Find the index of first 1 in a sorted array of 0's and 1's

Last Updated : 03 Oct, 2022

Given a sorted array consisting 0's and 1's. The problem is to find the index of first '1' in the sorted array. It could be possible that the array consists of only 0's or only 1's. If 1's are not present in the array then print "-1".

Examples :

Input : arr[] = {0, 0, 0, 0, 0, 0, 1, 1, 1, 1}
Output : 6
Explanation: The index of first 1 in the array is 6.

Input : arr[] = {0, 0, 0, 0}
Output : -1
Explanation: 1's are not present in the array.

Source: Asked in Amazon Interview

Naive Approach: Traverse the array from left to right and return the index of first '1'. If 1's are not present in the array, then print "-1"

Implementation:

C++

// C++ implementation to find the index of
// first '1' in a sorted array of 0's and 1's
#include <bits/stdc++.h>
using namespace std;

// function to find the index of first '1'
int indexOfFirstOne(int arr[], int n)
{
    // traverse the array from left to right
    for (int i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above
int main()
{
    int arr[] = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << indexOfFirstOne(arr, n);
    return 0;
}

Java

// Java program to find the index of
// first '1' in a sorted array of 0's and 1's
class GFG {
    

    // function to find the index of first '1'
    public static int indexOfFirstOne(int arr[], int n)
    {
        // traverse the array from left to right
        for (int i = 0; i < n; i++)
     
            // if true, then return i
            if (arr[i] == 1)
                return i;
     
        // 1's are not present in the array
        return -1;
    }
    
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int arr[] = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        int n = arr.length;
        System.out.println(indexOfFirstOne(arr, n));
        
    }
  }
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python3 implementation to find 
# the index of first '1' in a 
# sorted array of 0's and 1's

# function to find the index of first '1'
def indexOfFirstOne(arr, n):

    # traverse the array from left to right
    for i in range(0, n):
        
        # if true, then return i
        if (arr[i] == 1):
            return i

    # 1's are not present in the array
    return -1

# Driver program to test above
arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ]
n = len(arr)
ans = indexOfFirstOne(arr, n)
print(ans)

# This code is contributed by saloni1297

// C# program to find the index of
// first '1' in a sorted array 
// of 0's and 1's
using System;

class GFG
{ 
    // function to find the index of first '1'
    public static int indexOfFirstOne(int []arr, int n)
    {
        // traverse the array from left to right
        for (int i = 0; i < n; i++)
    
            // if true, then return i
            if (arr[i] == 1)
                return i;
    
        // 1's are not present in the array
        return -1;
    }
    
    // Driver program 
    public static void Main() 
    {
        int []arr = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        int n = arr.Length;
        Console.Write(indexOfFirstOne(arr, n));
        
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP implementation to find the index of
// first '1' in a sorted array of 0's and 1's
// function to find the index of first '1'

function indexOfFirstOne($arr, $n)
{
    
    // traverse the array from
    // left to right
    for ($i = 0; $i < $n; $i++)

        // if true, then return i
        if ($arr[$i] == 1)
            return $i;

    // 1's are not present
    // in the array
    return -1;
}

    // Driver Code
    $arr = array(0, 0, 0, 0, 0, 0, 1, 1, 1, 1);
    $n = sizeof($arr) / sizeof($arr[0]);
    echo indexOfFirstOne($arr, $n);
    return 0;

// This code is contributed by nitin mittal.
?>

JavaScript

<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>
<script>

// Javascript implementation to find the index of
// first '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
function indexOfFirstOne(arr, n)
{
    // traverse the array from left to right
    for (let i = 0; i < n; i++)

        // if true, then return i
        if (arr[i] == 1)
            return i;

    // 1's are not present in the array
    return -1;
}

// Driver program to test above

    let arr = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ];
    let n = arr.length;
    document.write(indexOfFirstOne(arr, n));

//This code is contributed by Mayank Tyagi
</script>

Output

Time Complexity: O(n)
Auxiliary Space: O(1)

Efficient Approach(Binary Search): Use the technique of binary search on the sorted array, so as to find the index of first '1'.

Implementation:

C++

// C++ implementation to find the index of first
// '1' in a sorted array of 0's and 1's
#include <bits/stdc++.h>
using namespace std;

// function to find the index of first '1'
// binary search technique is applied
int indexOfFirstOne(int arr[], int low, int high)
{
    while (low <= high) {
        int mid = (low + high) / 2;

        // if true, then 'mid' is the index of first '1'
        if (arr[mid] == 1 && (mid == 0 || arr[mid - 1] == 0))
            return mid;

        // first '1' lies to the left of 'mid'
        else if (arr[mid] == 1)
            high = mid - 1;

        // first '1' lies to the right of 'mid'
        else
            low = mid + 1;
    }

    // 1's are not present in the array
    return -1;
}

// Driver program to test above
int main()
{
    int arr[] = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << indexOfFirstOne(arr, 0, n - 1);
    return 0;
}

