# 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;
};

1. Write a recursive function to compute the length of a linked list. It should have this signature:

int listLength(struct node *l) { ... }

2. 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) { ... }

3. Write a recursive functions to check whether a list is sorted in ascending order. It should have this signature:

bool listIsSorted(struct node *l) { ... }

4. 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) { ... }

5. 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 {
};


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
1. 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.

1. Write the algorithm in pseudocode.
2. Analyse the worst-case time complexity of your algorithm.
3. 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 prototype size_t strlen(char *), is defined in <string.h>, and which computes the length of a string (without counting its terminating '\0' character).
2. 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.

1. Write the algorithm in pseudocode.
2. Analyse the worst-case time complexity of your algorithm.
3. Implement your algorithm as a function in C. The algorithm should accept an array and a value as input and return true or false.