Maximize jobs that can be completed under given constraint

Given an integer N denoting number of jobs and a matrix ranges[] consisting of a range [start day, end day] for each job within which it needs to be completed, the task is to find the maximum possible jobs that can be completed.
Examples: 
 

Input: N = 5, Ranges = {{1, 5}, {1, 5}, {1, 5}, {2, 3}, {2, 3}} 
Output: 5 
Explanation: Job 1 on day 1, Job 4 on day 2, Job 5 on day 3, Job 2 on day 4, Job 3 on day 5

Input: N=6, Ranges = {{1, 3}, {1, 3}, {2, 3}, {2, 3}, {1, 4}, {2, 5}} 
Output: 5 
 

Approach: The above problem can be solved using a Priority Queue. Follow the steps below to solve the problems: 
 

• Find the minimum and maximum day in the range of jobs.
• Sort all jobs in increasing order of start day.
• Iterate from the minimum to maximum day, and for every i^th day, select the job having least end day which can be completed on that day.
• In order to perform the above step, maintain a Min Heap, and on every i^th day, insert the jobs that can be completed on that day, into the Min Heap sorted by end day. If any job can completed on the i^th day, consider the one with the lowest end day and increase the count of jobs completed.
• Repeat this process for all the days and finally print the count of jobs completed.

Below is an implementation of the above approach:
 

5

Time Complexity: O(Xlog(N)), where X is the difference between maximum and minimum day and N is the number of jobs. 
Auxiliary Space: O(N²)