All possible numbers of N digits and base B without leading zeros
Given a number of digits ‘N’ and base ‘B’, the task is to count all the ‘N’ digit numbers without leading zeros that are in base ‘B’.
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Input: N = 2, B = 2 Output: 2 All possible numbers without leading zeros are 10 and 11. Input: N = 5, B = 8 Output: 28672
- If the base is ‘B’ then every digit of the number can take any value within the range [0, B-1].
- So, B‘N’ digit numbers are possible with base ‘B’ (including the numbers with leading zeros).
- And, if we fix the first digit as ‘0’ then the rest of the ‘N-1’ digits can form a total of Bnumbers.
- So, the total number of ‘N’ digit numbers with base ‘B’ possible without leading zeros are B– B.
Below is the implementation of the above approach: