Add weighted_interval_scheduling under dynamic programming

Author: DataWorshipper

dynamic_programming/weighted_interval_scheduling.py

@@ -0,0 +1,83 @@
+"""
+Author  : Abhiraj Mandal
+Date    : October 3, 2025
+
+Weighted Interval Scheduling (Dynamic Programming) implementation in Python.
+
+Problem:
+Given a set of intervals with start time, end time, and weight,
+find a subset of non-overlapping intervals with the maximum total weight.
+"""
+
+from __future__ import annotations
+
+from typing import NamedTuple
+
+
+class Interval(NamedTuple):
+    start: int
+    end: int
+    weight: int
+
+
+def weighted_interval_scheduling(intervals: list[Interval]) -> int:
+    """
+    Compute the maximum total weight of non-overlapping intervals.
+
+    >>> intervals = [Interval(1, 3, 5), Interval(2, 5, 6), Interval(4, 6, 5)]
+    >>> weighted_interval_scheduling(intervals)
+    10
+    """
+    if not intervals:
+        return 0
+
+    intervals.sort(key=lambda x: x.end)
+
+    p = [0] * len(intervals)
+    for j in range(len(intervals)):
+        p[j] = -1
+        for i in range(j - 1, -1, -1):
+            if intervals[i].end <= intervals[j].start:
+                p[j] = i
+                break
+
+    n = len(intervals)
+    dp = [0] * n
+    for j in range(n):
+        incl = intervals[j].weight
+        if p[j] != -1:
+            incl += dp[p[j]]
+        dp[j] = max(incl, dp[j - 1] if j > 0 else 0)
+
+    return dp[-1]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print("All doctests passed!")
+
+    # Manual test suite
+    test_cases = [
+        ([Interval(1, 3, 5), Interval(2, 5, 6), Interval(4, 6, 5)], 10),
+        ([Interval(1, 2, 50)], 50),
+        ([Interval(1, 4, 5), Interval(2, 5, 6), Interval(3, 6, 5)], 6),
+        ([Interval(1, 2, 10), Interval(3, 4, 20), Interval(5, 6, 30)], 60),
+        (
+            [
+                Interval(1, 2, 50),
+                Interval(3, 5, 20),
+                Interval(6, 19, 100),
+                Interval(2, 100, 200),
+            ],
+            250,
+        ),
+    ]
+
+    for idx, (intervals, expected) in enumerate(test_cases, 1):
+        result = weighted_interval_scheduling(intervals)
+        print(f"Testcase {idx}: Expected={expected}, Got={result}")
+        assert result == expected, f"Testcase {idx} failed!"
+
+    print("\nAll manual test cases successfully passed!")