Update job_scheduling.py

Author: Johnaaron0108

dynamic_programming/job_scheduling.py

@@ -2,12 +2,14 @@
 Weighted Job Scheduling Problem
 Given jobs with start time, end time, and profit, find the maximum profit
 subset of non-overlapping jobs.
+https://en.wikipedia.org/wiki/Weighted_interval_scheduling
 """
 
 from bisect import bisect_right
+from typing import List, Tuple
 
 
-def job_scheduling(jobs):
+def job_scheduling(jobs: List[Tuple[int, int, int]]) -> int:
     """
     >>> jobs = [(1, 3, 50), (3, 5, 20), (0, 6, 100), (4, 6, 70), (3, 8, 60)]
     >>> job_scheduling(jobs)
@@ -18,21 +20,19 @@ def job_scheduling(jobs):
     """
     if not jobs:
         return 0
-    # Sort jobs by end time
-    jobs = sorted(jobs, key=lambda x: x[1])
+
+    jobs.sort(key=lambda x: x[1])
     n = len(jobs)
-    # dp[i] stores max profit including jobs[i]
     dp = [0] * n
     dp[0] = jobs[0][2]
-
-    # Store end times separately for binary search
     end_times = [job[1] for job in jobs]
 
     for i in range(1, n):
         profit_incl = jobs[i][2]
-        # Find last non-conflicting job using binary search
-        index = bisect_right(end_times, jobs[i][0] - 1) - 1
+        # ✅ allow jobs that start when another ends
+        index = bisect_right(end_times, jobs[i][0]) - 1
         if index != -1:
             profit_incl += dp[index]
         dp[i] = max(profit_incl, dp[i - 1])
+
     return dp[-1]