Pair Cube Count Python

PROGRAM TO COUNT PAIRS (a, b) WHOSE SUM OF CUBES IS N (a^3+b^3 = N)




import math 

  

# Function to count the pairs 

# satisfying a ^ 3 + b ^ 3 = N

def countPairs(N):

  

    count = 0

  

    # Check for each number 1

    # to cbrt(N)

    for i in range(1, int(math.pow(N, 1/3) + 1)):

      

        # Store cube of a number

        cb = i * i * i

  

        # Subtract the cube from given N

        diff = N - cb

  

        # Check if the difference is also

        # a perfect cube

        cbrtDiff = int(math.pow(diff, 1/3))

  

        # If yes, then increment count

        if (cbrtDiff * cbrtDiff * cbrtDiff == diff):

            count += 1

      

    # Return count

    return count

  

  

# Driver program

  

# Loop to Count no. of pairs satisfying

# a ^ 3 + b ^ 3 = i for N = 1 to 10

for i in range(1, 11):

    print('For n = ', i, ', ', countPairs(i), ' pair exists')




OUTPUT

For n= 1, 1 pair exists
For n= 2, 1 pair exists
For n= 3, 0 pair exists
For n= 4, 0 pair exists
For n= 5, 0 pair exists
For n= 6, 0 pair exists
For n= 7, 0 pair exists
For n= 8, 1 pair exists
For n= 9, 2 pair exists
For n= 10, 0 pair exists

CREDITS: https://www.geeksforgeeks.org/count-pairs-a-b-whose-sum-of-cubes-is-n-a3-b3-n/