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Recursive program to find all Indices of a Number

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  • Difficulty Level : Medium
  • Last Updated : 30 Nov, 2021

Given an array arr of size N and an integer X. The task is to find all the indices of the integer X in the array
Examples: 
 

Input: arr = {1, 2, 3, 2, 2, 5}, X = 2 
Output: 1 3 4 
Element 2 is present at indices 1, 3, 4 (0 based indexing)
Input: arr[] = {7, 7, 7}, X = 7 
Output: 0 1 2 
 

 

The iterative approach is simple, just traverse the given array and keep on storing the indices of the element in the another array.
Recursive approach
 

  • If the start index reaches the length of the array, then return empty array
  • Else keep the first element of the array with yourself and pass the rest of the array to recursion. 
    • If the element at start index is not equal to x then just simply return the answer which came from recursion. 
       
    • Else if the element at start index is equal to x then shift the elements of the array (which is the answer of recursion) one step to the right and then put the start index in the front of the array (which came through recursion) 
       

Below is the implementation of the above approach:
 

C++




// CPP program to find all indices of a number
#include <bits/stdc++.h>
using namespace std;
 
// A recursive function to find all
// indices of a number
int AllIndexesRecursive(int input[], int size,
                    int x, int output[])
{
     
    // If an empty array comes
    // to the function, then
    // return zero
    if (size == 0) {
        return 0;
    }
 
    // Getting the recursive answer
    int smallAns = AllIndexesRecursive(input + 1,
                                    size - 1, x, output);
 
    // If the element at index 0 is equal
    // to x then add 1 to the array values
    // and shift them right by 1 step
    if (input[0] == x) {
        for (int i = smallAns - 1; i >= 0; i--) {
            output[i + 1] = output[i] + 1;
        }
 
        // Put the start index in front
        // of the array
        output[0] = 0;
        smallAns++;
    }
    else {
         
        // If the element at index 0 is not equal
        // to x then add 1 to the array values
        for (int i = smallAns - 1; i >= 0; i--) {
            output[i] = output[i] + 1;
        }
    }
    return smallAns;
}
 
// Function to find all indices of a number
void AllIndexes(int input[], int n, int x)
{
    int output[n];
    int size = AllIndexesRecursive(input, n,
                                x, output);
    for (int i = 0; i < size; i++) {
        cout << output[i] << " ";
    }
}
 
// Driver Code
int main()
{
    int arr[] = { 1, 2, 3, 2, 2, 5 }, x = 2;
     
    int n = sizeof(arr) / sizeof(arr[0]);
     
    // Function call
    AllIndexes(arr, n, x);
     
    return 0;
}

Java




// Java program to find all
// indices of a number
public class GFG {
 
    public int[] AllIndexesRecursive(int input[],
                                int x, int start)
    {
        // If the start index reaches the
        // length of the array, then
        // return empty array
        if (start == input.length) {
            int[] ans = new int[0]; // empty array
            return ans;
        }
 
        // Getting the recursive answer in
        // smallIndex array
        int[] smallIndex = AllIndexesRecursive(input, x,
                                              start + 1);
 
        // If the element at start index is equal
        // to x then
        // (which is the answer of recursion) and then
        // (which came through recursion)
        if (input[start] == x) {
            int[] myAns = new int[smallIndex.length + 1];
 
            // Put the start index in front
            // of the array
            myAns[0] = start;
            for (int i = 0; i < smallIndex.length; i++) {
                 
                // Shift the elements of the array
                // one step to the right
                // and putting them in
                // myAns array
                myAns[i + 1] = smallIndex[i];
            }
            return myAns;
        }
        else {
             
            // If the element at start index is not
            // equal to x then just simply return the
            // answer which came from recursion.
            return smallIndex;
        }
    }
 
    public int[] AllIndexes(int input[], int x)
    {
 
        return AllIndexesRecursive(input, x, 0);
    }
     
    // Driver Code
    public static void main(String args[])
    {
        GFG g = new GFG();
        int arr[] = { 1, 2, 3, 2, 2, 5 }, x = 2;
         
        int output[] = g.AllIndexes(arr, x);
         
        // Printing the output array
        for (int i = 0; i < output.length; i++) {
            System.out.print(output[i] + " ");
        }
    }
}

Python3




# Python3 program to find all
# indices of a number
def AllIndexesRecursive(input, x, start):
     
    # If the start index reaches the
    # length of the array, then
    # return empty array
    if (start == len(input)):
        ans = [] # empty array
        return ans
 
    # Getting the recursive answer in
    # smallIndex array
    smallIndex = AllIndexesRecursive(input, x,
                                     start + 1)
 
    # If the element at start index is equal
    # to x then
    # (which is the answer of recursion) and then
    # (which came through recursion)
    if (input[start] == x):
        myAns = [0 for i in range(len(smallIndex) + 1)]
 
        # Put the start index in front
        # of the array
        myAns[0] = start
        for i in range(len(smallIndex)):
 
            # Shift the elements of the array
            # one step to the right
            # and putting them in
            # myAns array
            myAns[i + 1] = smallIndex[i]
 
        return myAns
    else:
 
