# LeetCode - 0611. Valid Triangle Number
### 題目網址：https://leetcode.com/problems/valid-triangle-number/
###### tags: `LeetCode` `Medium` `數學` `幾何`

/*
    -LeetCode format-
    Problem: 611. Valid Triangle Number
    Difficulty: Medium
    
    by Inversionpeter
*/



static const auto Initialize = []{
    ios::sync_with_stdio(false); cin.tie(nullptr);
    return nullptr;
}();

class Solution {
public:
    int triangleNumber(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int total = 0, lower, upper;
        for (int i = nums.size() - 1; i >= 2; --i) {
            lower = 0; upper = i - 1;
            while (lower < upper)
                if (nums[lower] + nums[upper] > nums[i]) {
                    total += upper - lower;
                    --upper;
                }
                else
                    ++lower;
        }
        return total;
    }
};