Python: Find the number of combinations

Last update on April 17 2025 13:05:39 (UTC/GMT +8 hours)

Sum Combination Counter

Write a Python program to find the number of combinations that satisfy p + q + r + s = n where n is a given number <= 4000 and p, q, r, s are between 0 to 1000.

Sample Solution:

Python Code:

# Import the Counter class from the collections module
from collections import Counter

# Print statement to instruct the user to input a positive integer (ctrl+d to exit)
print("Input a positive integer: (ctrl+d to exit)")

# Create a Counter object to store pairs of integers and their counts
pair_dict = Counter()

# Assign counts to pairs of integers based on their minimum and maximum values
for i in range(2001):
    pair_dict[i] = min(i, 2000 - i) + 1

# Continuous loop to read input until EOFError (ctrl+d) is encountered
while True:
    try:
        # Read a positive integer from the user
        n = int(input())
        
        # Initialize a variable to store the number of combinations
        ans = 0

        # Iterate over possible values of 'i' and calculate combinations
        for i in range(n + 1):
            ans += pair_dict[i] * pair_dict[n - i]
        
        # Print the number of combinations of a, b, c, d
        print("Number of combinations of a, b, c, d:", ans)

    # Break the loop when EOFError is encountered
    except EOFError:
        break

Sample Output:

Input a positive integer: (ctrl+d to exit)
 252
Number of combinations of a,b,c,d: 2731135

Explanation:

Here is a breakdown of the above Python code:

Import the Counter class from the "collections" module.
Print a statement instructing the user to input a positive integer (ctrl+d to exit).
Create a Counter object (pair_dict) to store pairs of integers and their counts.
Assign counts to pairs of integers based on their minimum and maximum values.
Enter a continuous loop to read input until EOFError (ctrl+d) is encountered.
Read a positive integer from the user.
Initialize a variable to store the number of combinations (ans).
Iterate over possible values of 'i' and calculate combinations.
Print the number of combinations of a, b, c, d.
Break the loop when EOFError is encountered.

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to count the number of quadruple combinations (p, q, r, s) that sum to a given number using nested loops.
Write a Python program to compute the number of solutions for p + q + r + s = n using a combinatorial approach.
Write a Python program to count the number of ways to partition an integer n into four non-negative parts using dynamic programming.
Write a Python program to iterate over a constrained range and count all quadruplets that satisfy the equation p + q + r + s = n.

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Python Code Editor:

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