        # If the element at start index is not
        # equal to x then just simply return the
        # answer which came from recursion.
        return smallIndex
 
# Function to find all indices of a number
def AllIndexes(input, x):
 
    return AllIndexesRecursive(input, x, 0)
 
# Driver Code
arr = [ 1, 2, 3, 2, 2, 5 ]
x = 2
 
output=AllIndexes(arr, x)
 
# Printing the output array
for i in output:
    print(i, end = " ")
 
# This code is contributed by Mohit Kumar

C#




// C# program to find all
// indices of a number
using System;
class GFG
{
    public int[] AllIndexesRecursive(int []input,
                                        int x, int start)
    {
        // If the start index reaches the
        // length of the array, then
        // return empty array
        if (start == input.Length)
        {
            int[] ans = new int[0]; // empty array
            return ans;
        }
 
        // Getting the recursive answer in
        // smallIndex array
        int[] smallIndex = AllIndexesRecursive(input, x,
                                               start + 1);
 
        // If the element at start index is equal
        // to x then
        // (which is the answer of recursion) and
        // then (which came through recursion)
        if (input[start] == x)
        {
            int[] myAns = new int[smallIndex.Length + 1];
 
            // Put the start index in front
            // of the array
            myAns[0] = start;
            for (int i = 0; i < smallIndex.Length; i++)
            {
                 
                // Shift the elements of the array
                // one step to the right
                // and putting them in
                // myAns array
                myAns[i + 1] = smallIndex[i];
            }
            return myAns;
        }
        else
        {
             
            // If the element at start index is not
            // equal to x then just simply return the
            // answer which came from recursion.
            return smallIndex;
        }
    }
 
    public int[] AllIndexes(int []input, int x)
    {
        return AllIndexesRecursive(input, x, 0);
    }
     
    // Driver Code
    public static void Main()
    {
        GFG g = new GFG();
        int []arr = { 1, 2, 3, 2, 2, 5 };
        int x = 2;
         
        int []output = g.AllIndexes(arr, x);
         
        // Printing the output array
        for (int i = 0; i < output.Length; i++)
        {
            Console.Write(output[i] + " ");
        }
    }
}
 
// This code is contributed by anuj_67..

Javascript




<script>
    // Javascript program to find all indices of a number
     
    function AllIndexesRecursive(input, x, start)
    {
        // If the start index reaches the
        // length of the array, then
        // return empty array
        if (start == input.length)
        {
            let ans = new Array(0); // empty array
            return ans;
        }
   
        // Getting the recursive answer in
        // smallIndex array
        let smallIndex = AllIndexesRecursive(input, x, start + 1);
   
        // If the element at start index is equal
        // to x then
        // (which is the answer of recursion) and
        // then (which came through recursion)
        if (input[start] == x)
        {
            let myAns = new Array(smallIndex.length + 1);
   
            // Put the start index in front
            // of the array
            myAns[0] = start;
            for (let i = 0; i < smallIndex.length; i++)
            {
                   
                // Shift the elements of the array
                // one step to the right
                // and putting them in
                // myAns array
                myAns[i + 1] = smallIndex[i];
            }
            return myAns;
        }
        else
        {
               
            // If the element at start index is not
            // equal to x then just simply return the
            // answer which came from recursion.
            return smallIndex;
        }
    }
   
    function AllIndexes(input, x)
    {
        return AllIndexesRecursive(input, x, 0);
    }
     
    let arr = [ 1, 2, 3, 2, 2, 5 ];
    let x = 2;
 
    let output = AllIndexes(arr, x);
 
    // Printing the output array
    for(let i = 0; i < output.length; i++)
    {
      document.write(output[i] + " ");
    }
     
    // This code is contributed by mukesh07.
</script>

Output

1 3 4 

Simpler Recursive approach:  (Traversing from the End)

  • If the last index reaches the length of the array, then return empty array
  • Else reduce the last index and pass the whole array to recursion.
  • If the element at the last index is not equal to x then just simply return the answer which came from recursion.
  • Else if the element at the last index is equal to x then simply insert the last element at the last index into index pointed by ans.

This avoids the complication of shifting all the elements by one index and also incrementing all the elements in the output array.

