611. Valid Triangle Number ------------M ~~~~~~~~~

 Given an array consists of non-negative integers, your task is to count the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle.

Example 1:

Input: [2,2,3,4]
Output: 3
Explanation:
Valid combinations are: 
2,3,4 (using the first 2)
2,3,4 (using the second 2)
2,2,3

Note:

1. The length of the given array won't exceed 1000.
2. The integers in the given array are in the range of [0, 1000].

A:

method 1 :   sort and brute force. 

class Solution {
public:
    int triangleNumber(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int res = 0;
        int n = nums.size();
        for(int i = 0;i<n-2; i++){
            for(int j = i+1; j<n-1; j++){
                for(int k = j+1; k<n; k++){
                    if(nums[i]+nums[j]>nums[k]){
                        ++res;
                    }else{
                        break;
                    }
                }
            }
        }
        return res;
    }
};

Method 2 :  when search the last value, , and find the index that's min than first two, via binary search

Method 3：sort, then when find 2,3 value, use idea like 2sum, to find  pairs.