Time: 814 ms (5.02%), Space: 57 MB (17.32%) - LeetHub

2050-parallel-courses-iii/2050-parallel-courses-iii.py

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+class Solution:
+    def minimumTime(self, n: int, relations: List[List[int]], time: List[int]) -> int:
+        """
+        Complexities:
+        Time:  O(n^2)
+        Space: O(r)
+
+        where n = n, r = len(relations)
+        """
+
+        # courses been taken array
+        # - O(r) time / O(r) space
+        hasPrereq = [False] * n
+        prereqMap = [set() for i in range(n)]
+        leadsToMap = [set() for i in range(n)]
+        for prevCourse, nextCourse in relations:
+            hasPrereq[nextCourse - 1] = True
+            prereqMap[nextCourse - 1].add(prevCourse)
+            leadsToMap[prevCourse - 1].add(nextCourse)
+
+        # O(n) space
+        timeUntilComplete = [-1] * n
+        coursesCalculated = 0
+        maxOverallTimeFound = 0
+        toResolve = set()
+
+        # calculate timeUntilComplete for no prereq courses
+        # - O(n) time
+        for i in range(n):
+            if not hasPrereq[i]:
+                timeUntilComplete[i] = time[i]
+                maxOverallTimeFound = max(maxOverallTimeFound, time[i])
+                coursesCalculated += 1
+                toResolve.update(leadsToMap[i])
+
+        # find all timeUntilComplete
+        # - if all prereq times are known, then calc
+        # - O(n^2) time
+        while len(toResolve) > 0:
+            nextCourse = toResolve.pop()
+            maxPrereqTime = -1
+            for prereq in prereqMap[nextCourse - 1]:
+                if timeUntilComplete[prereq - 1] == -1:
+                    maxPrereqTime = -1
+                    break
+                maxPrereqTime = max(maxPrereqTime, timeUntilComplete[prereq - 1])
+
+            if maxPrereqTime > -1:
+                timeUntilComplete[nextCourse - 1] = maxPrereqTime + time[nextCourse - 1]
+                maxOverallTimeFound = max(maxOverallTimeFound, timeUntilComplete[nextCourse - 1])
+                coursesCalculated += 1
+                toResolve.update(leadsToMap[nextCourse - 1])
+        
+
+
+        return maxOverallTimeFound