# Longest substring consisting of vowels using Binary Search

Given string str of length N, the task is to find the longest substring which contains only vowels using the Binary Search technique.
Examples:

Input: str = “baeicba”
Output:
Explanation:
Longest substring which contains vowels only is “aei”.
Input: str = “aeiou”
Output:

Approach: Refer to the Longest substring of vowels for an approach in O(N) complexity.
Binary Search Approach: In this article, we are using a Binary Search based approach:
Follow the steps below to solve the problem:

1. Apply binary search on the lengths ranging from 1 to N.
2. For each mid-value check if there exists a substring of length mid consisting only of vowels in that substring.
3. If there exists a substring of length mid, then update the value of max and update l as mid+1 to check if a substring of length greater than mid exists or not which consists only of vowels.
4. If no such substring of length mid exists, update r as mid-1 to check if a substring of length smaller than mid exists or not which consists only of vowels.
5. Repeat the above three steps until l is less than or equal to r.
6. Return the max length obtained finally.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to check if a character` `// is vowel or not` `bool` `vowel(``int` `vo)` `{` `    ``// 0-a 1-b 2-c and so on 25-z` `    ``if` `(vo == 0 || vo == 4` `        ``|| vo == 8 || vo == 14` `        ``|| vo == 20)` `        ``return` `true``;` `    ``else` `        ``return` `false``;` `}`   `// Function to check if any` `// substring of length k exists` `// which contains only vowels` `bool` `check(string s, ``int` `k)` `{` `    ``vector<``int``> cnt(26, 0);` `    ``for` `(``int` `i = 0; i < k - 1; i++) {` `        ``cnt[s[i] - ``'a'``]++;` `    ``}`   `    ``// Applying sliding window to get` `    ``// all substrings of length K` `    ``for` `(``int` `i = k - 1; i < s.size();` `         ``i++) {` `        ``cnt[s[i] - ``'a'``]++;` `        ``int` `flag1 = 0;` `        ``for` `(``int` `j = 0; j < 26; j++) {` `            ``if` `(vowel(j) == ``false` `                ``&& cnt[j] > 0) {` `                ``flag1 = 1;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(flag1 == 0)` `            ``return` `true``;`   `        ``// Remove the occurence of` `        ``// (i-k+1)th character` `        ``cnt[s[i - k + 1] - ``'a'``]--;` `    ``}`   `    ``return` `false``;` `}`   `// Function to perform  Binary Search` `int` `longestSubstring(string s)` `{` `    ``int` `l = 1, r = s.size();` `    ``int` `maxi = 0;`   `    ``// Doing binary search on the lengths` `    ``while` `(l <= r) {` `        ``int` `mid = (l + r) / 2;` `        ``if` `(check(s, mid)) {` `            ``l = mid + 1;` `            ``maxi = max(maxi, mid);` `        ``}` `        ``else` `            ``r = mid - 1;` `    ``}` `    ``return` `maxi;` `}`   `// Driver Code` `int` `main()` `{` `    ``string s = ``"sedrewaefhoiu"``;` `    ``cout << longestSubstring(s);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of` `// the above approach` `import` `java.util.*;` `class` `GFG{`   `// Function to check if a character` `// is vowel or not` `static` `boolean` `vowel(``int` `vo)` `{` `    ``// 0-a 1-b 2-c and so on 25-z` `    ``if` `(vo == ``0` `|| vo == ``4` `|| ` `        ``vo == ``8` `|| vo == ``14` `|| ` `        ``vo == ``20``)` `        ``return` `true``;` `    ``else` `        ``return` `false``;` `}`   `// Function to check if any` `// subString of length k exists` `// which contains only vowels` `static` `boolean` `check(String s, ``int` `k)` `{` `    ``int` `[]cnt = ``new` `int``[``26``];` `    ``for` `(``int` `i = ``0``; i < k - ``1``; i++) ` `    ``{` `        ``cnt[s.charAt(i) - ``'a'``]++;` `    ``}`   `    ``// Applying sliding window to get` `    ``// all subStrings of length K` `    ``for` `(``int` `i = k - ``1``; i < s.length(); i++)` `    ``{` `        ``cnt[s.charAt(i) - ``'a'``]++;` `        ``int` `flag1 = ``0``;` `        ``for` `(``int` `j = ``0``; j < ``26``; j++) ` `        ``{` `            ``if` `(vowel(j) == ``false` `&& cnt[j] > ``0``) ` `            ``{` `                ``flag1 = ``1``;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(flag1 == ``0``)` `            ``return` `true``;`   `        ``// Remove the occurence of` `        ``// (i-k+1)th character` `        ``cnt[s.charAt(i - k + ``1``) - ``'a'``]--;` `    ``}`   `    ``return` `false``;` `}`   `// Function to perform Binary Search` `static` `int` `longestSubString(String s)` `{` `    ``int` `l = ``1``, r = s.length();` `    ``int` `maxi = ``0``;`   `    ``// Doing binary search on the lengths` `    ``while` `(l <= r) ` `    ``{` `        ``int` `mid = (l + r) / ``2``;` `        ``if` `(check(s, mid)) ` `        ``{` `            ``l = mid + ``1``;` `            ``maxi = Math.max(maxi, mid);` `        ``}` `        ``else` `            ``r = mid - ``1``;` `    ``}` `    ``return` `maxi;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``String s = ``"sedrewaefhoiu"``;` `    ``System.out.print(longestSubString(s));` `}` `}`   `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 implementation of` `# the above approach`   `# Function to check if a character` `# is vowel or not` `def` `vowel(vo):`   `    ``# 0-a 1-b 2-c and so on 25-z` `    ``if` `(vo ``=``=` `0` `or` `vo ``=``=` `4` `or` `        ``vo ``=``=` `8` `or` `vo ``=``=` `14` `or` `        ``vo ``=``=` `20``):` `        ``return` `True` `    ``else``:` `        ``return` `False`   `# Function to check if any` `# substring of length k exists` `# which contains only vowels` `def` `check(s, k):`   `    ``cnt ``=` `[``0``] ``*` `26` `    ``for` `i ``in` `range` `(k ``-` `1``):` `        ``cnt[``ord``(s[i]) ``-` `ord``(``'a'``)] ``+``=` `1` `   `  `    ``# Applying sliding window to get` `    ``# all substrings of length K` `    ``for` `i ``in` `range` `(k ``-` `1``, ``len``(s)):` `        ``cnt[``ord``(s[i]) ``-` `ord``(``'a'``)] ``+``=` `1` `        ``flag1 ``=` `0` `        ``for` `j ``in` `range` `(``26``):` `            ``if` `(vowel(j) ``=``=` `False` `                ``and` `cnt[j] > ``0``):` `                ``flag1 ``=` `1` `                ``break` `        `  `        ``if` `(flag1 ``=``=` `0``):` `            ``return` `True`   `        ``# Remove the occurence of` `        ``# (i-k+1)th character` `        ``cnt[``ord``(s[i ``-` `k ``+` `1``]) ``-` `ord``(``'a'``)] ``-``=` `1`   `    ``return` `False`   `# Function to perform  Binary Search` `def` `longestSubstring(s):`   `    ``l ``=` `1` `    ``r ``=` `len``(s)` `    ``maxi ``=` `0`   `    ``# Doing binary search on the lengths` `    ``while` `(l <``=` `r):` `        ``mid ``=` `(l ``+` `r) ``/``/` `2` `        ``if` `(check(s, mid)):` `            ``l ``=` `mid ``+` `1` `            ``maxi ``=` `max``(maxi, mid)` `        ``else``:` `            ``r ``=` `mid ``-` `1` `    ``return` `maxi`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:  ` `    ``s ``=` `"sedrewaefhoiu"` `    ``print` `(longestSubstring(s))`   `# This code is contributed by Chitranayal`

