COMP 11 Class 23 Outline

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Daniel Montgomery
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1 Topics: Approach: Main Ideas: COMP 11 Class 23 Outline Recursion II Discussion, Explanation, Discussion A function calling itself 1. Admin a) Reading assignment: Chapter 14.2 and 14.3 b) Assignment 2B due tonight! 2. Review of Fibonacci: a) Fib sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, b) Recall: Fib(n) = Fib (n-1) + Fib (n-2) c) Two steps in a recursive function (fib.cpp) i. Base-case: the simplest case that returns a pre-defined answer ii. A induction step: A step that decomposes the problem into smaller problems by calling the function itself d) Trace through this program e) Write the same function using a loop (fib-loop.cpp) 3. Compare the differences between Recursive Function and Iterative (Loop) Functions a) What are the differences? b) What happens to a recursive function without a base-case? i. What happens to an iterative function without a stopping condition? ii. Base-case vs. condition iii. Induction step vs. incrementing c) Discussion: equivalence between recursion and loops. Languages without loop. Coverage of some of those languages in COMP 105 (Programming Languages) d) Exam question: be able to convert between loops (while, for, do/while) to a recursive function and vice versa. 4. Exercise: a) Computing the factorial i. Write a looped function that computes the factorial of m (fac-loop.cpp) ii. Write a recursive function that does the same (fac.cpp) b) Computing Power: i. Write a looped function that computes m to the nth power (power-loop.cpp) ii. Write a recursive function that does the same (power.cpp) c) Find the minimum i. Write a looped function that finds the minimum value in an array (findminloop.cpp) ii. Write a recursive function that does the same (findmin.cpp) 5. Recursion with Linked Data Structures a) Adding up all the elements in a linked list (linkedlist.cpp) b) Deleting a linked list c) Recursion with binary tree (binarytree.cpp) i. Building a tree ii. Printing a tree iii. Traversing a tree iv. Deleting a tree

2 :::::::::::::: fib.cpp ::::::::::::: int fib (int n); int num; cout << "computing the Fibonnaci number, input an integer: "; cin >> num; cout << fib(num) << endl; int fib (int n) { if (n == 0) { return 0; else if (n == 1) { return 1; return fib(n-1)+fib(n-2); :::::::::::::: fib-loop.cpp ::::::::::::: int fib (int n) { if (n == 0) { return 0; if (n == 1) { return 1; int i; int* fibarray = new int [n]; fibarray[0] = 0; fibarray[1] = 1; for (i=2; i<n ;i++) { fibarray[i] = fibarray[i-1] + fibarray[i-2]; int answer = (fibarray[n-1] + fibarray[n-2]); delete fibarray; return answer;

3 :::::::::::::: fac.cpp ::::::::::::: int fac (int n); int num; cout << "computing the Factorial, input an integer: "; cin >> num; cout << fac(num) << endl; int fac (int num) { if (num == 1) { return 1; return num * fac (num-1); :::::::::::::: fac-loop.cpp ::::::::::::: int fac (int num) { int i; int total = 1; for (i=1; i<=num; i++) { total = total * i; return total; :::::::::::::: power.cpp ::::::::::::: int power (int n, int m); int num; int pow; cout << "computing the Power, input an integer base: "; cin >> num; cout << "computing the Power, input an integer power: "; cin >> pow; cout << power(num, pow) << endl; int power (int num, int pow) { if (pow == 0) { return 1; return num * power (num, pow-1);

4 :::::::::::::: power-loop.cpp ::::::::::::: int power (int num, int pow) { int i; int answer = 1; for (i=0; i<pow; i++) { answer = answer * num; return answer; :::::::::::::: findmin.cpp ::::::::::::: #include <time.h> int findmin (int* array, int size, int index); int LENGTH = 10; //randomly populate an array srand(time(null)); int* array = new int [LENGTH]; for (int i=0; i<length; i++) { array[i] = rand() % 100; cout << array[i] << " "; cout << endl; //find the minimum cout << findmin(array, LENGTH, 0) << endl; //delete array delete [] array; int findmin (int* array, int size, int index) { //base case if (size <= 0) { return -1; if (index == (size-1)) { return array[index]; //induction step int nextmin = findmin(array, size, index+1); if (nextmin < array[index]) { return nextmin;

