Minimize steps to make given two number equal by adding LSB
Given two even numbers A, and B, the task is to find the minimum number of operations required to make both numbers equal if it is possible else print -1. In a single operation, the last digit of either number A or B can be added to itself i.e.,
- Either A = (A + (A % 10))
- or B = (B + (B % 10))
Input: A = 4, B = 12
Explanation: We can not make 4 and 12 equal so answer is -1.
Input: A = 2 , B = 8
Explanation: 2 -> 4 -> 8, so minimum 2 steps is required to make them equal.
Input: A = 6, B = 12 .
Explanation: 6 + 6 = 12 and 12 so by 1 step we can make elements equal.
Approach: To solve the problem follow the below observation:
- There is an observation that if last digit is 0 then we can not increase that number . So if last digit of the either number is 0 then the numbers should be equal else answer is -1 .
- The last digit of the even numbers contain 2, 4, 6, 8 . We will see the change if last digit is added 2->4->8->6->2 ->4->8->6->2 . . .
- So the pattern is repeating and in every cycle the increase in the number is 2+4+8+6=20 .
- Now if two number will be equal then last digit of the numbers must be equal .
- Now we can make last digit of the two numbers either equal to 2 or 4 or 6 or 8 and check if the difference between two numbers modulo 20 is equal to 0 or not .
- If modulo is 0 then possible to make them equal else not because if difference%20 = 0 then we can increase the smaller number by any multiple of 20 to make it equal to greater even number .
- To find the minimum number of steps we will make last digit of both numbers equal to the last digit of the greater number and find the number of steps to make them equal .
Follow the steps to solve the problem:
- If last digit of any number is 0.
- if the numbers are the same then the answer is 0.
- else the number is -1 as the numbers can’t be made equal.
- Store the minimum and maximum of A and B in different variables.
- Make the last digit of the smaller number equal to the greater number and count the steps.
- If the difference is not a multiple of 20 return -1 as the answer.
- Calculate the steps in the loop by using formula (((c – d) / 20) * 4).
- Return the sum of steps and loopSteps as the final answer.
Below is the implementation of the above approach :
Time complexity: O(1), as we will perform at most 3 steps in the while loop.
Auxiliary Space: O(1), since we did not use any extra space.