# Counts 1s that can be obtained in an Array by performing given operations

Given an array arr[] of size N consisting of only of 0s initially, the task is to count the number of 1s that can be obtained in the array by performing the following operation N times.

In i th operation, flip all the array elements whose index ( 1-based indexing ) is a multiple of i.

Examples:

Input: arr[] = { 0, 0, 0, 0, 0 }
Output:
Explanation:
Flipping array elements whose index is multiple of 1 modifies arr[] to { 1, 1, 1, 1, 1 }
Flipping array elements whose index is multiple of 2 modifies arr[] to { 1, 0, 1, 0, 1 }
Flipping array elements whose index is multiple of 3 modifies arr[] to { 1, 0, 0, 0, 1 }
Flipping array elements whose index is multiple of 4 modifies arr[] to { 1, 0, 0, 1, 1 }
Flipping array elements whose index is multiple of 5 modifies arr[] to { 1, 0, 0, 1, 0 }
Therefore, the required output is 2.

Input: arr[] = { 0, 0 }
Output:

Naive Approach: The simplest approach to solve this problem is to iterate over the range [1, N] using variable i and flip all the array elements whose index is a multiple of i. Finally, print the count of total number of 1s present in the array.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to count total number of 1s in` `// array by performing given operations` `int` `cntOnesArrWithGivenOp(``int` `arr[], ``int` `N)` `{` `    ``// Stores count of 1s in the array` `    ``// by performing the operations` `    ``int` `cntOnes = 0;`   `    ``// Iterate over the range [1, N]` `    ``for` `(``int` `i = 1; i <= N; i++) {`   `        ``// Flip all array elements whose` `        ``// index is multiple of i` `        ``for` `(``int` `j = i - 1; j < N;` `             ``j += i) {`   `            ``// Update arr[i]` `            ``arr[j] = !(arr[j]);` `        ``}` `    ``}`   `    ``// Traverse the array` `    ``for` `(``int` `i = 0; i < N; i++) {`   `        ``// If current element is 1` `        ``if` `(arr[i] == 1) {`   `            ``// Update cntOnes` `            ``cntOnes += 1;` `        ``}` `    ``}`   `    ``return` `cntOnes;` `}`   `// Driver Code` `int` `main()` `{`   `    ``int` `arr[] = { 0, 0, 0, 0, 0 };`   `    ``int` `N = ``sizeof``(arr)` `            ``/ ``sizeof``(arr[0]);`   `    ``cout << cntOnesArrWithGivenOp(arr, N);`   `    ``return` `0;` `}`

## Java

 `// Java program to implement` `// the above approach` `import` `java.io.*;` `class` `GFG ` `{`   `    ``// Function to count total number of 1s in` `    ``// array by performing given operations` `    ``static` `int` `cntOnesArrWithGivenOp(``int` `arr[], ``int` `N)` `    ``{` `      `  `        ``// Stores count of 1s in the array` `        ``// by performing the operations` `        ``int` `cntOnes = ``0``;`   `        ``// Iterate over the range [1, N]` `        ``for` `(``int` `i = ``1``; i <= N; i++)` `        ``{`   `            ``// Flip all array elements whose` `            ``// index is multiple of i` `            ``for` `(``int` `j = i - ``1``; j < N; j += i)` `            ``{`   `                ``// Update arr[i]` `                ``arr[j] = arr[j] == ``0` `? ``1` `: ``0``;` `            ``}` `        ``}`   `        ``// Traverse the array` `        ``for` `(``int` `i = ``0``; i < N; i++)` `        ``{`   `            ``// If current element is 1` `            ``if` `(arr[i] == ``1``)` `            ``{`   `                ``// Update cntOnes` `                ``cntOnes += ``1``;` `            ``}` `        ``}` `        ``return` `cntOnes;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``0``, ``0``, ``0``, ``0``, ``0` `};` `        ``int` `N = arr.length;` `        ``System.out.print(cntOnesArrWithGivenOp(arr, N));` `    ``}` `}`   `// This code is contributed by shikhasingrajput`

## Python3

 `# Python3 program to implement` `# the above approach`   `# Function to count total number of 1s in` `# array by performing given operations` `def` `cntOnesArrWithGivenOp(arr, N):` `    `  `    ``# Stores count of 1s in the array` `    ``# by performing the operations` `    ``cntOnes ``=` `0` `    `  `    ``# Iterate over the range [1, N]` `    ``for` `i ``in` `range``(``1``, N ``+` `1``):` `        `  `        ``# Flip all array elements whose` `        ``# index is multiple of i` `        ``for` `j ``in` `range``(i ``-` `1``, N, i):` `            `  `            ``# Update arr[i]` `            ``arr[j] ``=` `1` `if` `arr[j] ``=``=` `0` `else` `0`   `    ``# Traverse the array` `    ``for` `i ``in` `range``(N):`   `        ``# If current element is 1` `        ``if` `(arr[i] ``=``=` `1``):` `            `  `            ``# Update cntOnes` `            ``cntOnes ``+``=` `1`   `    ``return` `cntOnes`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``arr ``=` `[ ``0``, ``0``, ``0``, ``0``, ``0` `]` `    ``N ``=` `len``(arr)` `    `  `    ``print``(cntOnesArrWithGivenOp(arr, N))`   `# This code is contributed by 29AjayKumar`

