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# Longest Ordered Subsequence of Vowels

• Difficulty Level : Hard
• Last Updated : 09 Aug, 2021

Given a string consisting of only vowels, find the longest subsequence in the given string such that it consists of all five vowels and is a sequence of one or more a’s, followed by one or more e’s, followed by one or more i’s, followed by one or more o’s and followed by one or more u’s.

If there is more than one longest subsequence, print any one.

Examples:

```Input :  str = "aeiaaioooaauuaeiou"
Output :  {a, a, a, a, a, a, e, i, o, u}
There are two possible outputs in this case:
{a, a, a, a, a, a, e, i, o, u} and,
{a, e, i, i, o, o, o, u, u, u}
each of length 10

Input : str = "aaauuiieeou"
Output : No subsequence possible```

Approach:
We loop through all the characters in the string recursively and follow the given conditions:

1. If the subsequence is empty, we include the vowel at the current index only if it is ‘a’. Otherwise, we move on to the next index.
2. If the vowel at the current index is same as the last vowel included in the subsequence, we include it.
3. If the vowel at the current index is the next possible vowel (i.e a–> e–> i–> o–> u ) after the last vowel included in the subsequence, we have two options: either include it or move on to the next index. Hence we choose the one which gives the longest subsequence.
4. If none of the above conditions is satisfied, we move on to the next index (to avoid invalid ordering of vowels in the subsequence).
5. If we have reached the end of the string, we check if the current subsequence is valid or not. If it is valid (i.e if it contains all the vowels), we return it, else we return an empty list.

Method 1

Below is the implementation of the above approach:

## C++

 `// C++ program to find the longest subsequence``// of vowels in the specified order``#include ``using` `namespace` `std;` `vector<``char``> vowels = { ``'a'``, ``'e'``, ``'i'``, ``'o'``, ``'u'` `};` `// Mapping values for vowels``map<``char``, ``int``> mapping = { { ``'a'``, 0 }, { ``'e'``, 1 },``                           ``{ ``'i'``, 2 }, { ``'o'``, 3 },``                           ``{ ``'u'``, 4 } };`` ` `// Function to check if given subsequence``// contains all the vowels or not``bool` `isValidSequence(string subList)``{``    ``for``(``char` `c : vowels)``    ``{``        ` `        ``// not contain vowel``        ``if` `(subList.find(c) == std::string::npos)``            ``return` `0;``    ``} ``    ``return` `1;``}` `// Function to find the longest subsequence``// of vowels in the given string in specified``// order``string longestSubsequence(string str,``                          ``string subList,``                          ``int` `index)``{``    ` `    ``// If we have reached the end of the``    ``// string, return the subsequence``    ``// if it is valid, else return an``    ``// empty list``    ``int` `len = str.length();``    ` `    ``if` `(index >= len)``    ``{``        ``if` `(isValidSequence(subList))``            ``return` `subList;``        ``else``            ``return` `""``;``    ``}``    ` `    ``// If there is no vowel in the``    ``// subsequence yet, add vowel``    ``// at current index if it is 'a',``    ``// else move on to the next character``    ``// in the string ``    ``else` `if` `(subList.size() == 0)``   ``{``       ``if` `(str[index] != ``'a'``)``         ``return` `longestSubsequence(``             ``str, ``""``, index + 1);``       ``else``         ``return` `longestSubsequence(``             ``str, subList + str[index],``                    ``index + 1);``   ``}``   ` `    ``//  If the last vowel in the subsequence``    ``// until now is same as the vowel at``    ``// current index, add it to the subsequence``    ``else` `if` `(mapping[subList[subList.size() - 1]] ==``             ``mapping[str[index]])``        ``return` `longestSubsequence(``            ``str, subList+str[index], index + 1);``    ` `    ``// If the vowel at the current index comes``    ``// right after the last vowel in the``    ``// subsequence, we have two options:``    ``// either to add the vowel in the``    ``// subsequence, or move on to next character.``    ``// We choose the one which gives the longest``    ``// subsequence.``    ``else` `if` `(mapping[subList[subList.size() - 1]] + 1 ==``             ``mapping[str[index]])``    ``{``        ``string sub1 = longestSubsequence(``            ``str, subList + str[index], index + 1);``        ``string sub2 = longestSubsequence(``            ``str, subList, index + 1);``        ` `        ``if` `(sub1.length() > sub2.length())``            ``return` `sub1;``        ``else``            ``return` `sub2;``    ``}   ``    ``else``        ``return` `longestSubsequence(``            ``str, subList, index + 1);    ``}` `// Driver Code``int` `main()``{``    ``string  str= ``"aeiaaioooauuaeiou"``;``    ` `    ``string subsequence = longestSubsequence(``        ``str, ``""``, 0);``        ` `    ``if` `(subsequence.length() == 0)``        ``cout << ``"No subsequence possible\n"``;``    ``else``        ``cout << subsequence << ``"\n"``;``}` `// This code is contributed by ajaykr00kj`