Java

// Java program to find the index of
// first '1' in a sorted array of 0's and 1's
class GFG {
    
    // function to find the index of first '1'
    // binary search technique is applied
    public static int indexOfFirstOne(int arr[], int low,
                                                int high)
    {
        while (low <= high) {
            int mid = (low + high) / 2;
     
            // if true, then 'mid' is the index of first '1'
            if (arr[mid] == 1 && (mid == 0 || arr[mid - 1] 
                                                    == 0))
                return mid;
     
            // first '1' lies to the left of 'mid'
            else if (arr[mid] == 1)
                high = mid - 1;
     
            // first '1' lies to the right of 'mid'
            else
                low = mid + 1;
        }
     
        // 1's are not present in the array
        return -1;
    }
    
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int arr[] = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        int n = arr.length;
        System.out.println(indexOfFirstOne(arr, 0,
                                              n - 1));
        
    }
  }
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python3 implementation to find 
# the index of first '1' in a 
# sorted array of 0's and 1's

# function to find the index of first '1'
# binary search technique is applied
def indexOfFirstOne( arr, low, high):

    while (low <= high):
        
        mid = int((low + high) / 2)

        # if true, then 'mid' is the index of first '1'
        if (arr[mid] == 1 and (mid == 0 or arr[mid - 1] == 0)):
            return mid

        # first '1' lies to the left of 'mid'
        elif (arr[mid] == 1):
            high = mid - 1

        # first '1' lies to the right of 'mid'
        else:
            low = mid + 1
    

    # 1's are not present in the array
    return -1;

# Driver program to test above
arr = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ]
n = len(arr)
ans = indexOfFirstOne(arr, 0, n - 1)
print (ans)

# This code is contributed by saloni1297

// C# program to find the index of
// first '1' in a sorted array of 0's and 1's
using System;

class GFG
{ 
    // function to find the index of first '1'
    // binary search technique is applied
    public static int indexOfFirstOne(int []arr, int low,
                                                int high)
    {
        while (low <= high) {
            int mid = (low + high) / 2;
    
            // if true, then 'mid' is the index of first '1'
            if (arr[mid] == 1 && (mid == 0 || arr[mid - 1] 
                                                    == 0))
                return mid;
    
            // first '1' lies to the left of 'mid'
            else if (arr[mid] == 1)
                high = mid - 1;
    
            // first '1' lies to the right of 'mid'
            else
                low = mid + 1;
        }
    
        // 1's are not present in the array
        return -1;
    }
    
    // Driver program 
    public static void Main() 
    {
        int []arr = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        int n = arr.Length;
        Console.Write(indexOfFirstOne(arr, 0, n - 1));
        
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP implementation to find 
// the index of first '1' in
// a sorted array of 0's and 1's

// function to find the index 
// of first '1' binary search
// technique is applied
function indexOfFirstOne($arr, 
                         $low, 
                         $high)
{
    while ($low <= $high) 
    {
        $mid = ceil($low + 
                    $high) / 2;

        // if true, then 'mid' is
        // the index of first '1'
        if ($arr[$mid] == 1 and 
            ($mid == 0 or 
              $arr[$mid - 1] == 0))
            return $mid;

        // first '1' lies to the
        // left of 'mid'
        else if ($arr[$mid] == 1)
            $high = $mid - 1;

        // first '1' lies to 
        // the right of 'mid'
        else
            $low = $mid + 1;
    }

    // 1's are not present 
    // in the array
    return -1;
}

// Driver Code
$arr = array(0, 0, 0, 0, 0, 
             0, 1, 1, 1, 1);
$n = count($arr);
echo indexOfFirstOne($arr, 0, $n - 1);

// This code is contributed by anuj_67.
?>

JavaScript

<script>

// Javascript implementation to find the index of first
// '1' in a sorted array of 0's and 1's

// function to find the index of first '1'
// binary search technique is applied
function indexOfFirstOne(arr, low, high)
{
    while (low <= high) {
        var mid = parseInt((low + high) / 2);

        // if true, then 'mid' is the index of first '1'
        if (arr[mid] == 1 && (mid == 0 || arr[mid - 1] == 0))
            return mid;

        // first '1' lies to the left of 'mid'
        else if (arr[mid] == 1)
            high = mid - 1;

        // first '1' lies to the right of 'mid'
        else
            low = mid + 1;
    }

    // 1's are not present in the array
    return -1;
}

// Driver program to test above
var arr = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1];
var n = arr.length;
document.write( indexOfFirstOne(arr, 0, n - 1));

// This code is contributed by rrrtnx.
</script>

Output

Time Complexity: O(Logn)
Auxiliary Space: O(1)

Find start and ending index of an element in an unsorted array

Ayush Jauhari

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Find the index of first 1 in a sorted array of 0's and 1's

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