Week 02 Tutorial Questions
Recursion and Analysis of Algorithms
Recursion
For the questions below, use the following data type:
struct node {
int value;
struct node *next;
};

Write a recursive function to compute the length of a linked list. It should have this signature:
int listLength(struct node *l) { ... }

Write a recursive function to count the number of odd numbers in a linked list. It should have this signature:
int listCountOdds(struct node *l) { ... }

Write a recursive functions to check whether a list is sorted in ascending order. It should have this signature:
bool listIsSorted(struct node *l) { ... }

Write a recursive function to delete the first instance of a value from a linked list, if it exists. The function should return a pointer to the beginning of the updated list. Use the following interface:
struct node *listDelete(struct node *l, int value) { ... }

Recall that an alternative representation of a linked list uses a struct that contains a pointer to the first node of the list:
struct list { struct node *head; };
How would your recursive solutions for the above questions change if the functions took a
struct list
pointer instead of a node pointer? For example:int listLength(struct list *l);
Analysis of Algorithms

Design an algorithm to determine if a string of length \( n \) is a palindrome  that is, it reads the same backwards as forwards. For example, "racecar" is a palindrome, while "reviewer" is not.
 Write the algorithm in pseudocode.
 Analyse the worstcase time complexity of your algorithm.

Implement your algorithm in C. Your program should accept a single command line argument, and check whether it is a palindrome. Examples of the program executing are:
./palindrome racecar yes ./palindrome reviewer no
Hint: You may use the standard library function strlen(3), which has prototypesize_t strlen(char *)
, is defined in<string.h>
, and which computes the length of a string (without counting its terminating'\0'
character).

Using only techniques that you have learned so far, design an algorithm to determine if an array contains two elements that sum to a given value.
 Write the algorithm in pseudocode.
 Analyse the worstcase time complexity of your algorithm.
 Implement your algorithm as a function in C. The algorithm should accept an array and a value as input and return true or false.