## Python3

 `# Python3 program to find the longest subsequence``# of vowels in the specified order` `vowels ``=` `[``'a'``, ``'e'``, ``'i'``, ``'o'``, ``'u'``]` `# Mapping values for vowels``mapping ``=` `{``'a'``: ``0``, ``'e'``: ``1``, ``'i'``: ``2``, ``'o'``: ``3``, ``'u'``: ``4``}` `# Function to check if given subsequence``# contains all the vowels or not``def` `isValidSequence(subList):``    ` `    ``for` `vowel ``in` `vowels:``        ``if` `vowel ``not` `in` `subList:``            ``return` `False``            ` `    ``return` `True` `# Function to find the longest subsequence of vowels``# in the given string in specified order``def` `longestSubsequence(string, subList, index):``    ` `    ``# If we have reached the end of the string,``    ``# return the subsequence``    ``# if it is valid, else return an empty list``    ``if` `index ``=``=` `len``(string):``        ``if` `isValidSequence(subList) ``=``=` `True``:``            ``return` `subList``        ``else``:``            ``return` `[]``        ` `    ``else``:``        ``# If there is no vowel in the subsequence yet,``        ``# add vowel at current index if it is 'a',``        ``# else move on to the next character``        ``# in the string``        ``if` `len``(subList) ``=``=` `0``:``            ` `            ``if` `string[index] !``=` `'a'``:``                ``return` `longestSubsequence(string, subList, index ``+` `1``)``            ``else``:``                ``return` `longestSubsequence(string, subList ``+` `\``                            ``[string[index]], index ``+` `1``)``        ` `        ``# If the last vowel in the subsequence until``        ``# now is same as the vowel at current index,``        ``# add it to the subsequence``        ``elif` `mapping[subList[``-``1``]] ``=``=` `mapping[string[index]]:``            ``return` `longestSubsequence(string, subList ``+` `\``                            ``[string[index]], index ``+` `1``)``        ` `        ``# If the vowel at the current index comes``        ``# right after the last vowel``        ``# in the subsequence, we have two options:``        ``# either to add the vowel in``        ``# the subsequence, or move on to next character.``        ``# We choose the one which gives the longest subsequence.``        ``elif` `(mapping[subList[``-``1``]] ``+` `1``) ``=``=` `mapping[string[index]]:``            ` `            ``sub1 ``=` `longestSubsequence(string, subList ``+` `\``                                ``[string[index]], index ``+` `1``)``            ``sub2 ``=` `longestSubsequence(string, subList, index ``+` `1``)``            ` `            ``if` `len``(sub1) > ``len``(sub2):``                ``return` `sub1``            ``else``:``                ``return` `sub2``                ` `        ``else``:``            ``return` `longestSubsequence(string, subList, index ``+` `1``)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``        ` `    ``string ``=` `"aeiaaioooauuaeiou"``    ` `    ``subsequence ``=` `longestSubsequence(string, [], ``0``)``    ``if` `len``(subsequence) ``=``=` `0``:``        ``print``(``"No subsequence possible"``)``    ``else``:``        ``print``(subsequence)``                                               `
Output:
`['a', 'e', 'i', 'i', 'o', 'o', 'o', 'u', 'u', 'u']`

Method 2 (Dynamic Programming)

## Python3

 `from` `random ``import` `choice` `def` `longest_subsequence(string):``    ``def` `helper(chosen``=``"", i``=``0``):``        ``if` `i ``=``=` `len``(string):``            ``return` `chosen ``if` `set``(``"aeiou"``).issubset(``set``(chosen)) ``else` `""` `        ``hashable ``=` `(chosen[``-``1``] ``if` `chosen ``else` `None``, ``len``(chosen), i)` `        ``if` `hashable ``in` `memo:``            ``return` `memo[hashable]` `        ``if` `not` `chosen:``            ``res ``=` `helper(``"a"` `if` `string[i] ``=``=` `"a"` `else` `chosen, i ``+` `1``)``        ``elif` `chosen[``-``1``] ``=``=` `string[i]:``            ``res ``=` `helper(chosen ``+` `string[i], i ``+` `1``)``        ``elif` `mapping[chosen[``-``1``]] ``+` `1` `=``=` `mapping[string[i]]:``            ``sub1 ``=` `helper(chosen ``+` `string[i], i ``+` `1``)``            ``sub2 ``=` `helper(chosen, i ``+` `1``)` `            ``res ``=` `sub1 ``if` `len``(sub1) > ``len``(sub2) ``else` `sub2``        ``else``:``            ``res ``=` `helper(chosen, i ``+` `1``)` `        ``memo[hashable] ``=` `res``        ``return` `res` `    ``mapping ``=` `{x: i ``for` `i, x ``in` `enumerate``(``"aeiou"``)}``    ``memo ``=` `{}``    ``return` `helper()`  `if` `__name__ ``=``=` `"__main__"``:``    ``tests ``=` `[``        ``"aeiaaioooaauuaeiou"``,``        ``"aaauuiieeou"``,``        ``"``".join(choice("``aeiou") ``for` `_ ``in` `range``(``40``)),``        ``"``".join(choice("``aeiou") ``for` `_ ``in` `range``(``900``))``    ``]``    ` `    ``for` `string ``in` `tests:``        ``print``(``"original:"``, string)``        ``subsequence ``=` `longest_subsequence(string)``        ` `        ``if` `subsequence:``            ``print``(``"\nmax subsequence:"``, "".join(subsequence))``        ``else``:``            ``print``(``"No subsequence possible"``)` `        ``print``(``"-"` `*` `40``, ``"\n"``)`
Output:
```original: aeiaaioooaauuaeiou

