How should I practice Course Ordering with Concurrent Updates?

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Problem · Graph

Course Ordering with Concurrent Updates

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● Hard

NuroFULLTIMEPHONE SCREEN

Problem statement

Maintain prerequisites for numCourses courses numbered 0 through numCourses - 1. Process a finite operation history:

["ADD_PREREQUISITE", course, prerequisite] adds the edge prerequisite -> course. Adding the same edge again has no effect and produces "null".
["GET_ORDER"] produces the lexicographically smallest order that completes all courses, serialized without spaces, such as "[0,1,2]". If the graph contains a cycle, produce "[]".

Return one string for every operation. The history represents one legal linearization of concurrent calls: every update and query is atomic, and each query observes one complete committed graph state.

Function

courseOrderHistory(numCourses: int, operations: String[][]) → String[]

Examples

Example 1

numCourses = 4operations = [["ADD_PREREQUISITE","1","0"],["ADD_PREREQUISITE","2","0"],["GET_ORDER"],["ADD_PREREQUISITE","0","1"],["GET_ORDER"]]return = ["null","null","[0,1,2,3]","null","[]"]

The first query has two courses unlocked after 0, so the smaller label 1 comes first. The later reverse edge creates a cycle between 0 and 1.

Example 2

numCourses = 3operations = [["GET_ORDER"],["ADD_PREREQUISITE","2","1"],["ADD_PREREQUISITE","2","1"],["GET_ORDER"]]return = ["[0,1,2]","null","null","[0,1,2]"]

The empty graph sorts by course label. The duplicate edge is ignored.

Constraints

1 <= numCourses <= 2000.
1 <= operations.length <= 10000.
Each course and prerequisite is in [0, numCourses - 1], and an update never uses the same course twice.
Calls are linearizable; the provided history is their complete atomic order.