Two Sum I
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 have exactly one solution.
Example:
Given nums = [2, 7, 11, 15], target = 9, Because nums[0] + nums[1] = 2 + 7 = 9, return [0, 1].
分析：如果数组已经排序完，那么只需要双指针从两端往中间夹即可。但是没有排序的话，先排序复杂度就已经O(nlogn)了，所以没法用排序法。事实上是有O(n)的hash法：首先遍历一遍，全部放入hashtable（unordered_set）中，复杂度为O(n)；然后再对于每个数x，都在hashtable中找target - x的数在不在其中，如果在，就结束，因为题目说假设只有一个答案，复杂度为O(n)；总复杂度为O(n)。
Two Sum II - Input array is sorted
不用排序的排序法，因为数组已经排序完，从两端往中间夹的复杂度与hash法一样也为O(n)；但理论时间开销应该比hash法小的。
Two Sum III - Data structure design
略
3 Sum
与Two Sum题目类似，二元换成了三元。两种解法，复杂度均为O(n^2)
- hash法，把两两的和放到一个hashmap（unordered_multimap<int,pair<int,int>>），三个int分别为“和”，“第一个index”，“第二个index”。从头到尾匹配，遇到index在两个之中的，则非解；不在两个中的，则为合法解。
- 排序法，然后对任何一个选取x，都在x后面从两边往中间夹，选取和为target - x的
3 Sum Closest
这个3 Sum的排序法，可解出，复杂度为O(n ^ 2)。没法用hash法。
3 Sum Smaller
Given an array of n integers nums and a target, find the number of index triplets i, j, k with 0 <= i < j < k < n that satisfy the condition nums[i] + nums[j] + nums[k] < target.
For example, given nums = [-2, 0, 1, 3], and target = 2.
Return 2. Because there are two triplets which sums are less than 2:
[-2, 0, 1]
[-2, 0, 3]
Follow up: Could you solve it in O(n^2) runtime?
暴力解法是O(n^3)。用Sum的排序法，可接出，复杂度为O(n ^ 2)。
没法用hash法，顶多用multimap做，但复杂度为O(n^2*logn)。
4 Sum
从二元到三元再到四元
- 用排序法，复杂度有O(n^3)
- 用hash法，复杂度为O(n^2)，通过两个unorder_multiple<int, pair<int, int>>，然后比对pair中的index是否重复了，来决定结果是否符合要求。
【总结】到这里为止，我们基本也可以总结出这NSum类型的解法：
- 排序法是万能的，复杂度为O(max(nlogn, n^(N-1))；
- hash法能也不错，复杂度为O(n^(ceiling(log2N)))
【Combination Sum I】
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. (ie, 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]
【Combination Sum II】
Given a collection of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.
Each number in C may only be used once in the combination.
For example, given candidate set 10,1,2,7,6,1,5 and target 8,
A solution set is: [1, 7] [1, 2, 5] [2, 6] [1, 1, 6]
【Combination Sum III】
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.
Ensure that numbers within the set are sorted in ascending order.
Example:
Input: k = 3, n = 9
Output:
[[1,2,6], [1,3,5], [2,3,4]]
思路