## C#

 `// C# program to implement` `// the above approach` `using` `System;` `class` `GFG ` `{`   `    ``// Function to count total number of 1s in` `    ``// array by performing given operations` `    ``static` `int` `cntOnesArrWithGivenOp(``int` `[]arr, ``int` `N)` `    ``{` `      `  `        ``// Stores count of 1s in the array` `        ``// by performing the operations` `        ``int` `cntOnes = 0;`   `        ``// Iterate over the range [1, N]` `        ``for` `(``int` `i = 1; i <= N; i++)` `        ``{`   `            ``// Flip all array elements whose` `            ``// index is multiple of i` `            ``for` `(``int` `j = i - 1; j < N; j += i)` `            ``{`   `                ``// Update arr[i]` `                ``arr[j] = arr[j] == 0 ? 1 : 0;` `            ``}` `        ``}`   `        ``// Traverse the array` `        ``for` `(``int` `i = 0; i < N; i++)` `        ``{`   `            ``// If current element is 1` `            ``if` `(arr[i] == 1)` `            ``{`   `                ``// Update cntOnes` `                ``cntOnes += 1;` `            ``}` `        ``}` `        ``return` `cntOnes;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int` `[]arr = { 0, 0, 0, 0, 0 };` `        ``int` `N = arr.Length;` `        ``Console.Write(cntOnesArrWithGivenOp(arr, N));` `    ``}` `}`   `// This code contributed by shikhasingrajput`

## Javascript

 ``

Output:

`2`

Time Complexity: O(N2)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is based on the fact that only perfect squares contain odd number of factors. Follow the steps below to solve the problem:

• Initialize a variable, say cntOnes, to store the count of 1s in the array by performing the operations.
• Update cntOnes = sqrt(N)
• Finally, print the value of cntOnes.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to count total number of 1s in` `// array by performing the given operations` `int` `cntOnesArrWithGivenOp(``int` `arr[], ``int` `N)` `{`   `    ``// Stores count of 1s in the array` `    ``// by performing the operations` `    ``int` `cntOnes = 0;`   `    ``// Update cntOnes` `    ``cntOnes = ``sqrt``(N);`   `    ``return` `cntOnes;` `}`   `// Driver Code` `int` `main()` `{`   `    ``int` `arr[] = { 0, 0, 0, 0, 0 };`   `    ``int` `N = ``sizeof``(arr)` `            ``/ ``sizeof``(arr[0]);`   `    ``cout << cntOnesArrWithGivenOp(arr, N);`   `    ``return` `0;` `}`

## Java

 `// Java program to implement ` `// the above approach ` `import` `java.io.*;` `class` `GFG` `{`   `  ``// Function to count total number of 1s in` `  ``// array by performing the given operations` `  ``static` `int` `cntOnesArrWithGivenOp(``int` `arr[], ``int` `N)` `  ``{`   `    ``// Stores count of 1s in the array` `    ``// by performing the operations` `    ``int` `cntOnes = ``0``;`   `    ``// Update cntOnes` `    ``cntOnes = (``int``)Math.sqrt(N); ` `    ``return` `cntOnes;` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `main(String[] args)` `  ``{` `    ``int` `arr[] = { ``0``, ``0``, ``0``, ``0``, ``0` `};` `    ``int` `N = arr.length;` `    ``System.out.println(cntOnesArrWithGivenOp(arr, N));` `  ``}` `}`   `// This code is contributed by susmitakundugoaldanga`

## Python3

 `# Python3 program to implement` `# the above approach`   `# Function to count total number of 1s in` `# array by performing the given operations` `def` `cntOnesArrWithGivenOp(arr, N) :`   `    ``# Stores count of 1s in the array` `    ``# by performing the operations` `    ``cntOnes ``=` `0``;`   `    ``# Update cntOnes` `    ``cntOnes ``=` `int``(N ``*``*` `(``1``/``2``));` `    ``return` `cntOnes;`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[ ``0``, ``0``, ``0``, ``0``, ``0` `];` `    ``N ``=` `len``(arr);` `    ``print``(cntOnesArrWithGivenOp(arr, N));`   `    ``# This code is contributed by AnkThon`

## C#

 `// C# program to implement ` `// the above approach ` `using` `System;` `class` `GFG` `{`   `  ``// Function to count total number of 1s in` `  ``// array by performing the given operations` `  ``static` `int` `cntOnesArrWithGivenOp(``int` `[]arr, ``int` `N)` `  ``{`   `    ``// Stores count of 1s in the array` `    ``// by performing the operations` `    ``int` `cntOnes = 0;`   `    ``// Update cntOnes` `    ``cntOnes = (``int``)Math.Sqrt(N); ` `    ``return` `cntOnes;` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `Main(String[] args)` `  ``{` `    ``int` `[]arr = { 0, 0, 0, 0, 0 };` `    ``int` `N = arr.Length;` `    ``Console.WriteLine(cntOnesArrWithGivenOp(arr, N));` `  ``}` `}`   `// This code is contributed by shikhasingrajput`

## Javascript

 ``

Output:

`2`

Time Complexity: O(log2(N))
Auxiliary Space: O(1)

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