The main objective of this lab is to implement Java programs and algorithms using recursion.

Exercise $1(10$ marks$)$

Implement a recursive function to count the number of zeros in a number.

Note:

Example: $2030$ has $2$ zeros

If n has two or more digits

the number of zeros is the number of zeros in $n_{{?}_{?}}$ with the last digit removed

plus an additional $1$ if the last digit is zero

Examples:

number of zeros in $20030$ is number of zeros in $2003$ plus $1$

number of zeros in $20031$ is number of zeros in $2003$ plus $0$

numberOfZeros in the number N

$K=$ number of digits in N

Decomposition:

numberOfZeros in the first $K-1$ digits

Last digit

Composition:

Add:

numberOfZeros in the first K $-1$digits

$1$ if the last digit is zero

Base case:

$N$ has one digit $(K=1)$