# Largest increasing subsequence of consecutive integers

Given an array of n positive integers. We need to find the largest increasing sequence of consecutive positive integers.

Examples:

```Input : arr[] = {5, 7, 6, 7, 8}
Output : Size of LIS = 4
LIS = 5, 6, 7, 8

Input : arr[] = {5, 7, 8, 7, 5}
Output : Size of LIS = 2
LIS = 7, 8
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

This problem can be solved easily by the concept of LIS where each next greater element differ from earlier one by 1. But this will take O(n^2) time complexity.

With the use of hashing we can finding the size of longest increasing sequence with consecutive integers in time complexity of O(n).

We create a hash table.. Now for each element arr[i], we perform hash[arr[i]] = hash[arr[i] – 1] + 1. So, for every element we know longest consecutive increasing subsequence ending with it. Finally we return maximum value from hash table.

 `// C++ implementation of longest continuous increasing ` `// subsequence ` `#include ` `using` `namespace` `std; ` ` `  `// Function for LIS ` `int` `findLIS(``int` `A[], ``int` `n) ` `{ ` `    ``unordered_map<``int``, ``int``> hash; ` ` `  `    ``// Initialize result ` `    ``int` `LIS_size = 1; ` `    ``int` `LIS_index = 0; ` ` `  `    ``hash[A] = 1; ` ` `  `    ``// iterate through array and find ` `    ``// end index of LIS and its Size ` `    ``for` `(``int` `i = 1; i < n; i++) { ` `        ``hash[A[i]] = hash[A[i] - 1] + 1; ` `        ``if` `(LIS_size < hash[A[i]]) { ` `            ``LIS_size = hash[A[i]]; ` `            ``LIS_index = A[i]; ` `        ``} ` `    ``} ` ` `  `    ``// print LIS size ` `    ``cout << ``"LIS_size = "` `<< LIS_size << ````" "````; ` ` `  `    ``// print LIS after setting start element ` `    ``cout << ``"LIS : "``; ` `    ``int` `start = LIS_index - LIS_size + 1; ` `    ``while` `(start <= LIS_index) { ` `        ``cout << start << ``" "``; ` `        ``start++; ` `    ``} ` `} ` ` `  `// driver ` `int` `main() ` `{ ` `    ``int` `A[] = { 2, 5, 3, 7, 4, 8, 5, 13, 6 }; ` `    ``int` `n = ``sizeof``(A) / ``sizeof``(A); ` `    ``findLIS(A, n); ` `    ``return` `0; ` `} `

Output:

```LIS_size = 5
LIS : 2 3 4 5 6
```

## tags:

Arrays Hash cpp-unordered_map LIS Arrays Hash