Java: Find the number of combinations

Last update on April 01 2025 10:52:29 (UTC/GMT +8 hours)

Count Combinations Satisfying Sum of Variables

Write a Java 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 range from 0 to 1000.

Sample Solution:

Java Code:

// Importing the necessary Java utility package
import java.util.*;

// Main class named "Main"
public class Main {
   
    // Main method, the entry point of the program
    public static void main(String[] args) {
        
        // Creating a Scanner object to read input from the console
        Scanner sc = new Scanner(System.in);

        // Prompting the user to input a positive integer
        System.out.println("Input a positive integer:");

        // Initializing arrays to store temporary and final results
        int[] temp = new int[2001];
        int[] ans = new int[4001];

        // Nested loops to calculate combinations and populate the 'temp' array
        for (int i = 0; i <= 1000; i++) {
            for (int j = 0; j <= 1000; j++) {
                temp[i + j]++;
            }
        }

        // Nested loops to calculate combinations and populate the 'ans' array
        for (int i = 0; i <= 2000; i++) {
            for (int j = 0; j <= 2000; j++) {
                ans[i + j] += temp[i] * temp[j];
            }
        }

        // Reading a positive integer from the user
        int n = sc.nextInt();

        // Prompting the user with the result
        System.out.println("Number of combinations of a, b, c, d:");

        // Printing the final result
        System.out.println(ans[n]);
    }
} 

Sample Output:

Input a positive integer:
252
Number of combinations of a,b,c,d:
2731135

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Java program to count the number of quadruple combinations (p, q, r, s) that sum to n using recursion with memoization.
• Write a Java program to determine the number of combinations of four variables summing to n using iterative dynamic programming.
• Write a Java program to count combinations satisfying p + q + r + s = n where each variable is restricted to prime numbers.
• Write a Java program to enumerate all valid combinations (p, q, r, s) that satisfy the sum condition and output the total count.

Java Code Editor:

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