## C#

 `// C# implementation of` `// the above approach` `using` `System;` `class` `GFG{` ` `  `// Function to check if a character` `// is vowel or not` `static` `bool` `vowel(``int` `vo)` `{` `    ``// 0-a 1-b 2-c and so on 25-z` `    ``if` `(vo == 0 || vo == 4 || ` `        ``vo == 8 || vo == 14 || ` `        ``vo == 20)` `        ``return` `true``;` `    ``else` `        ``return` `false``;` `}` ` `  `// Function to check if any` `// subString of length k exists` `// which contains only vowels` `static` `bool` `check(String s, ``int` `k)` `{` `    ``int` `[]cnt = ``new` `int``;` `    ``for` `(``int` `i = 0; i < k - 1; i++) ` `    ``{` `        ``cnt[s[i] - ``'a'``]++;` `    ``}` ` `  `    ``// Applying sliding window to get` `    ``// all subStrings of length K` `    ``for` `(``int` `i = k - 1; i < s.Length; i++)` `    ``{` `        ``cnt[s[i] - ``'a'``]++;` `        ``int` `flag1 = 0;` `        ``for` `(``int` `j = 0; j < 26; j++) ` `        ``{` `            ``if` `(vowel(j) == ``false` `&& cnt[j] > 0) ` `            ``{` `                ``flag1 = 1;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(flag1 == 0)` `            ``return` `true``;` ` `  `        ``// Remove the occurence of` `        ``// (i-k+1)th character` `        ``cnt[s[i - k + 1] - ``'a'``]--;` `    ``}` ` `  `    ``return` `false``;` `}` ` `  `// Function to perform Binary Search` `static` `int` `longestSubString(String s)` `{` `    ``int` `l = 1, r = s.Length;` `    ``int` `maxi = 0;` ` `  `    ``// Doing binary search on the lengths` `    ``while` `(l <= r) ` `    ``{` `        ``int` `mid = (l + r) / 2;` `        ``if` `(check(s, mid)) ` `        ``{` `            ``l = mid + 1;` `            ``maxi = Math.Max(maxi, mid);` `        ``}` `        ``else` `            ``r = mid - 1;` `    ``}` `    ``return` `maxi;` `}` ` `  `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    ``String s = ``"sedrewaefhoiu"``;` `    ``Console.Write(longestSubString(s));` `}` `}`   `// This code is contributed by sapnasingh4991`

Output:

```3

```

Time Complexity: O(NlogN)
Auxiliary Space: O(N)

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