LeetCode题解：Two Sum

题目：
Given an array of integers, return indices of the two numbers such that they add up to a specific target.
You may assume that each input would haveexactly** one solution.
翻译：
给定一个数组和一个特定的数sum，找出数组中的两个数，使其和为sum，返回这两个数的索引。

解法一：

暴力循环

vector twoSum(vector& numbers, int sum) {
    vector res(2);
    for (unsigned int i = 0; i < numbers.size(); ++i) {
        for (unsigned int j = i + 1; j < numbers.size(); ++j) {
            if (numbers[i] + numbers[j] == sum) {
                res[0] = i;
                res[1] = j;
                return res;
            }
       }
   }
   return res;
}

显然，空间复杂度：O(1)，时间复杂度O(n^2)

解法二：

借用hash查找时O(1)的特性，可以把时间复杂度降低到O(n)，但同时也付出了空间复杂度O(n)的代价

vector twoSum(vector& nums, int target) {
    vector res(2);
    map mp;
    for (unsigned int i = 0; i < nums.size(); ++i) {
        mp[nums[i]] = i;
    }
    for (unsigned int i = 0; i < nums.size(); ++i) {
        map::iterator it = mp.find(target - nums[i]);
        if (it != mp.end() && i != mp[target-nums[i]]) {
            res[0] = i;
            res[1] = mp[target - nums[i]];
            return res;
        }
    }
    return res;
}

稍微优化一下：

vector twoSum(vector& nums, int target) {
    vector res(2);
    map mp;
    for (unsigned int i = 0; i < nums.size(); ++i) {
        map::iterator it = mp.find(target - nums[i]);
        if (it != mp.end() && i != mp[target-nums[i]]) {
            if (i < mp[target - nums[i]]) {
                res[0] = i;
                res[1] = mp[target - nums[i]];
            } else {
                res[0] = mp[target - nums[i]];
                res[1] = i;
            }
            return res;
        }
        mp[nums[i]] = i;
    }
    return res;
}

解法三：

先将数组排个序，然后利用二分查找的思想，从两头往中间逼，这样下来时间复杂度为O(nlogn) + O(n)，空间复杂度，因为需要保存原始数组值与索引的对应关系，故为O(n)

 bool less_cmp(pair a, pair b) {
    return a.first < b.first;
}

class Solution {
public:
    vector twoSum(vector& nums, int target) {
        vector res(2);
        vector > index;
        for (unsigned int i = 0; i < nums.size(); ++i) {
            index.push_back(make_pair(nums[i], i));
        }
        sort(index.begin(), index.end(), less_cmp);
        //sort()
        unsigned int begin = 0;
        unsigned int end   = index.size() - 1;
        while (begin < end) {
            if (index[begin].first + index[end].first == target) {
                res[0] = index[begin].second;
                res[1] = index[end].second;
                return res;
            } else if (index[begin].first + index[end].first < target) {
                ++begin;
            } else {
                 --end;
            }
        }
        return res;
    }
};