Question

Maximum and minimum sums from two numbers with digit replacements

Answer 1

Maximum and minimum sums from two numbers with digit replacements

Given two positive numbers calculate the minimum and maximum possible sums of two numbers. We are allowed to replace digit 5 with digit 6 and vice versa in either or both the given numbers.

Examples:

Input : x1 = 645 x2 = 666 Output : Minimum Sum: 1100 (545 + 555) Maximum Sum: 1312 (646 + 666) Input: x1 = 5466 x2 = 4555 Output: Minimum sum: 10010 Maximum Sum: 11132

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.



Since both numbers are positive, we always get maximum sum if replace 5 with 6 in both numbers. And we get minimum sum if we replace 6 with 5 in both numbers. Below is C++ implementation based on this fact.

C++

// C++ program to find maximum and minimum

// possible sums of two numbers that we can

// get if replacing digit from 5 to 6 and vice

// versa are allowed.

#include<bits/stdc++.h>

using namespace std;

 

// Find new value of x after replacing digit

// "from" to "to"

int replaceDig(int x, int from, int to)

{

    int result = 0;

    int multiply = 1;

 

    while (x % 10 > 0)

    {

        int reminder = x % 10;

 

        // Required digit found, replace it

        if (reminder == from)

            result = result + to * multiply;

 

        else

            result = result + reminder * multiply;

 

        multiply *= 10;

        x = x / 10;

    }

    return result;

}

 

// Returns maximum and minimum possible sums of

// x1 and x2 if digit replacements are allowed.

void calculateMinMaxSum(int x1, int x2)

{

    // We always get minimum sum if we replace

    // 6 with 5.

    int minSum = replaceDig(x1, 6, 5) +

                 replaceDig(x2, 6, 5);

 

    // We always get maximum sum if we replace

    // 5 with 6.

    int maxSum = replaceDig(x1, 5, 6) +

                 replaceDig(x2, 5, 6);

    cout << "Minimum sum = " << minSum;

 cout << "nMaximum sum = " << maxSum;
}

 

// Driver code

int main()

{

    int x1 = 5466, x2 = 4555;

    calculateMinMaxSum(x1, x2);

    return 0;

}