【Grind75Hard】7問目 1235. Maximum Profit in Job Scheduling

grind75_hard/07_1235_Maximum Profit in Job Scheduling/level_1.py

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+# startTimeでソートして、繋げられるものを順番に確認していく
+# 終了時刻の早いものから見ていき、最大の利益になるものを選択していく
+# (最大の利益にならないものは、それ以降でも最大にならないため捨てて良い)
+# 例:(start, end, profit) = ((1, 3 50), (2, 3, 10), (3, 5, 40), (4, 6, 70))
+# 3項目の選択肢は
+# (1, 3, 50) -> (3, 5, 40)の順番で選択すると最大の利益になる
+# (2, 3, 10) -> (3, 5, 40)は最大の利益にならない(4項目以降でも最大の利益にならないので捨てる)
+# 4項目の選択肢は
+# (1, 3, 50) -> (4, 6, 70)の順番で選択すると最大の利益になる
+# (2, 3, 10)は3項目の検討時に捨てた
+class Solution:
+    def jobScheduling(
+        self, startTime: List[int], endTime: List[int], profit: List[int]
+    ) -> int:
+        sorted_starts = sorted([(startTime[i], i) for i in range(len(startTime))])
+        max_profit = 0
+        end_profit_heap = [(0, 0)]
+        for start, i in sorted_starts:
+            max_profit_use_i = 0
+            pre_info = ()
+            while end_profit_heap and end_profit_heap[0][0] <= start:
+                pre_end, pre_profit = heapq.heappop(end_profit_heap)
+                if pre_profit + profit[i] <= max_profit_use_i:
+                    continue
+                max_profit_use_i = pre_profit + profit[i]
+                pre_info = (pre_end, pre_profit)
+            heapq.heappush(end_profit_heap, (endTime[i], max_profit_use_i))
+            max_profit = max(max_profit, max_profit_use_i)
+            if pre_info:
+                heapq.heappush(end_profit_heap, pre_info)
+        return max_profit

grind75_hard/07_1235_Maximum Profit in Job Scheduling/level_2.py

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+# DP
+# i番目以降のjobを使った時の最大利益をメモしていく
+class Solution:
+    def jobScheduling(
+        self, startTime: List[int], endTime: List[int], profit: List[int]
+    ) -> int:
+        jobs = list(zip(startTime, endTime, profit))
+        jobs.sort()
+        max_profit_begin_i = [None] * len(jobs)
+        max_profit_begin_i.append(0)
+
+        def find_max_profit(i):
+            if max_profit_begin_i[i] is not None:
+                return max_profit_begin_i[i]
+            profit_skip_i = find_max_profit(i + 1)
+            next_index = bisect.bisect_left(jobs, (jobs[i][1], 0, 0), lo=i + 1)
+            profit_use_i = find_max_profit(next_index) + jobs[i][2]
+            max_profit_begin_i[i] = max(profit_skip_i, profit_use_i)
+            return max_profit_begin_i[i]
+
+        return find_max_profit(0)

grind75_hard/07_1235_Maximum Profit in Job Scheduling/level_3.py

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+class Solution:
+    def jobScheduling(
+        self, startTime: List[int], endTime: List[int], profit: List[int]
+    ) -> int:
+        jobs = list(zip(startTime, endTime, profit))
+        jobs.sort()
+
+        @cache
+        def find_max_profit(i):
+            if i >= len(jobs):
+                return 0
+            profit_skip_i = find_max_profit(i + 1)
+            next_index = bisect_left(jobs, (jobs[i][1], 0, 0), lo=i + 1)
+            profit_use_i = find_max_profit(next_index) + jobs[i][2]
+            return max(profit_skip_i, profit_use_i)
+
+        return find_max_profit(0)

grind75_hard/07_1235_Maximum Profit in Job Scheduling/level_4.py

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+# DP
+class Solution:
+    def jobScheduling(
+        self, startTime: List[int], endTime: List[int], profit: List[int]
+    ) -> int:
+        jobs = list(sorted(zip(startTime, endTime, profit)))
+        max_profit = [0] * (len(jobs) + 1)
+        for i in range(len(jobs) - 1, -1, -1):
+            profit_skip_running_job = max_profit[i + 1]
+            next_index = bisect_left(jobs, (jobs[i][1], 0, 0), lo=i + 1)
+            profit_use_running_job = max_profit[next_index] + jobs[i][2]
+            max_profit[i] = max(profit_skip_running_job, profit_use_running_job)
+        return max_profit[0]
+
+
+# level_1の書き直し
+class Solution:
+    def jobScheduling(
+        self, startTime: List[int], endTime: List[int], profit: List[int]
+    ) -> int:
+        jobs = list(sorted(zip(startTime, endTime, profit)))
+        jobs.append((float("inf"), float("inf"), 0))
+        max_profit = 0
+        running_jobs = []
+        for job_start, job_end, job_profit in jobs:
+            while running_jobs and running_jobs[0][0] <= job_start:
+                _, max_profit_from_running_job = heapq.heappop(running_jobs)
+                max_profit = max(max_profit, max_profit_from_running_job)
+            heapq.heappush(running_jobs, (job_end, max_profit + job_profit))
+        return max_profit