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AVAILABLE LESSONS:

Lesson 1

Iterations

Lesson 2

Arrays

Lesson 3

Time Complexity

Lesson 4

Counting Elements

Lesson 5

Prefix Sums

Lesson 6

Sorting

Lesson 7

Stacks and Queues

Lesson 8

Leader

Lesson 9

Maximum slice problem

Lesson 10

Prime and composite numbers

Lesson 11

Sieve of Eratosthenes

Lesson 12

Euclidean algorithm

Lesson 13

Fibonacci numbers

Lesson 14

Binary search algorithm

Lesson 15

Caterpillar method

Lesson 16

Greedy algorithms

Lesson 17

Dynamic programming

Lesson 99

Future training

Check whether two numbers have the same prime divisors.

Spoken language:

A *prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

A prime D is called a *prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

You are given two positive integers N and M. The goal is to check whether the sets of prime divisors of integers N and M are exactly the same.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

int solution(int A[], int B[], int Z);

that, given two non-empty arrays A and B of Z integers, returns the number of positions K for which the prime divisors of A[K] and B[K] are exactly the same.

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

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

A *prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

A prime D is called a *prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

You are given two positive integers N and M. The goal is to check whether the sets of prime divisors of integers N and M are exactly the same.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

that, given two non-empty arrays A and B of Z integers, returns the number of positions K for which the prime divisors of A[K] and B[K] are exactly the same.

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

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

A *prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

A prime D is called a *prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

You are given two positive integers N and M. The goal is to check whether the sets of prime divisors of integers N and M are exactly the same.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

that, given two non-empty arrays A and B of Z integers, returns the number of positions K for which the prime divisors of A[K] and B[K] are exactly the same.

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

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

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

int solution(List<int> A, List<int> B);

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

function solution(A, B);

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

fun solution(A: IntArray, B: IntArray): Int

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

function solution(A, B)

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

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.

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

function solution(A: array of longint; B: array of longint; Z: longint): longint;

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

function solution($A, $B);

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

def solution(A, B)

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

def solution(a, b)

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

function solution(A: number[], B: number[]): number;

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].

*prime* is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.

*prime divisor* of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.

For example, given:

- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.

Write a function:

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

For example, given:

the function should return 1, because only one pair (15, 75) has the same set of prime divisors.

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

- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].