Soluție HackerRank pentru Count Solutions, subdomeniul Algebra, în Python 3. Include cerința formatată, exemple, explicația pașilor și cod sursă.
- Problemă: Count Solutions
- Domeniu: Algebra
- Limbaj: Python 3
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
Cerință
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 × a) + (y × b)
where 1 ≤ x ≤ c and 1 ≤ y ≤ 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 ≤ q ≤ 10
+ 1 ≤ a,b,c,d ≤ 10^5
Cod sursă
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()