Merge pull request #1 from Johnaaron0108/Johnaaron0108-patch-1

Create job_scheduling.py

Author: Johnaaron0108

dynamic_programming/job_scheduling.py

@@ -0,0 +1,40 @@
+"""
+Weighted Job Scheduling Problem
+Given jobs with start time, end time, and profit, find the maximum profit
+subset of non-overlapping jobs.
+"""
+
+from bisect import bisect_right
+
+def job_scheduling(jobs):
+    """
+    >>> jobs = [(1, 3, 50), (3, 5, 20), (0, 6, 100), (4, 6, 70), (3, 8, 60)]
+    >>> job_scheduling(jobs)
+    120
+    >>> jobs = [(1, 2, 50), (3, 5, 20), (6, 19, 100), (2, 100, 200)]
+    >>> job_scheduling(jobs)
+    250
+    """
+    # Sort jobs by end time
+    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
+        if index != -1:
+            profit_incl += dp[index]
+        dp[i] = max(profit_incl, dp[i-1])
+    return dp[-1]
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()