# Find the Longest Increasing Subsequence in Circular manner

Given an array, the task is to find to LIS (Longest Increasing Subsequence) in a circular way.

Examples :

```Input : arr[] = {5, 4, 3, 2, 1}
Output : 2
Although there is no LIS in a given array
but in a circular form there can be
{1, 5}, {2, 5}, ......

Input : arr[]= {5, 6, 7, 1, 2, 3}
Output : 6
{1, 2, 3, 5, 6, 7} will be the LIS in the
circular manner.
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

1. Append the same elements(i.e. whole array) with the given array.
2. For every window of size n(no. of elements in the given array), perform LIS.
3. Return maximum length.
```For example : Given array is {1, 4, 6, 2, 3}

After appending elements resultant array
will be {1, 4, 6, 2, 3, 1, 4, 6, 2, 3}.

Now for every consecutive n elements perform LIS.
1- {1, 4, 6, 2, 3} --3 is length of LIS.
2- {4, 6, 2, 3, 1} --2 is length of LIS.
3- {6, 2, 3, 1, 4} --3
4- {2, 3, 1, 4, 6}-- 4 {2, 3, 4, 6}
5- {3, 1, 4, 6, 2} --3.
6- {1, 4, 6, 2, 3} Original list.

So, maximum length of LIS in circular manner is 4. ```

As in the last window we will have the same elements as in the given array which we don’t need to compute again, so we can append only n-1 elements to reduce the number of operations.

 `// C++ implementation to find LIS in circular way ` `#include ` `using` `namespace` `std; ` ` `  `// Utility function to find LIS using Dynamic programming ` `int` `computeLIS(``int` `circBuff[], ``int` `start, ``int` `end, ``int` `n) ` `{ ` `    ``int` `LIS[end-start]; ` ` `  `    ``/* Initialize LIS values for all indexes */` `    ``for` `(``int` `i = start; i < end; i++) ` `        ``LIS[i] = 1; ` ` `  `    ``/* Compute optimized LIS values in bottom up manner */` `    ``for` `(``int` `i = start + 1; i < end; i++) ` ` `  `        ``// Set j on the basis of current window ` `        ``// i.e. first element of the current window ` `        ``for` `(``int` `j = start; j < i; j++ ) ` `            ``if` `(circBuff[i] > circBuff[j] && LIS[i] < LIS[j] + 1) ` `                ``LIS[i] = LIS[j] + 1; ` ` `  `    ``/* Pick maximum of all LIS values */` `    ``int` `res = INT_MIN; ` `    ``for` `(``int` `i = start; i < end; i++) ` `        ``res = max(res, LIS[i]); ` ` `  `    ``return` `res; ` `} ` ` `  `// Function to find Longest Increasing subsequence in ` `// Circular manner ` `int` `LICS(``int` `arr[], ``int` `n) ` `{ ` `    ``// Make a copy of given array by appending same ` `    ``// array elements  to itself ` `    ``int` `circBuff[2 * n]; ` `    ``for` `(``int` `i = 0; i

 `// Java implementation to find LIS in circular way ` ` `  `class` `Test ` `{ ` `    ``// Utility method to find LIS using Dynamic programming ` `    ``static` `int` `computeLIS(``int` `circBuff[], ``int` `start, ``int` `end, ``int` `n) ` `    ``{ ` `        ``int` `LIS[] = ``new` `int``[n+end-start]; ` `      `  `        ``/* Initialize LIS values for all indexes */` `        ``for` `(``int` `i = start; i < end; i++) ` `            ``LIS[i] = ``1``; ` `      `  `        ``/* Compute optimized LIS values in bottom up manner */` `        ``for` `(``int` `i = start + ``1``; i < end; i++) ` `      `  `            ``// Set j on the basis of current window ` `            ``// i.e. first element of the current window ` `            ``for` `(``int` `j = start; j < i; j++ ) ` `                ``if` `(circBuff[i] > circBuff[j] && LIS[i] < LIS[j] + ``1``) ` `                    ``LIS[i] = LIS[j] + ``1``; ` `      `  `        ``/* Pick maximum of all LIS values */` `        ``int` `res = Integer.MIN_VALUE; ` `        ``for` `(``int` `i = start; i < end; i++) ` `            ``res = Math.max(res, LIS[i]); ` `      `  `        ``return` `res; ` `    ``} ` `      `  `    ``// Function to find Longest Increasing subsequence in ` `    ``// Circular manner ` `    ``static` `int` `LICS(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Make a copy of given array by appending same ` `        ``// array elements  to itself ` `        ``int` `circBuff[] = ``new` `int``[``2` `* n]; ` `        ``for` `(``int` `i = ``0``; i

