Soluție HackerRank pentru Simple One, subdomeniul Algebra, în Python 3. Include cerința formatată, exemple, explicația pașilor și cod sursă.
- Problemă: Simple One
- Domeniu: Algebra
- Limbaj: Python 3
Challenge: Simple One
Subdomeniu: Algebra (algebra)
Scor cont: 30.0 / 30
Submission status: Accepted
Submission score: 1.0
Submission ID: 464727326
Limbaj: python3
Link challenge: https://www.hackerrank.com/challenges/simple-one/problem
Cerință
You are given the equation tanalpha = (p / q) and a positive integer, n. Calculate tan nalpha. There are T test cases.
Input Format
The first line contains T, the number of test cases.
The next T lines contain three space separated integers: p, q and n, respectively.
Constraints
0 ≤ p ≤ 10^9
1 ≤ q ≤ 10^9
1 ≤ n ≤ 10^9
T ≤ 10^4
Output Format
If the result is defined, it is always a rational number. However, it can be very big.
Output the answer modulo (10^9 + 7).
If the answer is (a / b) and b is not divisible by (10^9+7), there is a unique integer 0 ≤ x < 10^9 + 7 where a equiv bx mod (10^9 + 7).
Output this integer, x.
It is guaranteed that b is not divisible by (10^9 + 7) for all test cases.
Cod sursă
M = 1000000007
def power(x, y):
x %= M
ans = 1
while y > 0:
if y & 1 == 1:
ans = ans*x % M
x = x*x % M
y >>= 1
return(ans)
def tan(b, n):
if n == 1:
return b
if n % 2 == 0:
a = tan(b, n//2)
return(2*a % M*power((1-a**2 % M+M) % M, M-2) % M)
else:
a = tan(b, n-1)
soorat = (a+b) % M
makhraj = (1-a*b % M+M) % M
return(soorat*power(makhraj, M-2) % M)
def solve(p, q, n):
return(tan(p*power(q, M-2) % M, n))
for _ in range(int(input())):
p, q, n = map(int, input().split())
print(solve(p, q, n))