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Java Project 6: Recursion, Searching & Sorting Algorithms
(60 points + 10 pts bonus)
Submission due date: Sunday 11:59 pm, 4/14/2024
CSCI 1302
Submission includes:
1)
The screenshots of the required
program and the correct result for Q1
2)
The answers for Q2 ~ Q3
Q1
. (10 pts) Write Java program with a recursive method called evenfact(
N
) which
takes in a number N and returns the factorial of the even numbers between the given number N and 2. For example:
evenfact
(4) returns 8, because 2*4=8
evenfact
(9) returns 384, because 2*4*6*8=384
Q2.
(10 pts) Given the sorted list:
2 8 15 38 76 100 138 270 386
To trace the execution for a binary search
, searching for the number 270
.
Step 1: find index 4, compare 76 and 270, because 76 < 270, pointer moves to left N Right Y.
Step 2: find index 6, compare 138 and 270, because 138 < 270, pointer moves to left N Right Y.
Step 3: find index 7, compare 270 and 270, because 270 = 270, pointer moves to left N Right N.
Result: Number 270 is found at index 7.
Q3. (Total 40 pts) Given the following list:
100 15 8 76 138 270 38 To implement the different sort algorithms to sort values from smallest to the biggest. Please fill out each step and find the update list content. If some change happens in the step, please fill the change information, otherwise leave the blank because there is no change.
1)
Selection sort (10 pts)
Step 1: swap 100 and 8, the list: 8, 15, 100, 76, 138, 270, 38
Step 2: swap 15 and 15, the list: 8, 15, 100, 76, 138, 270, 38
Step 3: swap 100 and 38, the list: 8, 15, 38, 76, 138, 270. 100
Step 4: swap 76 and 76, the list: 8, 15, 38, 76, 138, 270, 100
Step 5: swap 138 and 100, the list: 8, 15, 38, 76, 100, 270, 138
Step 6: swap 270 and 138, the list: 8, 15, 38, 76, 100, 138, 270
2)
Insertion sort (10 pts)
Step 1: insert 15, the list: 100, 15, 8, 76, 138, 270
Step 2: insert 8, the list: 8, 100, 15, 76, 138, 270, 38
Step 3: insert 76, the list: 8, 100, 15, 76, 138, 270, 38
Step 4: insert 138, the list: 8, 15, 76, 100, 138, 270, 38
Step 5: insert 270, the list: 8, 15, 76, 100, 138, 270, 38
Step 6: insert 38, the list: 8, 15, 38, 76, 100, 138, 270
3)
Bubble sort
(10 pts)
Stage 1:
the first iteration
Step 1: swap 100 and 15, the list: [15, 100, 8, 76, 138, 270, 38]
Step 2: swap 100 and 8, the list: [15, 8, 100, 76, 138, 270, 38]
Step 3: swap 100 and 76, the list: [15, 8, 76, 100, 138, 270, 38]
Step 4: swap 100 and 138, the list: [15, 8, 76, 100, 138, 270, 38]
Step 5: swap 138 and 270, the list: [15, 8, 76, 100, 138, 270, 38]
Step 6: swap 270 and 38, the list: [15, 8, 76, 100, 138, 38, 270]
After the first iteration, the list is partially sorted as follows: [15, 8, 76,
100, 138, 38, 270]
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Method body:
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Instructions: Use any size of bond paper. Write your name, course and year, date in your
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I.
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7
the output is:
fibonacci(7) is 13
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# TODO: Write recursive fibonacci() functiondef fibonacci():
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Alert dont submit AI generated answer.
Write Java program with a recursive method called evenfact(N) which takes in a number N and returns the factorial of the even numbers between the given number N and 2.
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Part 2. Trace the recursion and observe the recursive solution provided below.
a) Which line(s) of this program define(s) the base case of myMethod() method?
b) Which line(s) of this program include recursive call(s)?
c) Trace the recursion below. You must show the trace step by step, otherwise – little to no credit.
1 public class Test
2 {
3 public statice void main(String [ ] args)
4 {
5
System.out.println( myMethod(3, 6) );
6 }
7 public static int myMethod(int a, int b)
8 {
if (a==b)
10
else if (a > b)
9.
return b;
11
12
return myMethod(a-1, b) + 1;
13
else
14
return myMethod(a, b-1) - 1;
15 }
16 }
d) At what step of your recursion tracing did you hit the base case?
e) What is the final output of this code?
