HackerRank Algebra – Count Solutions

Challenge: Count Solutions

Subdomeniu: Algebra (algebra)

Scor cont: 40.0 / 40

Submission status: Accepted

Submission score: 1.0

Submission ID: 464740537

Limbaj: python3

Link challenge: https://www.hackerrank.com/challenges/count-solutions/problem

Cerinta

Eric has four integers $a$, $b$, $c$, and $d$. 

Instantly, he wondered how many pairs of _integers_, $(x, y)$, satisfy the following equation:

$$x^2 + y^2 = (x \times a) + (y \times b)$$

where $1 \le x \le c$ and $1 \le y \le d$. 

Find and print the number of pairs that satisfy the above equation.

Input Format

The first line contains an integer $q$, the number of queries.  
$q$ lines follow, each containing four integers, $a$, $b$, $c$, and $d$, in that order.

Output Format

For each test case, print one line, the number of pairs $(x,y)$ that are valid solutions to Eric's equation.

Constraints

+ $1 \le q \le 10$  
+ $1 \le a,b,c,d \le 10^5$

Cod sursa

import sys
import math

def count_query(a, b, c, d):
    ans = 0
    b2 = b * b
    for x in range(1, c + 1):
        disc = b2 + 4 * x * (a - x)
        if disc < 0:
            continue
        s = math.isqrt(disc)
        if s * s != disc:
            continue
        # y = (b ± s) / 2
        if (b + s) % 2 == 0:
            y1 = (b + s) // 2
            if 1 <= y1 <= d:
                ans += 1
        if s != 0 and (b - s) % 2 == 0:
            y2 = (b - s) // 2
            if 1 <= y2 <= d:
                ans += 1
    return ans

def main():
    data = sys.stdin.buffer.read().split()
    if not data:
        return
    q = int(data[0])
    out = []
    idx = 1
    for _ in range(q):
        a = int(data[idx]); b = int(data[idx + 1]); c = int(data[idx + 2]); d = int(data[idx + 3]); idx += 4
        out.append(str(count_query(a, b, c, d)))
    sys.stdout.write('\n'.join(out))

if __name__ == '__main__':
    main()