# Introduction to Programming in C Week 5

Session: JAN-APR 2024

Course Name: Introduction to Programming in C

#### These are Introduction to Programming in C Assignment 5 Answers

Question 1

Convergence depth of Collatz function
The Collatz function is defined for a positive integer n as follows.
f(n)={3n+1,n/2,if n oddif n is even
Sample Input
7
Sample Output
16

Solution:

``````#include <stdio.h>

int collatzConvergenceDepth(int n) {
int count = 0;
while (n != 1) {
if (n % 2 == 0) {
n /= 2;
} else {
n = 3 * n + 1;
}
count++;
}
return count;
}

int main() {
int n;
scanf("%d", &n);

int depth = collatzConvergenceDepth(n);

printf("%d", depth);

return 0;
}``````

These are Introduction to Programming in C Assignment 5 Answers

Question 2

BlockSum of an Array
Given an integer array M having size n which is power of 2, Write a recursive code to find the BlockSum of the array M.
The following is the recursive definition of BlockSum:
If size of M is 2, say M=[a,b], where a and b are integers, then BlockSum(M)=a−b.

Solution:

``````#include <stdio.h>

int blockSum(int arr[], int n) {
if (n == 2) {
return arr[0] - arr[1];
} else {
int mid = n / 2;
int sumA = blockSum(arr, mid);
int sumB = blockSum(arr + mid, mid);
return sumA - sumB;
}
}

int main() {
int n;
scanf("%d", &n);

int arr[1024];
for (int i = 0; i < n; i++) {
scanf("%d", &arr[i]);
}

int result = blockSum(arr, n);
printf("%d", result);

return 0;
}``````

These are Introduction to Programming in C Assignment 5 Answers

Course Name: Introduction to programming in C

These are Introduction to Programming in C Assignment 5 Answers

Question 1

#### Write a recursive program that inputs a line of characters from the user.The line may contain blanks. It outputs the line with the characters reversed. The input ends with EOF (end of file).NOTE: You have to use recursion to solve this, and are NOT allowed to use array to store the input!!Example:INPUTThis is easyOUTPUTysae si sihT

These are Introduction to Programming in C Assignment 5 Answers

Code:-

``````#include <stdio.h>
void revstr(){
int ch = getchar();
if (ch == EOF) return;
revstr();
putchar(ch);
}
int main(){
revstr();
return 0;
}``````

These are Introduction to Programming in C Assignment 5 Answers

Question 2

The Collatz function is defined for a positive integer n as follows.
f(n)={3n+1,n/2,if n oddif n is even
We consider the repeated application of the Collatz function starting with a given integer n, as
follows:
f(n),f(f(n)),f(f(f(n))),…
It is conjectured that no matter which positive integer n you start from, this sequence eventually will have 1 in it. It has been verified to hold for numbers up to 5 × 260 [Wikipedia: Collatz Conjecture].

These are Introduction to Programming in C Assignment 5 Answers

e.g. If n=7, the sequence is
f(7) = 22
f(f(7)) = f(22) = 11
f(11) = 34
f(34) = 17
f(17) = 52
f(52) = 26
f(26) = 13
f(13) = 40
f(40) = 20
f(20) = 10
f(10) = 5
f(5) = 16
f(16) = 8
f(8) = 4
f(4) = 2
f(2) = 1
Thus if you start from n=7, you need to apply f 16 times in order to first get 1.
In this question, you will be given a positive number <= 32,000. You have to output how many
times f has to be applied repeatedly in order to first reach 1.

These are Introduction to Programming in C Assignment 5 Answers

Code:-

``````#include <stdio.h>
int collatz(int m);
int c=0;
int main()
{
int n,c;
scanf("%d",&n);
if(n<=0)
{
printf("0");
}
else if(n==1)
{
printf("0");
}
else
{
c = collatz(n);
printf("%d",c);
}
}
int collatz(int m)
{
int n=m;
if(n%2==0)
{
n=n/2;
c++;
if(n!=1)
{
collatz(n);
}
else
{
return c;
}
}
else
{
n=(3*n)+1;
c++;
if(n!=1)
{
collatz(n);
}
else
{
return c;
}
}
}``````

These are Introduction to Programming in C Assignment 5 Answers

Question 3

Description
Write a recursive code to find the block product of an array.
The following is the algorithm to find the block product recursively:
Given an array A partition it into four quadrants of equal size:
M=[ABCD]
The block product of the array is defined recursively as :
|M|=|A|∗|D|−|B|∗|C|
With the base case, when n = 4 , |[a,b,c,d]|=ad−bc
Note : You can assume that n is a power of 4. n>=4 and n <= 1024.

These are Introduction to Programming in C Assignment 5 Answers

Input
The first line contains the array size n
The next n lines contains the elements of the array.
Output
Block product |M|
Example 1
M=[3215]
|M|=3∗5−2∗1=13
Example 2
M=[32152−25510750−256]

Code:-

``//Code``

These are Introduction to Programming in C Assignment 5 Answers