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How can I apply this python code?
def createList(n): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call>
#remove the line after this once you've completed all the TODO for this function return []
def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call>
#remove the line after this once you've completed all the TODO for this function return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else: return [list[0]] + Sieve_of_Eratosthenes(removeMultiples(list[0],…
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- JAVA Question 2: For two integers m and n, their GCD (Greatest Common Divisor) can be computed by a recursive method. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Method body: If m is 0, the method returns n. If n is 0, the method returns m. If neither is 0, the method can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n (or m % n). The recursive method cannot have loops. Note: although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. main method: Prompt and read in two numbers to find the greatest common divisor. Call the gcd method with the two numbers as its argument. Print the result to the monitor. Example program run: Enter m: 12 Enter n: 28 GCD(12,28) = 4 And here is what I have so far, package CSCI1302;import java.util.*;public class RecursionDemo { public static void…arrow_forwardDo not use static variables to implement recursive methods. USING JAVA 1. Using Big Oh notation, indicate the time requirement for each of the following tasks in the worst case. Describe which operations are assumed to take constant time to. After arriving at a party, you shake hands with each person there. n is the number of persons in the party. Each person in a room shakes hands with everyone else in the room. n is the number of persons in the room. You climb a flight of stairs. n is the number of stairs After entering an elevator, you press a button to choose a floor. n is the number of floors You ride the elevator from the ground floor up to the nth floor. You read a book twice. n is the number of pages in the book Using Big Oh notation, indicate the time requirement of each of the following tasks in the worst case. Display all the integers in an array of integers. Display all the integers in a chain of linked nodes. Display the nth integer in an array of integers. Compute…arrow_forwardQuestion 5 When writing a recursive method, O you do not need to know ahead of time exactly how many levels of recursion will occur. O you must keep count of how many recursion call levels you have traversed. O you must make sure the method does not take any input parameters.arrow_forward
- Determine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…arrow_forwardWrite factorial1 function in python 3.8 follow the directions provided below, don't need anything else as long as it meets all the requirements below. Function: factorial1 The function implements an iterative factorial. It takes an integer n as argument and returns n! The method needs to be computed interactively (not recursivelyarrow_forwardPascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }arrow_forward
- 1. What is the difference between an iterative algorithm and a recursive algorithm? 2. What is a recursive algorithm’s base case? What is the recursive case? 3. What is the base case of each of the recursive methods listed in Algorithm Workbench 3, 4, and 5? 4. What type of recursive method do you think would be more difficult to debug: one that uses direct recursion or one that uses indirect recursion? Why? 5. Which repetition approach is less efficient: a loop or a recursive method? Why? 6. When recursion is used to solve a problem, why must the recursive method call itself to solve a smaller version of the original problem? 7. How is a problem usually reduced with a recursive method?arrow_forwardExercise-3: Write a recursive and iterative methods to convert a decimal number to its binary equivalent string. The iterative algorithm (in pseudo-code) for converting a decimal integer into a binary integer as follows: 1. If the integer is 0 or 1, its binary equivalent is 0 or 1. 2. If the integer is greater than or equal to 2 do the following: 3. Divide the integer by 2. 4. Separate the result into a quotient and remainder. 5. Divide the quotient again and repeat the process until the quotient is zero. 6. Write down all remainders in reverse order as a string. 7. This string is the binary equivalent of the given integer. // Recursive decimal to binary method public static String dec2binRecursive(int n) { if (n<2) return n+ " ". else return dec2binRecursive(n/2) + n%2; } a) Write the Complete program for above Recursive decimal to binary method Algorit b) Iterative decimal to binary methodarrow_forwardHow to apply this python code in the problem? What are the base cases and recursive cases that should be used? def createList(n): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else:…arrow_forward
- Java language Write a recursive method to add all of the odd numbers between two numbers (start and end) and return the result. The method receives these numbers as parameters.arrow_forwardUsing Java programming write a recursive function that accepts two arguments into the parameters x and y. The function should return the value of x times y. Remember, multiplication can be performed as repeated addition as follows: 7 * 4=4+4+4+4+4+4+4arrow_forward1. Let product(n,m) be a recursive addition-subtraction method for multiplying two positive integers. Recursive cases for m = 1 and m < 1 make this method. The return value should be n plus a recursive product() call with n and m - 1. Test a Java method.arrow_forward
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