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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

Count the semiprime numbers in the given range [a..b]

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 *semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

You are given two non-empty arrays P and Q, each consisting of M integers. These arrays represent queries about the number of semiprimes within specified ranges.

Query K requires you to find the number of semiprimes within the range (P[K], Q[K]), where 1 ≤ P[K] ≤ Q[K] ≤ N.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Assume that the following declarations are given:

struct Results { int * A; int M; // Length of the array };

Write a function:

struct Results solution(int N, int P[], int Q[], int M);

that, given an integer N and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M elements specifying the consecutive answers to all the queries.

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

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 *semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

You are given two non-empty arrays P and Q, each consisting of M integers. These arrays represent queries about the number of semiprimes within specified ranges.

Query K requires you to find the number of semiprimes within the range (P[K], Q[K]), where 1 ≤ P[K] ≤ Q[K] ≤ N.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

vector<int> solution(int N, vector<int> &P, vector<int> &Q);

that, given an integer N and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M elements specifying the consecutive answers to all the queries.

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

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 *semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

You are given two non-empty arrays P and Q, each consisting of M integers. These arrays represent queries about the number of semiprimes within specified ranges.

Query K requires you to find the number of semiprimes within the range (P[K], Q[K]), where 1 ≤ P[K] ≤ Q[K] ≤ N.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

vector<int> solution(int N, vector<int> &P, vector<int> &Q);

that, given an integer N and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M elements specifying the consecutive answers to all the queries.

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

class Solution { public int[] solution(int N, int[] P, int[] Q); }

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

List<int> solution(int N, List<int> P, List<int> Q);

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

func Solution(N int, P []int, Q []int) []int

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

class Solution { public int[] solution(int N, int[] P, int[] Q); }

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

class Solution { public int[] solution(int N, int[] P, int[] Q); }

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

function solution(N, P, Q);

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

fun solution(N: Int, P: IntArray, Q: IntArray): IntArray

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

function solution(N, P, Q)

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

NSMutableArray * solution(int N, NSMutableArray *P, NSMutableArray *Q);

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Assume that the following declarations are given:

Results = record A : array of longint; M : longint; {Length of the array} end;

Write a function:

function solution(N: longint; P: array of longint; Q: array of longint; M: longint): Results;

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

function solution($N, $P, $Q);

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

sub solution { my ($N, $P, $Q) = @_; my @P = @$P; my @Q = @$Q; ... }

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

def solution(N, P, Q)

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

def solution(n, p, q)

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

object Solution { def solution(n: Int, p: Array[Int], q: Array[Int]): Array[Int] }

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

public func solution(_ N : Int, _ P : inout [Int], _ Q : inout [Int]) -> [Int]

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

function solution(N: number, P: number[], Q: number[]): number[];

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].

*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.

*semiprime* is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.

For example, consider an integer N = 26 and arrays P, Q such that:

The number of semiprimes within each of these ranges is as follows:

- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.

Write a function:

Private Function solution(N As Integer, P As Integer(), Q As Integer()) As Integer()

For example, given an integer N = 26 and arrays P, Q such that:

the function should return the values [10, 4, 0], as explained above.

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

- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P and Q is an integer within the range [1..N];
- P[i] ≤ Q[i].