# Generate an array of size N according to the given rules

Given a number N, the task is to create an array arr[] of size N, where the value of the element at every index i is filled according to the following rules:

1. arr[i] = ((i – 1) – k), where k is the index of arr[i – 1] that has appeared second most recently. This rule is applied when arr[i – 1] is present more than once in the array
2. arr[i] = 0. This rule is applied when arr[i – 1] is present only once or when i = 1.

Examples:

Input: N = 8
Output: 0 0 1 0 2 0 2 2
Explanation:
For i = 0: There is no element in the array arr[]. So, 0 is placed in the first index. arr[] = {0}.
For i = 1: There is only one element in the array arr[]. The occurrence of arr[i – 1] (= 0) is only one. Therefore, the array is filled according to the rule 2. arr = {0, 0}.
For i = 2: There are two elements in the array. The second most occurrence of arr[i – 1] = arr = 0. So, arr = 1. arr[] = {0, 0, 1}.
For i = 3: There is no second occurrence of arr[i – 1] = 1. Therefore, arr = 0. arr[] = {0, 0, 1, 0}
For i = 4: The second recent occurrence of arr[i – 1] = 0 is 1. Therefore, (i – 1 – k) = (4 – 1 – 1) = 2. arr[] = {0, 0, 1, 0, 2}.
For i = 5: There is only one occurrence of arr[i – 1] = 2. Therefore, arr = 0. arr[] = {0, 0, 1, 0, 2, 0}.
For i = 6: The second recent occurrence of arr[i – 1] = 0 is 3. Therefore, (i – 1 – k) = (6 – 1 – 3) = 2. arr[] = {0, 0, 1, 0, 2, 0, 2}.
For i = 7: The second recent occurrence of arr[i – 1] = 2 is 4. Therefore, (i – 1 – k) = (7 – 1 – 4) = 2. arr[] = {0, 0, 1, 0, 2, 0, 2, 2}
Input: N = 5
Output: 0 0 1 0 2

Approach: The idea is to first create an array filled with zeroes of size N. Then for every iteration, we search if the element has occurred in the near past. If yes, then we follow rule 1. Else, rule 2 is followed to fill the array.
Below is the implementation of the above approach:

## C++

 `// C++ implementation to generate ` `// an array of size N by following ` `// the given rules` `#include ` `using` `namespace` `std;`   `// Function to search the most recent ` `// location of element N ` `// If not present in the array ` `// it will return -1 ` `int` `search(``int` `a[], ``int` `k, ``int` `x)` `{` `    ``int` `j;` `    `  `    ``for` `( j = k - 1; j > -1 ; j--)` `    ``{` `        ``if``(a[j] == x)` `            ``return` `j ;` `    ``}` `                `  `        ``return` `-1 ;` `}`   `// Function to generate an array ` `// of size N by following the given rules ` `void` `genArray(``int` `arr[], ``int` `N)` `{ `   `    ``// Loop to fill the array ` `    ``// as per the given rules ` `    ``for``(``int` `i = 0; i < N - 1; i++)` `    ``{ `   `        ``// Check for the occurrence ` `        ``// of arr[i - 1] ` `        ``if``(search(arr, i, arr[i]) == -1)` `                ``arr[i + 1] = 0 ;`   `        ``else` `            ``arr[i + 1] = (i-search(arr, i, arr[i])) ;` `    ``}` `} `   `// Driver code` `int` `main()` `{` `    ``int` `N = 5 ;` `    ``int` `size = N + 1 ;` `    ``int` `a[] = {0, 0, 0, 0, 0}; ` `    ``genArray(a, N) ;` `    `  `    ``for` `(``int` `i = 0; i < N ; i ++)` `        ``cout << a[i] << ``" "` `;` `        ``return` `0;` `}`     `// This code is contributed by shivanisinghss2110`