 `# Python3 implementation to find  ` `# LIS in circular way Utility  ` `# function to find LIS using  ` `# Dynamic programmi ` `def` `computeLIS(circBuff, start, end, n): ` `    ``LIS ``=` `[``0` `for` `i ``in` `range``(end)] ` `     `  `    ``# Initialize LIS values  ` `    ``# for all indexes  ` `    ``for` `i ``in` `range``(start, end): ` `        ``LIS[i] ``=` `1` `         `  `    ``# Compute optimized LIS values ` `    ``# in bottom up manner ` `    ``for` `i ``in` `range``(start ``+` `1``, end): ` `         `  `        ``# Set j on the basis of current  ` `        ``# window i.e. first element of ` `        ``# the current window  ` `        ``for` `j ``in` `range``(start,i): ` `            ``if` `(circBuff[i] > circBuff[j] ``and`  `                ``LIS[i] < LIS[j] ``+` `1``): ` `                ``LIS[i] ``=` `LIS[j] ``+` `1` `                 `  `    ``# Pick maximum of all LIS values ` `    ``res ``=` `-``100000` `    ``for` `i ``in` `range``(start, end): ` `        ``res ``=` `max``(res, LIS[i]) ` `    ``return` `res ` ` `  `# Function to find Longest Increasing  ` `# subsequence in Circular manner ` `def` `LICS(arr, n): ` `     `  `    ``# Make a copy of given  ` `    ``# array by appending same  ` `    ``# array elements to itself  ` `    ``circBuff ``=` `[``0` `for` `i ``in` `range``(``2` `*` `n)] ` `    ``for` `i ``in` `range``(n): ` `        ``circBuff[i] ``=` `arr[i] ` `    ``for` `i ``in` `range``(n, ``2` `*` `n): ` `        ``circBuff[i] ``=` `arr[i ``-` `n] ` `         `  `    ``# Perform LIS for each ` `    ``# window of size n  ` `    ``res ``=` `-``100000` `    ``for` `i ``in` `range``(n): ` `        ``res ``=` `max``(computeLIS(circBuff, i,  ` `                             ``i ``+` `n, n), res) ` `    ``return` `res ` ` `  `# Driver code ` `arr ``=` `[ ``1``, ``4``, ``6``, ``2``, ``3` `] ` `n ``=` `len``(arr) ` `print``(``"Length of LICS is"``, LICS(arr, n)) ` ` `  `# This code is contributed  ` `# by sahilshelangia `

 `// C# implementation to find  ` `// LIS in circular way ` `using` `System; ` ` `  `class` `Test ` `{ ` `    ``// Utility method to find LIS ` `    ``// using Dynamic programming ` `    ``static` `int` `computeLIS(``int` `[]circBuff, ``int` `start,  ` `                                     ``int` `end, ``int` `n) ` `    ``{ ` `        ``int` `[]LIS = ``new` `int``[n+end-start]; ` `     `  `        ``/* Initialize LIS values for all indexes */` `        ``for` `(``int` `i = start; i < end; i++) ` `            ``LIS[i] = 1; ` `     `  `        ``/* Compute optimized LIS values  ` `           ``in bottom up manner */` `        ``for` `(``int` `i = start + 1; i < end; i++) ` `     `  `            ``// Set j on the basis of current window ` `            ``// i.e. first element of the current window ` `            ``for` `(``int` `j = start; j < i; j++ ) ` `                ``if` `(circBuff[i] > circBuff[j] &&  ` `                            ``LIS[i] < LIS[j] + 1) ` `                    ``LIS[i] = LIS[j] + 1; ` `     `  `        ``/* Pick maximum of all LIS values */` `        ``int` `res = ``int``.MinValue; ` `        ``for` `(``int` `i = start; i < end; i++) ` `            ``res = Math.Max(res, LIS[i]); ` `     `  `        ``return` `res; ` `    ``} ` `     `  `    ``// Function to find Longest Increasing  ` `    ``// subsequence in Circular manner ` `    ``static` `int` `LICS(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``// Make a copy of given array by  ` `        ``// appending same array elements to itself ` `        ``int` `[]circBuff = ``new` `int``[2 * n]; ` `         `  `        ``for` `(``int` `i = 0; i

 ` ``\$circBuff``[``\$j``] &&  ` `                     ``\$LIS``[``\$i``] < ``\$LIS``[``\$j``] + 1) ` `                ``\$LIS``[``\$i``] = ``\$LIS``[``\$j``] + 1; ` ` `  `    ``/* Pick maximum of ` `    ``all LIS values */` `    ``\$res` `= PHP_INT_MIN; ` `    ``for` `(``\$i` `= ``\$start``; ``\$i` `< ``\$end``; ``\$i``++) ` `        ``\$res` `= max(``\$res``, ``\$LIS``[``\$i``]); ` ` `  `    ``return` `\$res``; ` `} ` ` `  `// Function to find LIS  ` `// in Circular manner ` `function` `LICS(``\$arr``, ``\$n``) ` `{ ` `    ``// Make a copy of given array ` `    ``// by appending same array ` `    ``// elements to itself ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``\$circBuff``[``\$i``] = ``\$arr``[``\$i``]; ` `    ``for` `(``\$i` `= ``\$n``; ``\$i` `< 2 * ``\$n``; ``\$i``++) ` `        ``\$circBuff``[``\$i``] = ``\$arr``[``\$i` `- ``\$n``]; ` ` `  `    ``// Perform LIS for each  ` `    ``// window of size n ` `    ``\$res` `= PHP_INT_MIN; ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``\$res` `= max(computeLIS(``\$circBuff``, ``\$i``,  ` `                              ``\$i` `+ ``\$n``, ``\$n``),  ` `                              ``\$res``); ` ` `  `    ``return` `\$res``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``(1, 4, 6, 2, 3); ` `\$n` `= sizeof(``\$arr``); ` ` `  `echo` `"Length of LICS is "` `,  ` `            ``LICS(``\$arr``, ``\$n``); ` `     `  `// This code is contributed by aj_36 ` `?> `

Output :
```Length of LICS is 4
```

Time complexity of above solution is O(n3). It can be reduced O(n2 Log n) using O(n Log n) algorithm to find LIS.

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.