5 return array[index]; :::::::::::::: findmin-loop.cpp ::::::::::::: int findmin (int* array, int size, int index) { if (size <= 0) { return -1; int i; int min = array[0]; for (i=1; i<size; i++) { if (array[i] < min) { min = array[i]; return min; :::::::::::::: linkedlist.cpp ::::::::::::: #include <time.h> #include "Node.H" int sum (Node* curnode); Node* buildlist(int size); void deletelist(node* curnode); srand(time(null)); Node* head = buildlist(10); cout << sum(head) << endl; deletelist(head); int sum (Node* curnode) { return 0; return curnode->getvalue() + sum(curnode->getnext()); void deletelist(node* curnode) { return; deletelist(curnode->getnext()); delete curnode;

6 Node* buildlist(int size) { Node* head = new Node(); head->setvalue(rand()%100); cout << head->getvalue() << " "; Node* tmp = head; for (int i=1; i<size; i++) { Node* newnode = new Node(); newnode->setvalue(rand()%100); cout << newnode->getvalue() << " "; tmp->setnext(newnode); tmp = newnode; cout << endl; return head; :::::::::::::: Node.H ::::::::::::: #ifndef NODE_H #define NODE_H class Node { public: Node(); ~Node(); void setvalue (int value); void setnext (Node* next); int getvalue(); Node* getnext(); private: int m_value; Node* m_next; ; #endif :::::::::::::: Node.cpp ::::::::::::: Node::Node() { m_value = 0; m_next = NULL; Node::~Node() { void Node::setValue (int value) { m_value = value;

7 void Node::setNext (Node* next) { m_next = next; int Node::getValue() { return m_value; Node* Node::getNext() { return m_next; :::::::::::::: binarytree.cpp ::::::::::::: #include <time.h> #include "Node.H" Node* buildtree(int size); void addtotree(node* curnode, Node* newnode); void deletetree(node* curnode); void printtree(node* curnode, string spacer); int sum (Node* curnode); srand(time(null)); Node* root = buildtree (10); printtree(root, ""); //find the minimum cout << "sum: " << sum(root) << endl; deletetree(root); int sum (Node* curnode) { //base case return 0; return curnode->getvalue() + sum(curnode->getright()) + sum(curnode->getleft()); void printtree(node* curnode, string spacer) { cout << spacer << " NULL" << endl; return; cout << spacer << " " << curnode->getvalue() << endl; printtree(curnode->getright(), spacer+" R:"); printtree(curnode->getleft(), spacer+" L:");

8 Node* buildtree(int size) { Node* root = new Node(); root->setvalue(rand()%100); cout << root->getvalue() << " "; Node* tmp = root; for (int i=1; i<size; i++) { Node* newnode = new Node(); newnode->setvalue(rand()%100); cout << newnode->getvalue() << " "; addtotree(root, newnode); cout << endl; return root; void addtotree(node* curnode, Node* newnode) { int curval = curnode->getvalue(); int newval = newnode->getvalue(); if (newval > curval) { if (curnode->getright() == NULL) { curnode->setright(newnode); addtotree(curnode->getright(), newnode); if (curnode->getleft() == NULL) { curnode->setleft(newnode); addtotree(curnode->getleft(), newnode); void deletetree(node* curnode) { return; deletetree(curnode->getright()); deletetree(curnode->getleft()); delete curnode; :::::::::::::: Node2.H ::::::::::::: #ifndef NODE_H #define NODE_H class Node {

9 public: Node(); ~Node(); void setvalue (int value); void setleft (Node* left); void setright (Node* right); int getvalue(); Node* getleft(); Node* getright(); private: int m_value; Node* m_left; Node* m_right; ; #endif :::::::::::::: Node2.cpp ::::::::::::: #include "Node.H" Node::Node() { m_value = 0; m_left = NULL; m_right = NULL; Node::~Node() { void Node::setValue (int value) { m_value = value; void Node::setLeft (Node* left) { m_left = left; void Node::setRight (Node* right) { m_right = right; int Node::getValue() { return m_value; Node* Node::getLeft() { return m_left; Node* Node::getRight() { return m_right;

COMP-202: Foundations of Programming. Lecture 13: Recursion Sandeep Manjanna, Summer 2015

COMP-202: Foundations of Programming Lecture 13: Recursion Sandeep Manjanna, Summer 2015 Announcements Final exams : 26 th of June (2pm to 5pm) @ MAASS 112 Assignment 4 is posted and Due on 29 th of June