# 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.

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 ` `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#

 `// 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

 ``

## Javascript

 `` `` `` `` `` `` `` `` `` ``

Output

`6`

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 ` `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#

 `// 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

 ``

## Javascript

 ``

Output

`6`

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

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