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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;
}