How should I practice Team-Preferred Stable Matching?

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Team-Preferred Stable Matching

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Problem statement

There are n teams and n new employees. Every team has one position, and every employee joins exactly one team.

teamPreferences[t] lists all employee indices from most to least preferred by team t.
employeePreferences[e] lists all team indices from most to least preferred by employee e.

Return the team-optimal stable matching. In other words, among stable matchings, teams receive priority: run the team-proposing Gale-Shapley process. Return an array assignment where assignment[t] is the employee matched to team t.

A matching is stable when there is no unmatched pair (t, e) such that team t prefers employee e over its assigned employee and employee e prefers team t over their assigned team.

Function

teamPreferredMatching(teamPreferences: int[][], employeePreferences: int[][]) → int[]

Examples

Example 1

teamPreferences = [[0,1],[0,1]]employeePreferences = [[0,1],[1,0]]return = [0,1]

Both teams first propose to employee 0. Employee 0 keeps team 0, so team 1 next proposes to employee 1.

Example 2

teamPreferences = [[0,1,2],[1,0,2],[1,2,0]]employeePreferences = [[1,0,2],[0,2,1],[2,1,0]]return = [1,0,2]

Rejections cascade: employee 1 upgrades from team 1 to team 2 and then to team 0; employee 0 upgrades from team 0 to team 1, leaving team 2 with employee 2.

Example 3

teamPreferences = [[0]]employeePreferences = [[0]]return = [0]

The only team and employee must be matched.

Constraints

1 <= n == teamPreferences.length == employeePreferences.length <= 1000.
Every row in both matrices has length n.
Every team-preference row is a permutation of employee indices 0..n-1.
Every employee-preference row is a permutation of team indices 0..n-1.