# Minimal operations to make a number magical

Last Updated : 31 Jul, 2022

Given a 6 digit number, calculate the minimum number of digits that needs to be replaced in order to make the number magical. The number is considered magical if the sum of first three digits equals to the sum of last three digits. In one operation, we can choose a digit at any position and replace it with any arbitrary digit.

Examples :

```Input: 123456
Output: 2
Explanation : Replace 4 with 0 and 5 with 0,
then number = 123006, where
1 + 2 + 3 = 0 + 0 + 6,
hence number of replacements
done = 2

Input: 111000
Output: 1
Explanation: Replace 0 with 3, then
number = 111030, where
1 + 1 + 1 = 0 + 3 + 0,
hence number of replacements
done = 1```

Approach: The best approach will be to check with all the magical numbers and the number of replacements needed. Run a loop that generates all 6 digit numbers. Check if that number is magical, if it is then simply calculate the number of replacements needs to be done and compare with the ans, if it is smaller then make it the ans and at the end return ans.

Below is the implementation of the above approach.

## C++

 `// CPP program to make a number magical` `#include "bits/stdc++.h"` `using` `namespace` `std;`   `// function to calculate the minimal changes` `int` `calculate(string s)` `{` `    ``// maximum digits that can be changed` `    ``int` `ans = 6;`   `    ``// nested loops to generate all 6 ` `    ``// digit numbers` `    ``for` `(``int` `i = 0; i < 10; ++i) {` `        ``for` `(``int` `j = 0; j < 10; ++j) {` `            ``for` `(``int` `k = 0; k < 10; ++k) {` `                ``for` `(``int` `l = 0; l < 10; ++l) {` `                    ``for` `(``int` `m = 0; m < 10; ++m) {` `                        ``for` `(``int` `n = 0; n < 10; ++n) {` `                            ``if` `(i + j + k == l + m + n) {` `                                `  `                                ``// counter to count the number` `                                ``// of change required` `                                ``int` `c = 0;` `                                `  `                                ``// if first digit is equal` `                                ``if` `(i != s[0] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 2nd digit is equal    ` `                                ``if` `(j != s[1] - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 3rd digit is equal    ` `                                ``if` `(k != s[2] - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 4th digit is equal    ` `                                ``if` `(l != s[3] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 5th digit is equal    ` `                                ``if` `(m != s[4] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 6th digit is equal    ` `                                ``if` `(n != s[5] - ``'0'``) ` `                                    ``c++;`   `                                ``// checks if less than the` `                                ``// previous calculate changes` `                                ``if` `(c < ans)` `                                    ``ans = c;` `                            ``}` `                        ``}` `                    ``}` `                ``}` `            ``}` `        ``}` `    ``}` `    `  `    ``// returns the answer` `    ``return` `ans;` `}`   `// driver program to test the above function` `int` `main()` `{` `    ``// number stored in string` `    ``string s = ``"123456"``;`   `    ``// prints the minimum operations` `    ``cout << calculate(s);` `}`

## Java

 `// java program to make a number magical` `import` `java.io.*;` ` `  `class` `GFG {`   `// function to calculate the minimal changes` `static` `int` `calculate(String s)` `{` `    ``// maximum digits that can be changed` `    ``int` `ans = ``6``;`   `    ``// nested loops to generate ` `    ``// all 6 digit numbers` `    ``for` `(``int` `i = ``0``; i < ``10``; ++i) {` `        ``for` `(``int` `j = ``0``; j < ``10``; ++j) {` `            ``for` `(``int` `k = ``0``; k < ``10``; ++k) {` `                ``for` `(``int` `l = ``0``; l < ``10``; ++l) {` `                    ``for` `(``int` `m = ``0``; m < ``10``; ++m) {` `                        ``for` `(``int` `n = ``0``; n < ``10``; ++n) {` `                            ``if` `(i + j + k == l + m + n) {` `                                `  `                                ``// counter to count the number` `                                ``// of change required` `                                ``int` `c = ``0``;` `                                `  `                                ``// if first digit is equal` `                                ``if` `(i != s.charAt(``0``) - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 2nd digit is equal ` `                                ``if` `(j != s.charAt(``1``) - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 3rd digit is equal ` `                                ``if` `(k != s.charAt(``2``) - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 4th digit is equal ` `                                ``if` `(l != s.charAt(``3``) - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 5th digit is equal ` `                                ``if` `(m != s.charAt(``4``) - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 6th digit is equal ` `                                ``if` `(n != s.charAt(``5``) - ``'0'``) ` `                                    ``c++;`   `                                ``// checks if less than the` `                                ``// previous calculate changes` `                                ``if` `(c < ans)` `                                    ``ans = c;` `                            ``}` `                        ``}` `                    ``}` `                ``}` `            ``}` `        ``}` `    ``}` `    `  `    ``// returns the answer` `    ``return` `ans;` `}`   `   ``// Driver code` `    ``static` `public` `void` `main (String[] args)` `    ``{` `        ``// number stored in string` `        ``String s = ``"123456"``;`   `        ``// prints the minimum operations` `        ``System.out.println(calculate(s));` `    ``}` `}`   `// This code is contributed by vt_m.`

