# 1396. Design Underground System

## 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:

Input
["UndergroundSystem","checkIn","checkIn","checkIn","checkOut","checkOut","checkOut","getAverageTime","getAverageTime","checkIn","getAverageTime","checkOut","getAverageTime"]

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(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


Example 2:

Input
["UndergroundSystem","checkIn","checkOut","getAverageTime","checkIn","checkOut","getAverageTime","checkIn","checkOut","getAverageTime"]

Output
[null,null,null,5.00000,null,null,5.50000,null,null,6.66667]

Explanation
UndergroundSystem undergroundSystem = new UndergroundSystem();
undergroundSystem.checkIn(10, "Leyton", 3);
undergroundSystem.checkOut(10, "Paradise", 8); // Customer 10 "Leyton" -> "Paradise" in 8-3 = 5
undergroundSystem.getAverageTime("Leyton", "Paradise"); // return 5.00000, (5) / 1 = 5
undergroundSystem.checkIn(5, "Leyton", 10);
undergroundSystem.checkOut(5, "Paradise", 16); // Customer 5 "Leyton" -> "Paradise" in 16-10 = 6
undergroundSystem.getAverageTime("Leyton", "Paradise"); // return 5.50000, (5 + 6) / 2 = 5.5
undergroundSystem.checkIn(2, "Leyton", 21);
undergroundSystem.checkOut(2, "Paradise", 30); // Customer 2 "Leyton" -> "Paradise" in 30-21 = 9
undergroundSystem.getAverageTime("Leyton", "Paradise"); // return 6.66667, (5 + 6 + 9) / 3 = 6.66667


Constraints:

• 1 <= id, t <= 106
• 1 <= stationName.length, startStation.length, endStation.length <= 10
• All strings consist of uppercase and lowercase English letters and digits.
• There will be at most 2 * 104 calls in total to checkIn, checkOut, and getAverageTime.
• Answers within 10-5 of the actual value will be accepted.

## Solutions

Solution 1: Hash Table

We use two hash tables to store data:

• ts: Stores the passenger’s id, check-in time, and check-in station. The key is the passenger’s id, and the value is a tuple (t, stationName).
• d: Stores the passenger’s check-in station, check-out station, travel time, and number of trips. The key is a tuple (startStation, endStation), and the value is a tuple (totalTime, count).

When a passenger checks in, we store the passenger’s id, check-in time, and check-in station in ts, i.e., ts[id] = (t, stationName).

When a passenger checks out, we retrieve the passenger’s check-in time and station (t0, station) from ts, then calculate the passenger’s travel time $t - t_0$, and store the passenger’s travel time and number of trips in d.

When we want to calculate a passenger’s average travel time, we retrieve the passenger’s total travel time and number of trips (totalTime, count) from d, then calculate the average travel time as $totalTime / count$.

The time complexity is $O(1)$, and the space complexity is $O(n)$. Where $n$ is the number of passengers.

• class UndergroundSystem {
private Map<Integer, Integer> ts = new HashMap<>();
private Map<Integer, String> names = new HashMap<>();
private Map<String, int[]> d = new HashMap<>();

public UndergroundSystem() {
}

public void checkIn(int id, String stationName, int t) {
ts.put(id, t);
names.put(id, stationName);
}

public void checkOut(int id, String stationName, int t) {
String key = names.get(id) + "-" + stationName;
int[] v = d.getOrDefault(key, new int[2]);
v[0] += t - ts.get(id);
v[1]++;
d.put(key, v);
}

public double getAverageTime(String startStation, String endStation) {
String key = startStation + "-" + endStation;
int[] v = d.get(key);
return (double) v[0] / v[1];
}
}

/**
* Your UndergroundSystem object will be instantiated and called as such:
* UndergroundSystem obj = new UndergroundSystem();
* obj.checkIn(id,stationName,t);
* obj.checkOut(id,stationName,t);
* double param_3 = obj.getAverageTime(startStation,endStation);
*/

• class UndergroundSystem {
public:
UndergroundSystem() {
}

void checkIn(int id, string stationName, int t) {
ts[id] = {stationName, t};
}

void checkOut(int id, string stationName, int t) {
auto [station, t0] = ts[id];
auto key = station + "-" + stationName;
auto [tot, cnt] = d[key];
d[key] = {tot + t - t0, cnt + 1};
}

double getAverageTime(string startStation, string endStation) {
auto [tot, cnt] = d[startStation + "-" + endStation];
return (double) tot / cnt;
}

private:
unordered_map<int, pair<string, int>> ts;
unordered_map<string, pair<int, int>> d;
};

/**
* Your UndergroundSystem object will be instantiated and called as such:
* UndergroundSystem* obj = new UndergroundSystem();
* obj->checkIn(id,stationName,t);
* obj->checkOut(id,stationName,t);
* double param_3 = obj->getAverageTime(startStation,endStation);
*/

• class UndergroundSystem:
def __init__(self):
self.ts = {}
self.d = {}

def checkIn(self, id: int, stationName: str, t: int) -> None:
self.ts[id] = (t, stationName)

def checkOut(self, id: int, stationName: str, t: int) -> None:
t0, station = self.ts[id]
x = self.d.get((station, stationName), (0, 0))

# (startStation, endStation) => (totalTime, count)
# add up on all history data for start/end station
self.d[(station, stationName)] = (x[0] + t - t0, x[1] + 1)

def getAverageTime(self, startStation: str, endStation: str) -> float:
x = self.d[(startStation, endStation)]
return x[0] / x[1]

# Your UndergroundSystem object will be instantiated and called as such:
# obj = UndergroundSystem()
# obj.checkIn(id,stationName,t)
# obj.checkOut(id,stationName,t)
# param_3 = obj.getAverageTime(startStation,endStation)


• type UndergroundSystem struct {
ts map[int]pair
d  map[station][2]int
}

func Constructor() UndergroundSystem {
return UndergroundSystem{
ts: make(map[int]pair),
d:  make(map[station][2]int),
}
}

func (this *UndergroundSystem) CheckIn(id int, stationName string, t int) {
this.ts[id] = pair{t, stationName}
}

func (this *UndergroundSystem) CheckOut(id int, stationName string, t int) {
p := this.ts[id]
s := station{p.a, stationName}
if _, ok := this.d[s]; !ok {
this.d[s] = [2]int{t - p.t, 1}
} else {
this.d[s] = [2]int{this.d[s][0] + t - p.t, this.d[s][1] + 1}
}

}

func (this *UndergroundSystem) GetAverageTime(startStation string, endStation string) float64 {
s := station{startStation, endStation}
return float64(this.d[s][0]) / float64(this.d[s][1])
}

type station struct {
a string
b string
}

type pair struct {
t int
a string
}

/**
* Your UndergroundSystem object will be instantiated and called as such:
* obj := Constructor();
* obj.CheckIn(id,stationName,t);
* obj.CheckOut(id,stationName,t);
* param_3 := obj.GetAverageTime(startStation,endStation);
*/