Python: Find the number of combinations

Last update on December 21 2024 07:19:37 (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:

Python Code Editor:

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