## Java

 `// Java implementation to generate ` `// an array of size N by following ` `// the given rules` `class` `GFG ` `{`   `static` `int` `a[];`   `// Function to search the most recent ` `// location of element N ` `// If not present in the array ` `// it will return -1 ` `static` `int` `search(``int` `a[],``int` `k, ``int` `x)` `{` `    ``int` `j;` `    `  `    ``for` `( j = k - ``1``; j > -``1` `; j--)` `    ``{` `            ``if``(a[j] == x)` `                ``return` `j ;` `        ``}` `                `  `        ``return` `-``1` `;` `}`   `// Function to generate an array ` `// of size N by following the given rules ` `static` `void` `genArray(``int` `[]arr, ``int` `N)` `{ `   `    ``// Loop to fill the array ` `    ``// as per the given rules ` `    ``for``(``int` `i = ``0``; i < N - ``1``; i++)` `    ``{ `   `        ``// Check for the occurrence ` `        ``// of arr[i - 1] ` `        ``if``(search(arr, i, arr[i]) == -``1``)` `                ``arr[i + ``1``] = ``0` `;`   `        ``else` `            ``arr[i + ``1``] = (i-search(arr, i, arr[i])) ;` `    ``}` `} `   `// Driver code ` `public` `static` `void` `main (String[] args) ` `{` `    ``int` `N = ``5` `;` `    ``int` `size = N + ``1` `;` `    ``int` `a[] = ``new` `int` `[N]; ` `    ``genArray(a, N) ;` `    `  `    ``for` `(``int` `i = ``0``; i < N ; i ++)` `        ``System.out.print(a[i]+``" "` `);`   `}` `}`   `// This code is contributed by Yash_R`

## Python3

 `# Python implementation to generate ` `# an array of size N by following ` `# the given rules`     `# Function to search the most recent ` `# location of element N` `# If not present in the array ` `# it will return -1` `def` `search(a, k, x):` `        ``for` `j ``in` `range``(k``-``1``, ``-``1``, ``-``1``) :` `            ``if``(a[j]``=``=` `x):` `                ``return` `j` `                `  `        ``return` `-``1`   `# Function to generate an array ` `# of size N by following the given rules` `def` `genArray(arr, N):`   `    ``# Loop to fill the array` `    ``# as per the given rules` `    ``for` `i ``in` `range``(``0``, N``-``1``, ``1``):`   `        ``# Check for the occurrence ` `        ``# of arr[i - 1]` `        ``if``(search(arr, i, arr[i])``=``=``-``1``):` `                ``arr[i ``+` `1``]``=` `0`   `        ``else``:` `            ``arr[i ``+` `1``]``=``(i``-``search(arr, i, arr[i]))` `            `  `# Driver code      ` `if` `__name__ ``=``=` `"__main__"``:` `    ``N ``=` `5` `    ``size ``=` `N ``+` `1` `    ``a ``=``[``0``]``*``N` `    ``genArray(a, N)` `    `  `    ``print``(a)`

## C#

 `// C# implementation to generate ` `// an array of size N by following ` `// the given rules`   `using` `System;`   `public` `class` `GFG ` `{`   `static` `int` `[]a;`   `// Function to search the most recent ` `// location of element N ` `// If not present in the array ` `// it will return -1 ` `static` `int` `search(``int` `[]a,``int` `k, ``int` `x)` `{` `    ``int` `j;` `    `  `    ``for` `( j = k - 1; j > -1 ; j--)` `    ``{` `            ``if``(a[j] == x)` `                ``return` `j ;` `        ``}` `                `  `        ``return` `-1 ;` `}`   `// Function to generate an array ` `// of size N by following the given rules ` `static` `void` `genArray(``int` `[]arr, ``int` `N)` `{ `   `    ``// Loop to fill the array ` `    ``// as per the given rules ` `    ``for``(``int` `i = 0; i < N - 1; i++)` `    ``{ `   `        ``// Check for the occurrence ` `        ``// of arr[i - 1] ` `        ``if``(search(arr, i, arr[i]) == -1)` `                ``arr[i + 1] = 0 ;`   `        ``else` `            ``arr[i + 1] = (i-search(arr, i, arr[i])) ;` `    ``}` `} `   `// Driver code ` `public` `static` `void` `Main (``string``[] args) ` `{` `    ``int` `N = 5 ;` `    ``int` `size = N + 1 ;` `    ``int` `[]a = ``new` `int` `[N]; ` `    ``genArray(a, N) ;` `    `  `    ``for` `(``int` `i = 0; i < N ; i ++)` `        ``Console.Write(a[i]+``" "` `);`   `}` `}` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:

`[0, 0, 1, 0, 2]`

Time Complexity: O(N2)

Auxiliary Space: O(1)

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