Problem description:

An underground railway system is keeping track of customer travel times between different stations. They are using this data to calculate the average time it takes to travel from one station to another.

Implement the UndergroundSystem class:

  • void checkIn(int id, string stationName, int t)
    • A customer with a card ID equal to id, checks in at the station stationName at time t.
    • A customer can only be checked into one place at a time.
  • void checkOut(int id, string stationName, int t)
    • A customer with a card ID equal to id, checks out from the station stationName at time t.
  • double getAverageTime(string startStation, string endStation)
    • Returns the average time it takes to travel from startStation to endStation.
    • The average time is computed from all the previous traveling times from startStation to endStation that happened directly, meaning a check in at startStation followed by a check out from endStation.
    • The time it takes to travel from startStation to endStation may be different from the time it takes to travel from endStation to startStation.
    • There will be at least one customer that has traveled from startStation to endStation before getAverageTime is called.

You may assume all calls to the checkIn and checkOut methods are consistent. If a customer checks in at time t1 then checks out at time t2, then t1 < t2. All events happen in chronological order.

Example 1:

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Input
["UndergroundSystem","checkIn","checkIn","checkIn","checkOut","checkOut","checkOut","getAverageTime","getAverageTime","checkIn","getAverageTime","checkOut","getAverageTime"]
[[],[45,"Leyton",3],[32,"Paradise",8],[27,"Leyton",10],[45,"Waterloo",15],[27,"Waterloo",20],[32,"Cambridge",22],["Paradise","Cambridge"],["Leyton","Waterloo"],[10,"Leyton",24],["Leyton","Waterloo"],[10,"Waterloo",38],["Leyton","Waterloo"]]

Output
[null,null,null,null,null,null,null,14.00000,11.00000,null,11.00000,null,12.00000]

Explanation
UndergroundSystem undergroundSystem = new UndergroundSystem();
undergroundSystem.checkIn(45, "Leyton", 3);
undergroundSystem.checkIn(32, "Paradise", 8);
undergroundSystem.checkIn(27, "Leyton", 10);
undergroundSystem.checkOut(45, "Waterloo", 15);  // Customer 45 "Leyton" -> "Waterloo" in 15-3 = 12
undergroundSystem.checkOut(27, "Waterloo", 20);  // Customer 27 "Leyton" -> "Waterloo" in 20-10 = 10
undergroundSystem.checkOut(32, "Cambridge", 22); // Customer 32 "Paradise" -> "Cambridge" in 22-8 = 14
undergroundSystem.getAverageTime("Paradise", "Cambridge"); // return 14.00000. One trip "Paradise" -> "Cambridge", (14) / 1 = 14
undergroundSystem.getAverageTime("Leyton", "Waterloo");    // return 11.00000. Two trips "Leyton" -> "Waterloo", (10 + 12) / 2 = 11
undergroundSystem.checkIn(10, "Leyton", 24);
undergroundSystem.getAverageTime("Leyton", "Waterloo");    // return 11.00000
undergroundSystem.checkOut(10, "Waterloo", 38);  // Customer 10 "Leyton" -> "Waterloo" in 38-24 = 14
undergroundSystem.getAverageTime("Leyton", "Waterloo");    // return 12.00000. Three trips "Leyton" -> "Waterloo", (10 + 12 + 14) / 3 = 12

Solution:

We have several persons, defined by id, which Check In at some station and some time and then Check Out from some other station at another time. We need to calculate times this person spend to go from one station to another and then calculate average time for all persons. Let us keep 3 pieces of information:

  1. self.ids is dictionary, where for each person(id) we will keep pair (station, time) if the last action this person did is check In and empty if it was check OUt
  2. self.pairs is counter, where for each pair of stations we keep total time spend between two stations.
  3. self.freqs is counter, where for each pair of stations we keep how many trips we have between these two stations.

Now, let us discuss, what our functions will do:

  1. checkIn(self, id, stationName, t): we just put pair (stationName, t) into self.ids[id].
  2. checkOut(self, id, stationName, t). Here we look at person id, extract information about his last station visited (pop it from self.ids[id] and update self.pairs, self.freqs for these pairs of stations.
  3. getAverageTime(self, startStation, endStation): here we just look at dictionaries self.pairs and self.freqs and directly return result.
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class UndergroundSystem:

    def __init__(self):
        self.ids = {}
        self.route = Counter()
        self.freqs = Counter()
        
    def checkIn(self, id, startStation, t):
        self.ids[id] = (startStation, t)

    def checkOut(self, id, endStation, t):
        startStation, t1 = self.ids.pop(id)
        self.route[(startStation, endStation)] += t-t1
        self.freqs[(startStation, endStation)] += 1
        
    def getAverageTime(self, startStation, endStation):
        return self.route[startStation, endStation]/self.freqs[startStation, endStation]

time complexity: $O(1)$ for all operation
space complexity: $O(Q)$, Q is total number of queries
reference:
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