Maximum Profit in Job Scheduling

arraybinary searchdynamic programming

Problem Statement

We have n jobs, where every job is scheduled to be done from startTime[i] to endTime[i] , obtaining a profit of profit[i] .

You're given the startTime , endTime and profit arrays, return the maximum profit you can take such that there are no two jobs in the subset with overlapping time range.

If you choose a job that ends at time X you will be able to start another job that starts at time X .

Examples

Example 1

Input: startTime = [1,2,3,3], endTime = [3,4,5,6], profit = [50,10,40,70]
Output: 120
The subset chosen is the first and fourth job. 
Time range [1-3]+[3-6] , we get profit of 120 = 50 + 70.

Example 2

Input: startTime = [1,2,3,4,6], endTime = [3,5,10,6,9], profit = [20,20,100,70,60]
Output: 150
The subset chosen is the first, fourth and fifth job. 
Profit obtained 150 = 20 + 70 + 60.

Example 3

Input: startTime = [1,1,1], endTime = [2,3,4], profit = [5,6,4]
Output: 6

Constraints

1 <= startTime.length == endTime.length == profit.length <= 5 * 10 ^4

1 <= startTime[i] < endTime[i] <= 10 ^9

1 <= profit[i] <= 10 ^4

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search