Get Maximum Profit by Scheduling Jobs in Python

Suppose we have a list of intervals where each interval contains three values [start, end, profit]. We can perform only one task at a time, we have to find the most amount of profit we can get.

So, if the input is like intervals = [[1, 2, 100],[3, 5, 40],[6, 19, 150],[2, 100, 250]], then the output will be 350, as we can take these two intervals [1, 2, 100] and [2, 100, 250]

To solve this, we will follow these steps

• d := an empty map that contains lists as values
• n := 0
• for each (start, end, profit) in intervals, do
  • if end > n, then
    • n := end
• insert pair (start, end) into d[end]
• A := a list of size n + 1 and fill with 0
• for end in range 0 to size of A, do
  • if end is in d, then
    • for each (start, profit) pair in d[end], do
      • A[end] := maximum of A[end], (A[start] + profit) and A[end - 1]
  • otherwise,
    • A[end] := A[end - 1]
• return last value of A

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

from collections import defaultdict
class Solution:
   def solve(self, intervals):
      d = defaultdict(list)
      n = 0
      for start, end, profit in intervals:
         if end > n:
            n = end
         d[end].append([start, profit])
      A = [0 for i in range(n + 1)]
      for end in range(len(A)):
         if end in d:
            for start, profit in d[end]:
               A[end] = max(A[end], A[start] + profit, A[end - 1])
         else:
            A[end] = A[end - 1]
      return A[-1]
ob = Solution()
intervals = [[1, 2, 100],[3, 5, 40],[6, 19, 150],[2, 100, 250]]
print(ob.solve(intervals))

Input

[[1, 2, 100],[3, 5, 40],[6, 19, 150],[2, 100, 250]]

Output

350