Practical application $2$: Context$-$free language recognizer in java language.$($a$)$ Design an algorithm that recognizes $($accepts$)$ strings of the following context$-$free language: L $=\{0$n$1$n : where n $1\}.$ That is$,$ strings that contain a number of zerosfollowed by the same number of ones. Examples of strings in the language are: $01,0011,000111,$ etc. Strings that are not in the language are, for example, $10,00,111,1100,0101,$and many more. The algorithm should take a string of $0$s and $1$s as input and output Yesif the string belongs to the language, and No if the string doesnt belong to the language.The algorithm should use a stack. When it reads a $0$ from the string, it pushes $0$ onto thestack. When it reads a $1,$ it checks if the stack has a $0,$ in which case that $0$ is popped fromthe stack. When the stack is empty and the end of the string is reached, the string isrecognized as correct $($Yes$).$ Otherwise, the string is not in the language $($No$).($b$)[3$ marks$]$ Implement the algorithm of $($a$)$ in your favorite programming language and runit on different strings as follows: $01,000111,00000001111111,$ and $10,00,00111,0101,$and others.$($c$)[2$ marks$]$ Consider an input string of size n: $($i$)$ what is the worst$-$case time that youralgorithm takes to decide whether or not the string belongs to the language? $($ii$)$ Why? Giveyour answers in terms of the O$-$notation.$($d$)[2$ bonus marks$]$ Run your algorithm on strings of lengths n $=2,4,8,16,32,,220.$Compute the running time in nanoseconds and draw a table with the results. Draw a table ora plot of the results for different values of n and compare the results obtained with thecomplexity you found in $($c$).$ Note: if all $($or most of$)$ the running times become $0,$ tryrunning the program $1,000$ times and compute the average.