## Python3

 `# Python 3 program to make a number magical` ` `  `# function to calculate the minimal changes` `def` `calculate( s):`   `    ``# maximum digits that can be changed` `    ``ans ``=` `6` ` `  `    ``# nested loops to generate all 6 ` `    ``# digit numbers` `    ``for` `i ``in` `range``(``10``):` `        ``for` `j ``in` `range``(``10``):` `            ``for` `k ``in` `range``(``10``):` `                ``for` `l ``in` `range``(``10``):` `                    ``for`  `m ``in` `range``(``10``):` `                        ``for` `n ``in` `range``(``10``):` `                            ``if` `(i ``+` `j ``+` `k ``=``=` `l ``+` `m ``+` `n):` `                                 `  `                                ``# counter to count the number` `                                ``# of change required` `                                ``c ``=` `0` `                                 `  `                                ``# if first digit is equal` `                                ``if` `(i !``=` `ord``(s[``0``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` `                                     `  `                                ``# if 2nd digit is equal    ` `                                ``if` `(j !``=` `ord``(s[``1``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` `                                 `  `                                ``# if 3rd digit is equal    ` `                                ``if` `(k !``=` `ord``(s[``2``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` `                                 `  `                                ``# if 4th digit is equal    ` `                                ``if` `(l !``=` `ord``(s[``3``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` `                                     `  `                                ``# if 5th digit is equal    ` `                                ``if` `(m !``=` `ord``(s[``4``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` `                                     `  `                                ``# if 6th digit is equal    ` `                                ``if` `(n !``=` `ord``(s[``5``]) ``-` `ord``(``'0'``)): ` `                                    ``c``+``=``1` ` `  `                                ``# checks if less than the` `                                ``# previous calculate changes` `                                ``if` `(c < ans):` `                                    ``ans ``=` `c` `     `  `    ``# returns the answer` `    ``return` `ans` ` `  `# driver program to test the above function` `if` `__name__ ``=``=` `"__main__"``:` `    `  `    ``# number stored in string` `    ``s ``=` `"123456"` ` `  `    ``# prints the minimum operations` `    ``print``(calculate(s))`

## C#

 `// C# program to make a number magical` `using` `System;`   `class` `GFG {`   `// function to calculate the minimal changes` `static` `int` `calculate(``string` `s)` `{` `    ``// maximum digits that can be changed` `    ``int` `ans = 6;`   `    ``// nested loops to generate` `    ``// all 6 digit numbers` `    ``for` `(``int` `i = 0; i < 10; ++i) {` `        ``for` `(``int` `j = 0; j < 10; ++j) {` `            ``for` `(``int` `k = 0; k < 10; ++k) {` `                ``for` `(``int` `l = 0; l < 10; ++l) {` `                    ``for` `(``int` `m = 0; m < 10; ++m) {` `                        ``for` `(``int` `n = 0; n < 10; ++n) {` `                            ``if` `(i + j + k == l + m + n) {` `                                `  `                                ``// counter to count the number` `                                ``// of change required` `                                ``int` `c = 0;` `                                `  `                                ``// if first digit is equal` `                                ``if` `(i != s[0] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 2nd digit is equal ` `                                ``if` `(j != s[1] - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 3rd digit is equal ` `                                ``if` `(k != s[2] - ``'0'``) ` `                                    ``c++;` `                                `  `                                ``// if 4th digit is equal ` `                                ``if` `(l != s[3] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 5th digit is equal ` `                                ``if` `(m != s[4] - ``'0'``) ` `                                    ``c++;` `                                    `  `                                ``// if 6th digit is equal ` `                                ``if` `(n != s[5] - ``'0'``) ` `                                    ``c++;`   `                                ``// checks if less than the` `                                ``// previous calculate changes` `                                ``if` `(c < ans)` `                                    ``ans = c;` `                            ``}` `                        ``}` `                    ``}` `                ``}` `            ``}` `        ``}` `    ``}` `    `  `    ``// returns the answer` `    ``return` `ans;` `}`   `    ``// Driver code` `    ``static` `public` `void` `Main ()` `    ``{` `        ``// number stored in string` `        ``string` `s = ``"123456"``;`   `        ``// prints the minimum operations` `        ``Console.WriteLine(calculate(s));` `        `  `    ``}` `}`   `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output

`2`

Time complexity : O( 10^6)
Auxiliary Space : O(1)

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