C Exercises: Get the maximum product from a given integer after breaking the integer into the sum of at least two positive integers

Last update on August 07 2025 12:49:17 (UTC/GMT +8 hours)

15. Maximum Product After Integer Break Variants

Write a C program to get the maximum product of a given integer after breaking the integer into the sum of at least two positive integers.

Example:
Input: 12
Output: 81
Explanation: 12 = 3 + 3 + 3 + 3, 3 x 3 × 3 × 3 = 81.
Input: 7
Output: 12
Explanation: 7 = 3 + 2 + 2, 3 x 2 x 2 = 12.

Visual Presentation:

Sample Solution:

C Code:

#include <stdio.h> // Including standard input-output library
#include <math.h> // Including math library for pow function
#include <stdlib.h> // Including standard library for exit function

// Function to calculate the maximum product after breaking the integer
int integer_Break(int n) {
    if (n == 2) { // If n is equal to 2
        return 1; // Return 1 as maximum product
    } else if (n == 3) { // If n is equal to 3
        return 2; // Return 2 as maximum product
    } else if (n % 3 == 0) { // If n is divisible by 3
        return (int) pow(3, n / 3); // Calculate maximum product using pow function
    } else if (n % 3 == 1) { // If n leaves remainder 1 when divided by 3
        return 2 * 2 * (int) pow(3, (n - 4) / 3); // Calculate maximum product
    } else { // If n leaves remainder 2 when divided by 3
        return 2 * (int) pow(3, n / 3); // Calculate maximum product
    }
}

// Main function
int main(void)
{
    int n = 12; // Declare and initialize integer variable n with value 12
    printf("\nMaximum product of %d after breaking the integer %d ", n, integer_Break(n)); // Print the maximum product
    n = 7; // Assign value 7 to n
    printf("\nMaximum product of %d after breaking the integer %d ", n, integer_Break(n)); // Print the maximum product
    return 0; // Return 0 to indicate successful termination
}

Sample Output:

Maximum product of 12 after breaking the integer 81 
Maximum product of 7 after breaking the integer 12 

Flowchart:

For more Practice: Solve these Related Problems:

• Write a C program to break an integer into at least two parts such that the product of the parts is maximized, using recursion.
• Write a C program to compute the maximum product after integer break by applying dynamic programming.
• Write a C program to compare the product obtained by greedy splitting versus optimal splitting for an integer.
• Write a C program to calculate the maximum product with a memoized solution and display intermediate splits.

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