Program to Subtract two integers of given base
Given three positive integers X, Y, and B, where X and Y are Base-B integers, the task is to find the value of X – Y such that X >= Y.
Input: X = 1212, Y = 256, B = 8
Explanation: The value of 1212 – 256 in base 8 is 734.
Input: X = 546, Y = 248, B = 9
Approach: The given problem can be solved by using basic mathematics subtraction. Follow the steps below to solve the given problem:
- Initialize two variables say power = 1, carry = 0, to keep track of current power and carry generated while subtracting respectively.
- Initialize a variable, say finalVal = 0, to store the resultant value of X – Y.
- Iterate a loop until X > 0 and perform the following steps:
- Store last digits from the current value of X and Y in two variables, say n1 = X % 10 and n2 = Y % 10 respectively.
- Remove last digits from X and Y by updating X = X / 10 and Y = Y / 10.
- Initialize temp = n1 – n2 + carry.
- If temp < 0, then add base B to N, that is N = N + B and set carry = -1, which will act as a borrow. Otherwise, set carry = 0.
- Add current temp * power to finalVal, that is finalVal = finalVal + temp * power and set power = power * 10.
- After completing the above steps, print the value of finalVal as the result.
Below is the implementation of the above approach:
Time Complexity: O(log10N)
Auxiliary Space: O(1)