757. Set Intersection Size At Least Two

An integer interval [a, b] (for integers a < b) is a set of all consecutive integers from a to b, including a and b.

Find the minimum size of a set S such that for every integer interval A in intervals, the intersection of S with A has size at least 2.

Example 1:

Input: intervals = [[1, 3], [1, 4], [2, 5], [3, 5]]
Output: 3
Explanation:
Consider the set S = {2, 3, 4}.  For each interval, there are at least 2 elements from S in the interval.
Also, there isn't a smaller size set that fulfills the above condition.
Thus, we output the size of this set, which is 3.

 

Example 2:

Input: intervals = [[1, 2], [2, 3], [2, 4], [4, 5]]
Output: 5
Explanation:
An example of a minimum sized set is {1, 2, 3, 4, 5}.

 

Note:

1. intervals will have length in range [1, 3000].
2. intervals[i] will have length 2, representing some integer interval.
3. intervals[i][j] will be an integer in [0, 10^8].

 

 

Approach #1: C++. [greedy]

class Solution {
public:
    int intersectionSizeTwo(vector<vector<int>>& intervals) {
        int size = intervals.size();
        sort(intervals.begin(), intervals.end(), [](const vector<int>& a, const vector<int>& b) {
            if (a[1] == b[1]) return a[0] > b[0];
            else return a[1] < b[1];
        });
        
        int ans = 0, p1 = -1, p2 = -1;
        for (int i = 0; i < size; ++i) {
            if (intervals[i][0] <= p1) continue;
            if (intervals[i][0] > p2) {
                ans += 2;
                p2 = intervals[i][1];
                p1 = p2 - 1;
            } else {
                ans++;
                p1 = p2;
                p2 = intervals[i][1];
            }
        }
        
        return ans;
    }
};