Below is the implementation of the above approach:

C++




// CPP program to find all indices of a number
#include <bits/stdc++.h>
using namespace std;
 
// A recursive function to find all
// indices of a number
int AllIndexesRecursive(int input[], int size,
                    int x, int output[])
{
     
    // If the input array becomes empty
      if(size == 0)
        return 0;
 
         
    // Getting the recursive answer
      int smallAns = AllIndexesRecursive(input, size - 1, x, output);
     
      // If the last element of input array is equal to x
    if(input[size - 1] == x)
    {
      // Insert the index of last element of the input array into the output array
      // And increment ans
      output[smallAns++] = size - 1;
    }
    return smallAns;
}
 
// Function to find all indices of a number
void AllIndexes(int input[], int n, int x)
{
    int output[n];
    int size = AllIndexesRecursive(input, n,
                                x, output);
    for (int i = 0; i < size; i++) {
        cout << output[i] << " ";
    }
}
 
// Driver Code
int main()
{
    int arr[] = { 1, 2, 3, 2, 2, 5 }, x = 2;
     
    int n = sizeof(arr) / sizeof(arr[0]);
     
    // Function call
    AllIndexes(arr, n, x);
     
    return 0;
}

Java




// Java program to find all indices of a number
public class Main
{
    // A recursive function to find all
    // indices of a number
    static int AllIndexesRecursive(int[] input, int size, int x, int[] output)
    {
          
        // If the input array becomes empty
          if(size == 0)
            return 0;
      
              
        // Getting the recursive answer
        int smallAns = AllIndexesRecursive(input, size - 1, x, output);
          
          // If the last element of input array is equal to x
        if(input[size - 1] == x)
        {
          // Insert the index of last element of the input array into the output array
          // And increment ans
          output[smallAns++] = size - 1;
        }
        return smallAns;
    }
      
    // Function to find all indices of a number
    static void AllIndexes(int[] input, int n, int x)
    {
        int[] output = new int[n];
        int size = AllIndexesRecursive(input, n, x, output);
        for (int i = 0; i < size; i++) {
            System.out.print(output[i] + " ");
        }
    }
     
    public static void main(String[] args) {
        int[] arr = { 1, 2, 3, 2, 2, 5 };
        int x = 2;
          
        int n = arr.length;
          
        // Function call
        AllIndexes(arr, n, x);
    }
}
 
// This code is contributed by suresh07.

Python3




# Python3 program to find all indices of a number
 
# A recursive function to find all
# indices of a number
def AllIndexesRecursive(Input, size, x, output):
    # If the input array becomes empty
    if size == 0:
        return 0
    
    # Getting the recursive answer
    smallAns = AllIndexesRecursive(Input, size - 1, x, output)
        
    # If the last element of input array is equal to x
    if Input[size - 1] == x:
       
      # Insert the index of last element of the input array into the output array
      # And increment ans
      output[smallAns] = size - 1
      smallAns+=1
    return smallAns
    
# Function to find all indices of a number
def AllIndexes(Input, n, x):
    output = [0]*n
    size = AllIndexesRecursive(Input, n, x, output)
    for i in range(size):
        print(output[i], "", end = "")
 
arr = [ 1, 2, 3, 2, 2, 5 ]
x = 2
    
n = len(arr)
    
# Function call
AllIndexes(arr, n, x)
 
# This code is contributed by rameshtravel07

C#




// C# program to find all indices of a number
using System;
using System.Collections.Generic;
class GFG {
 
    // A recursive function to find all
    // indices of a number
    static int AllIndexesRecursive(int[] input, int size, int x, int[] output)
    {
          
        // If the input array becomes empty
          if(size == 0)
            return 0;
      
              
        // Getting the recursive answer
        int smallAns = AllIndexesRecursive(input, size - 1, x, output);
          
          // If the last element of input array is equal to x
        if(input[size - 1] == x)
        {
          // Insert the index of last element of the input array into the output array
          // And increment ans
          output[smallAns++] = size - 1;
        }
        return smallAns;
    }
      
    // Function to find all indices of a number
    static void AllIndexes(int[] input, int n, int x)
    {
        int[] output = new int[n];
        int size = AllIndexesRecursive(input, n, x, output);
        for (int i = 0; i < size; i++) {
            Console.Write(output[i] + " ");
        }
    }
 
  static void Main() {
    int[] arr = { 1, 2, 3, 2, 2, 5 };
    int x = 2;
      
    int n = arr.Length;
      
    // Function call
    AllIndexes(arr, n, x);
  }
}
 
// This code is contributed by decode22007.

Javascript




<script>
    // Javascript program to find all indices of a number
     
    // A recursive function to find all
    // indices of a number
    function AllIndexesRecursive(input, size, x, output)
    {
           
        // If the input array becomes empty
          if(size == 0)
            return 0;
       
               
        // Getting the recursive answer
        let smallAns = AllIndexesRecursive(input, size - 1, x, output);
           
          // If the last element of input array is equal to x
        if(input[size - 1] == x)
        {
          // Insert the index of last element of the input array into the output array
          // And increment ans
          output[smallAns++] = size - 1;
        }
        return smallAns;
    }
       
    // Function to find all indices of a number
    function AllIndexes(input, n, x)
    {
        let output = new Array(n);
        let size = AllIndexesRecursive(input, n, x, output);
        for (let i = 0; i < size; i++) {
            document.write(output[i] + " ");
        }
    }
     
    let arr = [ 1, 2, 3, 2, 2, 5 ];
    let x = 2;
       
    let n = arr.length;
       
    // Function call
    AllIndexes(arr, n, x);
 
// This code is contributed by divyeshrabadiya07.
</script>

Output

1 3 4 


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