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ambitious

Find the longest path in a weighted graph in which the weights are ascending.

Programming language:
Spoken language:

You are visiting the Royal Botanical Gardens. In the gardens there are N intersections connected by M roads. The intersections are numbered from 0 to N − 1. Each road connects two intersections and has an *attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

You are given a map of the gardens in the form of integer N and three arrays A, B and C. Each of the arrays contains M integers.

- For each I (0 ≤ I < M) there is a road between intersections A[I] and B[I] with an attractiveness level of C[I].
- There can be multiple roads connecting the same pair of intersections, or a road with both ends entering the same intersection.
- It is possible for roads to go through tunnels or over bridges (that is, the graph of intersections and roads doesn't have to be planar).

You want to find a walk in the gardens which will be as long as possible. You may start and finish at any intersections, and you may visit an intersection more than once during the walk. However, the walk must be *ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

int solution(int N, int A[], int B[], int C[], int M);

that, given an integer N and arrays A, B and C of M integers, returns the maximal number of roads that can be visited during an ascending walk in the gardens.

For example, given N = 6 and the following arrays:

the function should return 4. The longest ascending walk visits intersections 3, 1, 2, 3 and 4 (in that order). The attractiveness levels of the visited roads are 2, 3, 5 and 6, respectively.

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));
- expected worst-case space complexity is O(N+M) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

You are visiting the Royal Botanical Gardens. In the gardens there are N intersections connected by M roads. The intersections are numbered from 0 to N − 1. Each road connects two intersections and has an *attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

You are given a map of the gardens in the form of integer N and three arrays A, B and C. Each of the arrays contains M integers.

- For each I (0 ≤ I < M) there is a road between intersections A[I] and B[I] with an attractiveness level of C[I].
- There can be multiple roads connecting the same pair of intersections, or a road with both ends entering the same intersection.
- It is possible for roads to go through tunnels or over bridges (that is, the graph of intersections and roads doesn't have to be planar).

You want to find a walk in the gardens which will be as long as possible. You may start and finish at any intersections, and you may visit an intersection more than once during the walk. However, the walk must be *ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

int solution(int N, vector<int> &A, vector<int> &B, vector<int> &C);

that, given an integer N and arrays A, B and C of M integers, returns the maximal number of roads that can be visited during an ascending walk in the gardens.

For example, given N = 6 and the following arrays:

the function should return 4. The longest ascending walk visits intersections 3, 1, 2, 3 and 4 (in that order). The attractiveness levels of the visited roads are 2, 3, 5 and 6, respectively.

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));
- expected worst-case space complexity is O(N+M) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

You are visiting the Royal Botanical Gardens. In the gardens there are N intersections connected by M roads. The intersections are numbered from 0 to N − 1. Each road connects two intersections and has an *attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

You are given a map of the gardens in the form of integer N and three arrays A, B and C. Each of the arrays contains M integers.

- For each I (0 ≤ I < M) there is a road between intersections A[I] and B[I] with an attractiveness level of C[I].
- There can be multiple roads connecting the same pair of intersections, or a road with both ends entering the same intersection.
- It is possible for roads to go through tunnels or over bridges (that is, the graph of intersections and roads doesn't have to be planar).

You want to find a walk in the gardens which will be as long as possible. You may start and finish at any intersections, and you may visit an intersection more than once during the walk. However, the walk must be *ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

class Solution { public int solution(int N, int[] A, int[] B, int[] C); }

that, given an integer N and arrays A, B and C of M integers, returns the maximal number of roads that can be visited during an ascending walk in the gardens.

For example, given N = 6 and the following arrays:

the function should return 4. The longest ascending walk visits intersections 3, 1, 2, 3 and 4 (in that order). The attractiveness levels of the visited roads are 2, 3, 5 and 6, respectively.

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));
- expected worst-case space complexity is O(N+M) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

func Solution(N int, A []int, B []int, C []int) int

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

class Solution { public int solution(int N, int[] A, int[] B, int[] C); }

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

function solution(N, A, B, C);

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

function solution(N, A, B, C)

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

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.

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

int solution(int N, NSMutableArray *A, NSMutableArray *B, NSMutableArray *C);

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

function solution(N: longint; A: array of longint; B: array of longint; C: array of longint; M: longint): longint;

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

function solution($N, $A, $B, $C);

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

sub solution { my ($N, $A, $B, $C)=@_; my @A=@$A; my @B=@$B; my @C=@$C; ... }

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

def solution(N, A, B, C)

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

def solution(n, a, b, c)

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

object Solution { def solution(n: Int, a: Array[Int], b: Array[Int], c: Array[Int]): Int }

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

public func solution(N : Int, inout _ A : [Int], inout _ B : [Int], inout _ C : [Int]) -> Int

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

public func solution(_ N : Int, _ A : inout [Int], _ B : inout [Int], _ C : inout [Int]) -> Int

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

*attractiveness level*, which denotes how beautiful the plants along it are considered to be. The attractiveness level is a positive integer; the greater the better.

*ascending*: that is, the attractiveness level of each visited road must be greater than that of the previously visited road.

Write a function:

Private Function solution(N As Integer, A As Integer(), B As Integer(), C As Integer()) As Integer

For example, given N = 6 and the following arrays:

Assume that:

- N is an integer within the range [1..200,000];
- M is an integer within the range [0..200,000];
- each element of arrays A, B is an integer within the range [0..N−1];
- each element of array C is an integer within the range [1..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N+M*log(M));

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