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Programming in C++ Solutions 
Questions 
Problems: [25 marks]
Instructions:

Create a folder named Lab6 to store all the files from this lab.

All of your programs must have good internal documentation. You must document every class, every constructor, and every function.
Problem 1: [5 marks] Ackerman’s Function
(filename:AckermanFunction.cpp)
Ackerman’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function a(m, n) that solves Ackerman’s Function . Use the following logic in your function:
If m = 0then return n + 1
If n = 0 then return a(m  1, 1)
Otherwise, return a(m  1, a(m, n  1))
Write a test program that calls the Ackerman’s functiona(m, n)and displays the values with m and n having the following values:
m = 0, n = 0
m = 0, n = 1
m = 1, n = 1
m = 1, n = 2
m = 1, n = 3
m = 2, n = 1
m = 2, n = 2
m = 3, n = 2
Problem 2: [5 marks] Recursive insertion sort
(filename:TestRecusiveInsertionSort.cpp)
Write a recursive insertion sort function thatsorts an array of integers. Write a test program that creates an array of integers, call the recursive function, displays the sorted array.
Problem 3: [15 marks] String permutation(filename:StringPermutation.cpp)
Write a recursive function to print all the permutations of a string. For example, for a string abc, the permutation is
abc
acb
bac
bca
cab
cba
(Hint: Define the following two functions. The second is a helper function.)
void displayPermutation(const string& s)
void displayPermutation(const string& s1, const string& s2)
The first function simply invokes displayPermutation(“”, s). The second function uses a loop to move a character from s2 to s1 and recursively invoke it with a new s1 and s2. The base case is that s2 is empty and prints s1 to the console.
For example
s1:
s2: abc
s1: a b c
s2: bc ac ab
s1: ab ac ba bc ca cb
s2: c b c a b a
s1: abc acb bac bca cab cba
s2:
Write a test program that prompts the user to enter a string and displays all its permutations.
When and what to hand in
By the end of the lab time, demo Problem 1 to the instructor.
By 11:59pm, Monday, October 21, 2019, zip the other problems and submit them to BrightSpace.
Problem 3 Answer with C++ Code :
CPSC1160 – Algorithms and Data Structures I
Lab6: More Recursion
#include<iostream>
using namespace std;
void displayPermutation(const string& s1, const string& s2)
{
int i;
//base case if s2 is empty
if (s2 == "")
{
cout << s1<<" " << endl;
}
else
{
for ( i = 0; i < s2.length(); i++)
{
bool checkFound = false;
for (int j = 0; j < i; j++)
{
if (s2[j] == s2[i])
checkFound = true;
}
if(checkFound)
continue;
string newStringS1 = s1 + s2[i];
string newStringS2 = s2.substr(0, i) + s2.substr(i+1);
displayPermutation(newStringS1, newStringS2);
}
}
}
void displayPermutation(const string& s1)
{
displayPermutation("",s1);
}
int main()
{
string string1;
cout<<"\nEnter string1";
cin>>string1;
displayPermutation(string1);
return 0;
}