Test results - Codility

Tasks Details

medium

1. CountSemiprimes

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

Task Score

100%

Correctness

100%

Performance

100%

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:

P[0] = 1 Q[0] = 26 P[1] = 4 Q[1] = 10 P[2] = 16 Q[2] = 20

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)

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:

P[0] = 1 Q[0] = 26 P[1] = 4 Q[1] = 10 P[2] = 16 Q[2] = 20

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].

Solution

Programming language used Python

Time spent on task 8 minutes

Notes

not defined yet

Task timeline

Code: 14:08:37 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int[] solution(int N, int[] P, int[] Q) {
        // write your code in Java SE 8
    }
}

Code: 14:08:48 UTC, py, autosave

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# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")

def solution(N, P, Q):
    # write your code in Python 3.6
    pass

Code: 14:08:58 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    for (start, end) in zip(P, Q):
        count = 0 
        for idx in range(start, end + 1):
            if semi_prime[idx]:
                count += 1 
        answer.append(count)
    
    #print(answer)
    return answer

Code: 14:09:12 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []




    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:09:42 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_


    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:10:13 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]
    


    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:10:29 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate()
    


    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:10:49 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num
    


    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:11:15 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            count += 1 
        semi_prime_count[i] =
    


    for (start, end) in zip(P, Q):
        count = 0 
    
    #print(answer)
    return answer

Code: 14:11:41 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    

    for (start, end) in zip(P, Q):
        answer.append()
    
    #print(answer)
    return answer

Code: 14:11:56 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    

    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end])
    
    #print(answer)
    return answer

Code: 14:12:08 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    

    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start])
    
    #print(answer)
    return answer

Code: 14:12:09 UTC, py, verify, result: Failed

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    

    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start])
    
    #print(answer)
    return answer

Analysis

expand all Example tests

▶

example
example test

✘

WRONG ANSWER
got [10, 3, 0] expected [10, 4, 0]

0.036 s

WRONG ANSWER, got [10, 3, 0] expected [10, 4, 0]

Code: 14:12:38 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start])
    
    #print(answer)
    return answer

Code: 14:12:41 UTC, py, verify, result: Failed

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start])
    
    #print(answer)
    return answer

Analysis

expand all Example tests

▶

example
example test

✘

WRONG ANSWER
got [10, 3, 0] expected [10, 4, 0]

0.036 s

WRONG ANSWER, got [10, 3, 0] expected [10, 4, 0]

stdout:

[0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10]

Code: 14:15:53 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start -])
    
    #print(answer)
    return answer

Code: 14:15:55 UTC, py, verify, result: Passed

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start - 1])
    
    #print(answer)
    return answer

Analysis

expand all Example tests

▶

example
example test

✔

0.036 s

stdout:

[0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10]

Code: 14:16:05 UTC, py, autosave

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    #print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start - 1])
    
    #print(answer)
    return answer

Code: 14:16:09 UTC, py, verify, result: Passed

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    #print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start - 1])
    
    #print(answer)
    return answer

Analysis

expand all Example tests

▶

example
example test

✔

0.044 s

Code: 14:16:12 UTC, py, final, score: 100

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def solution(N, P, Q):

    sieve = [1 for _ in range(N + 1)]
    sieve[0]=sieve[1] = 0

    i = 0 
    while i * i <= N:
        if sieve[i]:
            k = i * i
            while k <= N:
                sieve[k] = 0 
                k += i
        i+= 1

    prime = []

    for i, is_prime in enumerate(sieve):
        if is_prime:
            prime.append(i)
    
    #print(prime)

    semi_prime = [0 for _ in range(N + 1)]

    for num in prime:
        for next_num in prime:
            if num * next_num > N:
                break 
            else:
                #print(num * next_num)
                semi_prime[num * next_num] = 1 
    #print(semi_prime)

    answer = []

    semi_count = 0 
    semi_prime_count = [0 for _ in range(N + 1)]

    for i, num in enumerate(semi_prime):
        if num:
            semi_count += 1 
        semi_prime_count[i] = semi_count
    
    #print(semi_prime_count)
    for (start, end) in zip(P, Q):
        answer.append(semi_prime_count[end] - semi_prime_count[start - 1])
    
    #print(answer)
    return answer

Analysis summary

The solution obtained perfect score.

Analysis

Detected time complexity:

O(N * log(log(N)) + M)

expand all Example tests

▶

example
example test

✔

0.040 s

expand all Correctness tests

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extreme_one
small N = 1

✔

0.036 s

▶

extreme_four
small N = 4

✔

0.036 s

▶

small_functional
small functional

✔

0.040 s

▶

small_random
small random, length = ~40

✔

0.036 s

expand all Performance tests

▶

medium_random
small random, length = ~300

✔

0.036 s

▶

large_small_slices
large with very small slices, length = ~30,000

✔

0.140 s

▶

large_random1
large random, length = ~30,000

✔

0.152 s

▶

large_random2
large random, length = ~30,000

✔

0.152 s

▶

extreme_large
all max ranges

✔

0.156 s