[MeetCoder] Count Pairs

Count Pairs

 

Description

You are given n circles centered on Y-aixs. The ith circle’s center is at point (i, 0) and its radius is A[i]. Count the number of pairs of circles that have at least one common point?

Input

The input should be a list of n positive integers A, each of them should be less than or equal to 1,000,000,000 and n should be less than or equal to 100,000.

Output

The output should be the number of pairs of circles that have at least one common point in the format of Integer.

Sample Input

1 2 3

Sample Output

3

图书馆排队问题。跟问题Number of Airplanes in the Sky差不多。将每个圆在x轴上的最左边的点与最右边的点放到vector中排序，同时标记是左边的点还是右边的点，注意如果多个点在同一个坐标，左边界的点要放在前面，然后一次遍历，遇到左边界就统计当前点在几个圆的范围内，即res += cnt，然后更新cnt，即++cnt，遇到右边界就--cnt。

 1 class Solution {
 2 public:
 3     long long countPairs(const vector<int> &A) {
 4         long long res = 0, cnt = 0;
 5         vector<pair<int, int>> v;
 6         for(int i = 0; i < A.size(); ++i) {
 7             v.push_back({i - A[i], -1});
 8             v.push_back({i + A[i], 1});
 9         }
10         sort(v.begin(), v.end());
11         for (auto vv : v) {
12             if (vv.second == -1) res += cnt++;
13             else --cnt;
14         }
15         return res;
16     }
17 };
18 /**************************************************************
19     Problem: 25
20     User: easonliu
21     Language: C++
22     Result: Accepted
23     Time:141 ms
24     Memory:8524 kb
25 ****************************************************************/