Attached is a programming question and its Java solution.My question regarding the recursion part: 1. "arr.add(j)" but then "arr.remove(arr.size() - 1)" follows soon after, and I think nothing should be printed. How does the program still print out permutations? Is it because the recursive method call only recurse all instructions from the start of the recursion method to that line? Otherwise, say the input is "5", how does "5=1+1+1+1+1" get printed? 2. Does the recursion stop when "j<=n" evaluates false because of "for(int j = i; j <= n; j++)"? Otherwise, which line of code tells the recursion to stop? Ryuk the shinigami wants to find out the different ways to add up to N apples! For example, if you have 3 apples, thepossible ways are:3=1+1+13=1+2total=2Ryuk wants you, to output the solution in the above format given the number of apples, N.Note: The sequence which you output the solution does not matter, meaning:3=1+1+13=1+2and3=1+23=1+1+1are both accepted. static int count=0;static void printOutput(ArrayList arr){count++;int sum=0;for (int i=0;i arr,int i,int n){if(n==0){printOutput (arr);}for(int ii; j <= n; j++){arr.add(j);findways (arr, ji, n: n - j);arr.remove( index: arr.size() - 1);}}public static void main(String[] args)throws IOException {BufferedReader br=new BufferedReader(new InputStreamReader (System.in));int n=Integer.parseInt(br.readLine());ArrayList arr = new ArrayList<>();findways (arr, : 1,n);System.out.println("total="+(count-1));

See the image below to understand the flow of the recursion.

static int count=0; static void printOutput(ArrayList arr){ count++; int sum=0; for(int i=0;i arr,int i,int n) { if(n==0){ printOutput(arr); } for(int į = i; j <= n; j++) { arr.add(j); findways(arr, i, n: n - j); arr.remove( index: arr.size() - 1); } } public static void main(String[] args)throws IOException { BufferedReader br=new BufferedReader (new InputStreamReader(System.in) int n=Integer.parseInt(br.readLine()); ArrayList arr = new ArrayList<>(); findways(arr, : 1,n); System.out.println("total="+(count-1));

static int count=0; static void printOutput(ArrayList arr){ count++; int sum=0; for(int i=0;i arr,int i,int n) { if(n==0){ printOutput(arr); } for(int į = i; j <= n; j++) { arr.add(j); findways(arr, i, n: n - j); arr.remove( index: arr.size() - 1); } } public static void main(String[] args)throws IOException { BufferedReader br=new BufferedReader (new InputStreamReader(System.in) int n=Integer.parseInt(br.readLine()); ArrayList arr = new ArrayList<>(); findways(arr, : 1,n); System.out.println("total="+(count-1));

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 21PE

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Concept explainers

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

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Attached is a programming question and its Java solution.

My question regarding the recursion part:

1. "arr.add(j)" but then "arr.remove(arr.size() - 1)" follows soon after, and I think nothing should be printed. How does the program still print out permutations? Is it because the recursive method call only recurse all instructions from the start of the recursion method to that line? Otherwise, say the input is "5", how does "5=1+1+1+1+1" get printed?

2. Does the recursion stop when "j<=n" evaluates false because of "for(int j = i; j <= n; j++)"? Otherwise, which line of code tells the recursion to stop?

Ryuk the shinigami wants to find out the different ways to add up to N apples! For example, if you have 3 apples, the
possible ways are:
3=1+1+1
3=1+2
total=2
Ryuk wants you, to output the solution in the above format given the number of apples, N.
Note: The sequence which you output the solution does not matter, meaning:
3=1+1+1
3=1+2
and
3=1+2
3=1+1+1
are both accepted.

static int count=0;
static void printOutput(ArrayList<Integer> arr){
count++;
int sum=0;
for (int i=0;i<arr.size();i++){
sum+=arr.get (i);
}
if (arr.size() != 1){
System.out.print(sum+"=");
for(int i=0;i<arr.size()-1;i++){
System.out.print(arr.get(i)+"+");
}
System.out.println(arr.get(arr.size()-1));|
}
}
static void findWays (ArrayList<Integer> arr,int i,int n)
{
if(n==0){
printOutput (arr);
}
for(int i
i; j <= n; j++)
{
arr.add(j);
findways (arr, ji, n: n - j);
arr.remove( index: arr.size() - 1);
}
}
public static void main(String[] args)throws IOException {
BufferedReader br=new BufferedReader(new InputStreamReader (System.in));
int n=Integer.parseInt(br.readLine());
ArrayList<Integer> arr = new ArrayList<>();
findways (arr, : 1,n);
System.out.println("total="+(count-1));

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