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

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.

Try It Yourself

Table of Content

[Naive Approach] Using Linear Search - O(n) Time O(1) Space
[Efficient Approach] Using Binary Search - O(Log n)Time O(1) Space

[Naive Approach] Using Linear Search - O(n) Time O(1) Space

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"

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 firstIndex(vector<int> &arr)
{
    int n = arr.size();  // fix: define n

    for (int i = 0; i < n; i++)
        if (arr[i] == 1)
            return i;

    return -1;
}

// Driver Code
int main()
{
    vector<int> arr = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
    cout << firstIndex(arr); 
    return 0;
}

Java

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

public class GfG {
    
    // function to find the index of first '1'
    static int firstIndex(int[] arr) {
        int n = arr.length;  // fix: define n

        for (int i = 0; i < n; i++)
            if (arr[i] == 1)
                return i;

        return -1;
    }
    
    // Driver Code
    public static void main(String[] args) {
        int[] arr = { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        System.out.println(firstIndex(arr)); 
    }
}

Python

# 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 firstIndex(arr):
    n = len(arr) 

    for i in range(n):
        if arr[i] == 1:
            return i

    return -1
    
#Driver Code
arr = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1]
print(firstIndex(arr))

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

public class GfG
{
    // function to find the index of first '1'
    public static int firstIndex(List<int> arr)
    {
        int n = arr.Count;  

        for (int i = 0; i < n; i++)
            if (arr[i] == 1)
                return i;

        return -1;
    }
    
    // Driver Code
    public static void Main()
    {
        List<int> arr = new List<int> { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 };
        Console.WriteLine(firstIndex(arr));
    }
}

JavaScript

// 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 firstIndex(arr) {
    let n = arr.length;  

    for (let i = 0; i < n; i++)
        if (arr[i] === 1)
            return i;

    return -1;
}
//Driver Code
let arr = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1];
console.log(firstIndex(arr));

Output

[Efficient Approach] Using Binary Search - O(Log n)Time O(1) Space

Use the technique of binary search on the sorted array, so as to find the index of first '1'.

Algorithm:

Initialize low = 0 and high = n - 1.
Find mid = (low + high) / 2 and check the value at mid.
If arr[mid] == 1 and it is the first occurrence, return mid.
If arr[mid] == 1, move left (high = mid - 1); else move right (low = mid + 1).
Repeat until found; if not, return -1.

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'
// using binary search technique
int firstIndex(vector<int> &arr)
{
    int low = 0;
    int high = arr.size() - 1;

    // iterate while search space is valid
    while (low <= high)
    {
        int mid = (low + high) / 2;

        // check if mid is the first occurrence of '1'
        if (arr[mid] == 1 && (mid == 0 || arr[mid - 1] == 0))
            return mid;

        // if '1' is found but not first, move to left half
        else if (arr[mid] == 1)
            high = mid - 1;

        // if '0' is found, move to right half
        else
            low = mid + 1;
    }

    // if '1' is not present in the array
    return -1;
}

// Driver program to test above function
int main()
{
    vector<int> arr = {0, 0, 0, 0, 0, 0, 1, 1, 1, 1};

    // function call
    cout << firstIndex(arr);

    return 0;
}