C++ Exercises: Break a given integer in at least two parts to maximize the product of those integers

Last update on December 20 2024 12:30:29 (UTC/GMT +8 hours)

Write a C++ program to break a given integer into at least two parts (positive integers) to maximize the product of those integers.

Sample Input: n = 5
After breaking in +ve integers maximumn product from 5 = 6
Sample Input: n = 12
After breaking in +ve integers maximumn product from 12 = 81

Sample Solution:

C++ Code :

#include <iostream>
#include <cmath>

using namespace std;

// Function to find the maximum product after breaking the integer 'n' into positive integers and multiplying them
int integer_Break(int n) {
    // Base cases for 'n' equals 2 and 3
    if (n == 2) {
        return 1;
    } else if (n == 3) {
        return 2;
    }
    // Check if 'n' is divisible by 3
    else if (n % 3 == 0) {
        return (int)pow(3, n / 3); // Return the maximum product for 'n' divisible by 3
    }
    // Check if 'n' modulo 3 equals 1
    else if (n % 3 == 1) {
        return 2 * 2 * (int)pow(3, (n - 4) / 3); // Return the maximum product for 'n' modulo 3 equals 1
    } else {
        return 2 * (int)pow(3, n / 3); // Return the maximum product for other cases
    }
}

int main() {
    int n = 5;  // (3 + 2) -> 3 x 2 = 6
    cout << "\nAfter breaking into positive integers, the maximum product from " << n << " = " << integer_Break(n) << endl;
    n = 12;  // (3 + 3 + 3 + 3) -> 3 x 3 x 3 x 3 = 81
    cout << "\nAfter breaking into positive integers, the maximum product from " << n << " = " << integer_Break(n) << endl;
    n = 17; // (3 + 3 + 3 + 3 + 3 + 2) -> 3 x 3 x 3 x 3 x 3 x 2 = 486
    cout << "\nAfter breaking into positive integers, the maximum product from " << n << " = " << integer_Break(n) << endl;
    return 0;
}

Sample Output:

After breaking in +ve integers maximumn product from 5 = 6

After breaking in +ve integers maximumn product from 12 = 81

After breaking in +ve integers maximumn product from 17 = 486

Flowchart:

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