Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 6.2, Problem 5E
Program Plan Intro
To write an efficient MAX-HEAPIFY procedure that uses iterative control structure instead of recursion.
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Implement a recursive function void deleteMax() on the IntList class (provided). The function will delete from the IntList the IntNode containing the largest value. If there are multiple nodes containing this largest value, only delete the 1st one.
Be careful not to cause any memory leaks or dangling pointers.
You may NOT use any kind of loop (must use recursion).
You may NOT use global or static variables.
You may NOT use any standard library functions.
Ex:
list: 5->7->1->16->4->16->3
list.deleteMax();
list: 5->7->1->4->16->3
IntList.h
#ifndef __INTLIST_H__#define __INTLIST_H__
#include <ostream>
using namespace std;
struct IntNode {int value;IntNode *next;IntNode(int value) : value(value), next(nullptr) {}};
class IntList {
private:IntNode *head;
public:
/* Initializes an empty list.*/IntList() : head(nullptr) {}
/* Inserts a data value to the front of the list.*/void push_front(int val) {if (!head) {head = new IntNode(val);} else {IntNode…
Dynamic Programming is mostly just a matter of taking a recursive algorithm and finding the overlapping subproblems. Do some research on dynamic programming, and then explain the following two question:
We have discussed how to apply recursion to finding the Fibonacci Sequence. The following code shows how to do it using dynamic programming. Explain why this code works.
AvgCompares(), a recursive function that calculates the average number of comparisons needed by a random search hit in a given BST (the internal path length of the tree divided by its size plus one), should be added to the BST. Create two implementations: a recursive method that adds a field to each node in the tree and takes linear space and constant time every query, and a method similar to size() that takes linear space and constant time per query.
Chapter 6 Solutions
Introduction to Algorithms
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3E
Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3P
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- In Java!!!. Design and implement a recursive version of a binary search. For the recursive version, instead of using a loop to repeatedly loop for the target value, allow each call to a recursive method check one value. If the value is not the target, refine the search space and call the method again. The indexes that define the range of viable candidates can be passed to the method. The base case is either finding the target value or running out of data to search. Design the program to work for on an array of sorted String objects.arrow_forwardThe Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…arrow_forwardIteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.arrow_forward
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- Write a tail-call recursive function in the Racket language called circles. This function should take two numbers, x and size, and a Scene scn. If size is less-than or equal to 2, then your function returns the scn unchanged (base case). Otherwise, your function should place a circle in the Scene that results from a recursive call to circles with x shifted by (+size (next-size size)), a new size of (next-size size), and using the original Scene. After evaluating such as (circles 100 48 ES), your function should output an image of five blue circles, with the first circle at (x,y) coordinate position (100, 80):arrow_forwardThe Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match! public class BinaryExplorer { public static void main(String[] args) {int[] testArray = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; binaryRec(testArray, 8, 0, testArray.length - 1); } /*** Add Print statements to the binaryRec method:* * Print Starting, ending, and midpoint values.* * Print when you find a match* * Print if you are…arrow_forwardThe Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match!arrow_forward
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