LeetCode之4Sum（经典）

题目：

Given an array S of n integers, are there elements a,b,c, and d in S such that a+b+c+d = target?
Find all unique quadruplets in the array which gives the sum of target.
Note:
• Elements in a quadruplet (a,b,c,d) must be in non-descending order. (ie, a ≤ b ≤ c ≤ d)
• The solution set must not contain duplicate quadruplets.
For example, given array S = {1 0 -1 0 -2 2}, and target = 0.
A solution set is:
(-1, 0, 0, 1)
(-2, -1, 1, 2)
(-2, 0, 0, 2)

分析：给定一个包含n个数的数组，问是否在数组中存在四个数abcd，使得a+b+c+d = target。在数组中找出所有的符合条件的四个数的集合。要求每个集合不重复，并且abcd从小到大排列。方法三种：

1.先排序，然后左右夹逼,时间复杂度 O(n^3)，空间复杂度 O(1)
2.先排序然后缓存两个数的和，最后，遍历。
3.先排序，然后缓存两个数的和，然后对这些和进行2sum。要求坐标不等。

代码：

#include "stdafx.h"
#include <ctime>

#include <iostream>
#include <vector>
#include <algorithm>
#include <unordered_map>

using namespace stdext;
using namespace std;

class Solution{
public:
	vector< vector<int> > FourSum1(vector<int>& num, int target){
		vector<vector<int>> result;
		vector<int> temp(4);
		sort(num.begin(),num.end());

		auto last = num.end();
		for (auto a = num.begin();a != last - 3;++a){
			for(auto b = next(a);b != prev(last,2);++b){
				auto c = next(b);
				auto d = prev(last);
				while(c < d){
					if (*a + *b + *c + *d < target){
						c++;
					}
					else if (*a + *b + *c + *d >target){ 
						d--;
					}else{
						temp[0]=*a;  temp[1]=*b;
						temp[2]=*c;  temp[3]=*d;
						result.push_back(temp);
						++c;--d;
					}
				}
			}
		}
		sort(result.begin(), result.end());
		//unique移除相邻重复的元素，然后返回的是新的结尾指针，erase擦除多余的内存部分。
		result.erase(unique(result.begin(),result.end()), result.end());

		return result;
	}

	vector< vector<int> > FourSum2(vector<int>& num, int target){
		vector<vector<int>> result;
		if (num.size() < 4) return result;

		vector<int> temp(4);
		sort(num.begin(),num.end());
		unordered_map<int, vector<pair<int, int>> > twoSum; //重复的键值，将其存放在一个vector中
		auto last = num.end();
		for (size_t a=0;a<num.size();++a){
			for (size_t b = a+1;b<num.size();++b){
				twoSum[num[a] + num[b]].push_back(pair<int,int>(num[a],num[b]));
			}
		}

		int sub = 0;
		for(size_t c=0;c<num.size();++c){
			for (size_t d=c+1;d<num.size();++d){
				sub = target - num[c] - num[d];
				if(twoSum.find(sub) == twoSum.end())
					continue;
				auto& subRst = twoSum[sub];//可能有多个结果。
				for (size_t i=0;i<subRst.size();++i){
					if(num[c] <= subRst[i].first || num[d] <= subRst[i].second) //去除重复的情况，pair中的元素从小到大排序，所以second
						continue;

					temp[0] = subRst[i].first;
					temp[1] = subRst[i].second;
					temp[2] = num[c];
					temp[3] = num[d];
					sort(temp.begin(),temp.end());
					result.push_back(temp);
				}
			}
		}
		sort(result.begin(), result.end());
		result.erase(unique(result.begin(),result.end()), result.end());

		return result;
	}


	vector< vector<int> > FourSum3(vector<int>& num, int target){
		vector<vector<int>> result;
		if (num.size() < 4) return result;

		vector<int> temp(4);
		sort(num.begin(),num.end());
		unordered_multimap< int,pair<int, int> > twoSum;
		for(size_t i = 0;i<num.size();++i){
			for (size_t j=i+1;j<num.size();++j){
				twoSum.insert(make_pair(num[i]+ num[j], make_pair(num[i],num[j])));			
			}
		}

		for(auto i=twoSum.begin();i!=twoSum.end();++i){
			int sub = target - i->first;
			auto range = twoSum.equal_range(sub);
			for(auto j=range.first;j!=range.second;++j){
				pair<int,int> k = i->second;
				int a = k.first ;
				int b = k.second;
				int c = j->second.first;
				int d = j->second.second;
				if(a!=c && a!=d && b != c && b!=d){
					temp[0] = a;
					temp[1] = b;
					temp[2] = c;
					temp[3] = d;
					sort(temp.begin(),temp.end());
					result.push_back(temp);
				}
			}

		}
		sort(result.begin(), result.end());
		result.erase(unique(result.begin(),result.end()), result.end());

		return result;
	}
};


int _tmain(int argc, _TCHAR* argv[])
{
	vector<int> v1;
	vector<vector<int>> result;

	v1.push_back(1);
	v1.push_back(0);
	v1.push_back(-1);
	v1.push_back(0);
	v1.push_back(-2);
	v1.push_back(2);

	//v1.push_back((rand()%200 - 100));v1.push_back((rand()%200 - 100));

	Solution s;
	clock_t start,finish;
	long i = 100000L;
	double duration;

	start = clock();
	result = s.FourSum1(v1,0);
	finish = clock();
	duration = (double)(finish - start)/CLOCKS_PER_SEC;
	cout<< "FourSum1 Runtime:" << duration << endl;

	start = clock();
	result = s.FourSum2(v1,0);
	finish = clock();
	duration = (double)(finish - start)/CLOCKS_PER_SEC;
	cout<< "FourSum2 Runtime:" << duration << endl;

	start = clock();
	result = s.FourSum3(v1,0);
	finish = clock();
	duration = (double)(finish - start)/CLOCKS_PER_SEC;
	cout<< "FourSum3 Runtime:" << duration << endl;
	return 0;
}

小结：

很值得研究的一道题目，建议自己写一遍，不仅对算法思想提升有帮助，而且在使用stl的学习上，也是有帮助的。根据我测试，就运行时间来说，方法一最快，二其次，三最慢。

另外，方法二实验unordered_map，其中key值相同的话，相同的key的value保存在一个vector桶中。而方法三使用unordered_multimap,当存在key相同的情况，并不是像前者那样存储，而是分开存储。

比如：unordered_map中形式如：   [1] = (-2, [2]((-2, 0),(-2, 0)))  相同的键值都放在一起。不允许重复的键值。

unordered_multimap中 形式如：(-2, (-2, 0)),(-2, (-2, 0))  虽然键值不一样，但是都是分开存放的。允许重复的键值。