LeetCode #611. Valid Triangle Number

题目描述：

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].

class Solution {
public:
    int triangleNumber(vector<int>& nums) {
        int n=nums.size();
        if(n<3) return 0;
        sort(nums.begin(),nums.end());
        int result=0;
        for(int i=0;i<=n-3;i++)
        {
            for(int j=nums.size()-1;j>i+1;j--)
            {
                // 先确定好两条边，二分搜索第三条边，它必须大于两边之差，直接用upper_bound即可
                int k=upper_bound(nums.begin(),nums.end(),nums[j]-nums[i])-nums.begin();
                // 得到的k是搜索整个数组的结果可能超过(i,j)的范围，需要修正
                if(k<=i) k=i+1; // 当k小于等于i时，说明第三条边可以比较小，[i+1,j)内的所有值都满足k的要求
                if(k>=j) continue; // 当k大于等于j时，说明第三条边要很大，已经超出了j的范围，没有符合要求的值
                result+=j-k;
            }
        }
        return result;
    }
};