max subsequence: aaaaaaeiou
----------------------------------------

original: aaauuiieeou
No subsequence possible
----------------------------------------

original: auaaioeoiaooaauoeuaueouuoeiiooiiaiiuioio

max subsequence: aaaaaaeeeiioou
----------------------------------------

original: eaaioeaieoaiueiuiaeiuueeueouoiuueeuaooooiuaiaeuaaieiauaiauuieaoeeeieeoiuaiuuuaaoieooooeioeiouuaoeaouooiauiuiioaoeeeuaoeooiueoaiuioeaeaaouiiiauiuuauoiaiaauaeooeuaiuoeeaaeoaiaoiueieeuaioieouuaaiieeaaeiioaoieoauieoueoauaieueoaeiaoaeoeuiaiauuauouoouaeaueeeioauaieiaieoaeiiueuaaoeuoiueaaiaiaouoouueoauoeieaioeeuueiaaoaiaiiaiueuauaeaieuioooiaeooeaueeoueiueeaueuuiaeuoiuiaeioeeuoaiuueuiaaueueuaeoueuaiaiiuiaouoiueuuueeaueeoaiaaouuiioeioeiaaiieaieiiieeeiaaoaeoououaooiioieuoaeaueuoeaueaoaieeeeauouaaaeiiuoiiuieuuoouuaaoiuaiaoaeeeeiauuuuoiuuoeiieuoaeaouaaooiuuuaeaeaeioeuuauaeaioiuuueuuiuieoieooeoiuioeouuuuaooeueaiooaeiieeieuauoeoaieaeiaaeeoiieiaeuouuuuououiuaueoeooaaeeuuiiaiiueoueaaauaiaieiuiiieauaaioauiuoiiiaieeuaieieiuooeaeooooeouioaooieooeaaaeeeuouiiooiaiieeeuoieeuueouiuuoioeeoiuaauuaaeaueeeiuuuueeeaaeuuoeeeuuieeueeuiaeioeaoiiiiauuoeieeioooaoaeueouiaoeouioaueoaioiuoieuoueuiuouiuaiiaeiuueaiaeuaaeouoa

max subsequence: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeiiiiiiiiiiiiiiiiiiiooooooooooooooouuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
----------------------------------------```

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