2824.count-pairs-whose-sum-is-less-than-target.cpp

//  Tag: Array, Two Pointers, Binary Search, Sorting
//  Time: O(NlogN)
//  Space: O(1)
//  Ref: -
//  Note: -

//  Given a 0-indexed integer array nums of length n and an integer target, return the number of pairs (i, j) where 0 <= i < j < n and nums[i] + nums[j] < target.
//   
//  Example 1:
//  
//  Input: nums = [-1,1,2,3,1], target = 2
//  Output: 3
//  Explanation: There are 3 pairs of indices that satisfy the conditions in the statement:
//  - (0, 1) since 0 < 1 and nums[0] + nums[1] = 0 < target
//  - (0, 2) since 0 < 2 and nums[0] + nums[2] = 1 < target 
//  - (0, 4) since 0 < 4 and nums[0] + nums[4] = 0 < target
//  Note that (0, 3) is not counted since nums[0] + nums[3] is not strictly less than the target.
//  
//  Example 2:
//  
//  Input: nums = [-6,2,5,-2,-7,-1,3], target = -2
//  Output: 10
//  Explanation: There are 10 pairs of indices that satisfy the conditions in the statement:
//  - (0, 1) since 0 < 1 and nums[0] + nums[1] = -4 < target
//  - (0, 3) since 0 < 3 and nums[0] + nums[3] = -8 < target
//  - (0, 4) since 0 < 4 and nums[0] + nums[4] = -13 < target
//  - (0, 5) since 0 < 5 and nums[0] + nums[5] = -7 < target
//  - (0, 6) since 0 < 6 and nums[0] + nums[6] = -3 < target
//  - (1, 4) since 1 < 4 and nums[1] + nums[4] = -5 < target
//  - (3, 4) since 3 < 4 and nums[3] + nums[4] = -9 < target
//  - (3, 5) since 3 < 5 and nums[3] + nums[5] = -3 < target
//  - (4, 5) since 4 < 5 and nums[4] + nums[5] = -8 < target
//  - (4, 6) since 4 < 6 and nums[4] + nums[6] = -4 < target
//  
//   
//  Constraints:
//  
//  1 <= nums.length == n <= 50
//  -50 <= nums[i], target <= 50
//  
//  

class Solution {
public:
    int countPairs(vector<int>& nums, int target) {
        int n = nums.size();
        sort(nums.begin(), nums.end());
        int l = 0;
        int r = n - 1;
        int res = 0;
        while (l <= r) {
            if (nums[l] + nums[r] < target) {
                res += r - l;
                l += 1;
            } else {
                r -= 1;
            }
        }
        return res;
    }
};