search II
- Word Ladder
- Spiral Matrix
- Jump Game
- Jump Game II
- Longest Substring Without Repeating Characters
- First Missing Positive
- Sort Colors
- Search for a Range
- First Bad Version
- Search Insert Position
- Wildcard Matching