Minimum rotations to unlock a circular lock
Last Updated :
10 Aug, 2022
You are given a lock which is made up of n-different circular rings and each ring has 0-9 digit printed serially on it. Initially all n-rings together show a n-digit integer but there is particular code only which can open the lock. You can rotate each ring any number of time in either direction. You have to find the minimum number of rotation done on rings of lock to open the lock.
Examples:
Input : Input = 2345, Unlock code = 5432
Output : Rotations required = 8
Explanation : 1st ring is rotated thrice as 2->3->4->5
2nd ring is rotated once as 3->4
3rd ring is rotated once as 4->3
4th ring is rotated thrice as 5->4->3->2
Input : Input = 1919, Unlock code = 0000
Output : Rotations required = 4
Explanation : 1st ring is rotated once as 1->0
2nd ring is rotated once as 9->0
3rd ring is rotated once as 1->0
4th ring is rotated once as 9->0
For a single ring we can rotate it in any of two direction forward or backward as:
- 0->1->2….->9->0
- 9->8->….0->9
But we are concerned with minimum number of rotation required so we should choose min (abs(a-b), 10-abs(a-b)) as a-b denotes the number of forward rotation and 10-abs(a-b) denotes the number of backward rotation for a ring to rotate from a to b. Further we have to find minimum number for each ring that is for each digit. So starting from right most digit we can easily the find minimum number of rotation required for each ring and end up at left most digit.
C++
#include <bits/stdc++.h>
using namespace std;
int minRotation(int input, int unlock_code)
{
int rotation = 0;
int input_digit, code_digit;
while (input || unlock_code) {
input_digit = input % 10;
code_digit = unlock_code % 10;
rotation += min(abs(input_digit - code_digit),
10 - abs(input_digit - code_digit));
input /= 10;
unlock_code /= 10;
}
return rotation;
}
int main()
{
int input = 28756;
int unlock_code = 98234;
cout << "Minimum Rotation = "
<< minRotation(input, unlock_code);
return 0;
}
|
Java
class GFG
{
static int minRotation(int input, int unlock_code)
{
int rotation = 0;
int input_digit, code_digit;
while (input>0 || unlock_code>0) {
input_digit = input % 10;
code_digit = unlock_code % 10;
rotation += Math.min(Math.abs(input_digit
- code_digit), 10 - Math.abs(
input_digit - code_digit));
input /= 10;
unlock_code /= 10;
}
return rotation;
}
public static void main (String[] args) {
int input = 28756;
int unlock_code = 98234;
System.out.println("Minimum Rotation = "+
minRotation(input, unlock_code));
}
}
|
Python3
def minRotation(input, unlock_code):
rotation = 0;
while (input > 0 or unlock_code > 0):
input_digit = input % 10;
code_digit = unlock_code % 10;
rotation += min(abs(input_digit - code_digit),
10 - abs(input_digit - code_digit));
input = int(input / 10);
unlock_code = int(unlock_code / 10);
return rotation;
input = 28756;
unlock_code = 98234;
print("Minimum Rotation =",
minRotation(input, unlock_code));
|
C#
using System;
class GFG {
static int minRotation(int input,
int unlock_code)
{
int rotation = 0;
int input_digit, code_digit;
while (input > 0 ||
unlock_code > 0)
{
input_digit = input % 10;
code_digit = unlock_code % 10;
rotation += Math.Min(Math.Abs(input_digit -
code_digit), 10 - Math.Abs(
input_digit - code_digit));
input /= 10;
unlock_code /= 10;
}
return rotation;
}
public static void Main ()
{
int input = 28756;
int unlock_code = 98234;
Console.Write("Minimum Rotation = "+
minRotation(input, unlock_code));
}
}
|
PHP
<?php
function minRotation($input,
$unlock_code)
{
$rotation = 0;
$input_digit; $code_digit;
while ($input || $unlock_code)
{
$input_digit = $input % 10;
$code_digit = $unlock_code % 10;
$rotation += min(abs($input_digit - $code_digit),
10 - abs($input_digit - $code_digit));
$input /= 10;
$unlock_code /= 10;
}
return $rotation;
}
$input = 28756;
$unlock_code = 98234;
echo "Minimum Rotation = "
, minRotation($input, $unlock_code);
?>
|
Javascript
<script>
function minRotation(input, unlock_code)
{
let rotation = 0;
let input_digit, code_digit;
while (input>0 || unlock_code>0) {
input_digit = input % 10;
code_digit = unlock_code % 10;
rotation += Math.min(Math.abs(input_digit
- code_digit), 10 - Math.abs(
input_digit - code_digit));
input = Math.floor(input / 10);
unlock_code = Math.floor(unlock_code / 10);
}
return rotation;
}
let input = 28756;
let unlock_code = 98234;
document.write("Minimum Rotation = "+
minRotation(input, unlock_code));
</script>
|
Output:
Minimum Rotation = 12
Time Complexity: O(log(input))
Auxiliary Space: O(1)
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