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36 changes: 36 additions & 0 deletions dynamic_programming/job_scheduling.py
Original file line number Diff line number Diff line change
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"""
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


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)
120
>>> jobs = [(1, 2, 50), (3, 5, 20), (6, 19, 100), (2, 100, 200)]
>>> job_scheduling(jobs)
250
"""
if not jobs:
return 0

jobs.sort(key=lambda job: job[1])
n = len(jobs)
dp = [0] * n
dp[0] = jobs[0][2]
end_times = [job[1] for job in jobs]

for i in range(1, n):
profit_incl = jobs[i][2]
index = bisect_right(end_times, jobs[i][0]) - 1 # allow adjacent jobs
if index != -1:
profit_incl += dp[index]
dp[i] = max(profit_incl, dp[i - 1])

return dp[-1]