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December 2010

PrefixSet edition (2010-10)

Plan trips to destination cities so as to visit a maximal number of other unvisited cities en route.

Spoken language:

A country network consisting of N cities and N − 1 roads connecting them is given. Cities are labeled with distinct integers within the range [0..(N − 1)]. Roads connect cities in such a way that each distinct pair of cities is connected either by a direct road or through a path consisting of direct roads. There is exactly one way to reach any city from any other city.

Starting out from city K, you have to plan a series of daily trips. Each day you want to visit a previously unvisited city in such a way that, on a route to that city, you will also pass through a maximal number of other unvisited cities (which will then be considered to have been visited). We say that the destination city is our daily travel target.

In the case of a tie, you should choose the city with the minimal label. The trips cease when every city has been visited at least once.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

The goal is to find the sequence of travel targets. In the above example we have the following travel targets: (2, 0, 6, 3, 5).

Assume that the following declarations are given:

struct Results { int * D; int X; // Length of the array };

Write a function:

struct Results solution(int K, int T[], int N);

that, given a non-empty array T consisting of N integers describing a network of N cities and N − 1 roads, returns the sequence of travel targets.

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

For example, given the following array T consisting of seven elements (this array describes the network shown above) and K = 2:

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A country network consisting of N cities and N − 1 roads connecting them is given. Cities are labeled with distinct integers within the range [0..(N − 1)]. Roads connect cities in such a way that each distinct pair of cities is connected either by a direct road or through a path consisting of direct roads. There is exactly one way to reach any city from any other city.

Starting out from city K, you have to plan a series of daily trips. Each day you want to visit a previously unvisited city in such a way that, on a route to that city, you will also pass through a maximal number of other unvisited cities (which will then be considered to have been visited). We say that the destination city is our daily travel target.

In the case of a tie, you should choose the city with the minimal label. The trips cease when every city has been visited at least once.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

The goal is to find the sequence of travel targets. In the above example we have the following travel targets: (2, 0, 6, 3, 5).

Write a function:

vector<int> solution(int K, vector<int> &T);

that, given a non-empty array T consisting of N integers describing a network of N cities and N − 1 roads, returns the sequence of travel targets.

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

For example, given the following array T consisting of seven elements (this array describes the network shown above) and K = 2:

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A country network consisting of N cities and N − 1 roads connecting them is given. Cities are labeled with distinct integers within the range [0..(N − 1)]. Roads connect cities in such a way that each distinct pair of cities is connected either by a direct road or through a path consisting of direct roads. There is exactly one way to reach any city from any other city.

Starting out from city K, you have to plan a series of daily trips. Each day you want to visit a previously unvisited city in such a way that, on a route to that city, you will also pass through a maximal number of other unvisited cities (which will then be considered to have been visited). We say that the destination city is our daily travel target.

In the case of a tie, you should choose the city with the minimal label. The trips cease when every city has been visited at least once.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

The goal is to find the sequence of travel targets. In the above example we have the following travel targets: (2, 0, 6, 3, 5).

Write a function:

vector<int> solution(int K, vector<int> &T);

that, given a non-empty array T consisting of N integers describing a network of N cities and N − 1 roads, returns the sequence of travel targets.

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

For example, given the following array T consisting of seven elements (this array describes the network shown above) and K = 2:

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

class Solution { public int[] solution(int K, int[] T); }

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

List<int> solution(int K, List<int> T);

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

func Solution(K int, T []int) []int

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

class Solution { public int[] solution(int K, int[] T); }

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

class Solution { public int[] solution(int K, int[] T); }

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

function solution(K, T);

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

fun solution(K: Int, T: IntArray): IntArray

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

function solution(K, T)

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

NSMutableArray * solution(int K, NSMutableArray *T);

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Assume that the following declarations are given:

Results = record D : array of longint; X : longint; {Length of the array} end;

Write a function:

function solution(K: longint; T: array of longint; N: longint): Results;

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

function solution($K, $T);

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

sub solution { my ($K, @T) = @_; ... }

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

def solution(K, T)

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

def solution(k, t)

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

object Solution { def solution(k: Int, t: Array[Int]): Array[Int] }

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

public func solution(_ K : Int, _ T : inout [Int]) -> [Int]

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

function solution(K: number, T: number[]): number[];

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.

For example, consider K = 2 and the following network consisting of seven cities and six roads:

You start in city 2. From here you make the following trips:

- day 1 − from city 2 to city 0 (cities 1 and 0 become visited),
- day 2 − from city 0 to city 6 (cities 4 and 6 become visited),
- day 3 − from city 6 to city 3 (city 3 becomes visited),
- day 4 − from city 3 to city 5 (city 5 becomes visited).

Write a function:

Private Function solution(K As Integer, T As Integer()) As Integer()

Array T describes a network of cities as follows:

- if T[P] = Q and P ≠ Q, then there is a direct road between cities P and Q.

the function should return a sequence [2, 0, 6, 3, 5], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..90,000];
- each element of array T is an integer within the range [0..(N−1)];
- there is exactly one (possibly indirect) connection between any two distinct roads.