Syntax error Program to find number of solutions for given equations with four parameters in Python

Program to find number of solutions for given equations with four parameters in Python

Suppose we have four numbers a, b, c and d and We have to find number of pairs (x, y) can be found such that that follows the equation: x^2 + y^2 = (x*a) + (y*b) where x in range [1, c] and y in range [1, d]

So, if the input is like a = 2 b = 3 c = 2 d = 4, then the output will be 1 because one pair is (1, 1).

To solve this, we will follow these steps −

  • ans := 0
  • for x in range 1 to c, do
    • l := x*(x-a)
    • det2 := b*b - 4*l
    • if det2 is same as 0 and b is even and 1 <= floor of (b/2) <= d, then
      • ans := ans + 1
      • go for next iteration
    • if det2 > 0, then
      • det := integer part of the square root of det2
      • if det^2 is same as det2 and (b+det) is even, then
        • if 1 <= floor of (b+det)/2 <= d, then
          • ans := ans + 1
        • if 1 <= floor of (b-det)/2 <= d, then
          • ans := ans + 1
  • return ans

Example

Let us see the following implementation to get better understanding −

def solve(a, b, c, d):
   ans = 0
   for x in range(1,c+1):
      l = x*(x-a)

      det2 = b*b - 4*l
      if det2 == 0 and b%2 == 0 and 1 <= b//2 <= d:
         ans += 1
         continue
      if det2 > 0:
         det = int(round(det2**0.5))
         if det*det == det2 and (b+det) % 2 == 0:
            if 1 <= (b+det)//2 <= d:
               ans += 1
            if 1 <= (b-det)//2 <= d:
               ans += 1
   return ans

a = 2
b = 3
c = 2
d = 4
print(solve(a, b, c, d))

Input

2, 3, 2, 4

Output

1
Updated on: 2021-10-25T07:27:41+05:30

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