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# Longest Balanced Substring Problem Statement

Find the longest balanced substring in a given string of letters. A string is balanced if every letter in the string appears in both uppercase and lowercase.

## Example One

``````{
}
``````

Output:

``````"GOogleLE"
``````

## Example Two

``````{
"s": "aPPle",
}
``````

Output:

``````""
``````

## Notes

• The input string consists of uppercase and lowercase english letters.
• Return any longest balanced substring of the given input string. If no such string is possible, return an empty string.

Constraints: 1 <= size of the input string <= 105

## Code For Longest Balanced Substring Solution: Divide And Conquer

``````/*
Asymptotic complexity in terms of the length of string \`s\` ( = \`n\`):
* Time: O(n).
* Auxiliary space: O(n).
* Total space: O(n).
*/

string longest_balanced_substring(string s) {
if (s.size() < 2) {
return "";
}

vector<bool> is_upper_present(26, false), is_lower_present(26, false);
for (char c: s) {
if (isupper(c)) {
is_upper_present[c - 'A'] = true;
} else {
is_lower_present[c - 'a'] = true;
}
}

// split_indices will store indices of characters that appear only in either uppercase or lowercase,
// and then split the string by these characters.
vector<int> split_indices;
split_indices.push_back(-1);
for (int i = 0; i < s.size(); i++) {
int char_index = toupper(s[i]) - 'A';
if (!is_upper_present[char_index] or !is_lower_present[char_index]) {
split_indices.push_back(i);
}
}
if (split_indices.size() == 1) {
return s;
}
split_indices.push_back(s.size());

string result = "";
for (int i = 0; i < split_indices.size() - 1; i++) {
string substring = s.substr(split_indices[i] + 1, split_indices[i + 1] - split_indices[i] - 1);
string balanced_substring = longest_balanced_substring(substring);
if (balanced_substring.size() > result.size()) {
result = balanced_substring;
}
}
return result;
}

string find_longest_balanced_substring(string &s) {
return longest_balanced_substring(s);
}

``````

We hope that these solutions to the longest balanced substring problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart’s FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

‍To learn more, register for the FREE webinar.

### Try yourself in the Editor

Note: Input and Output will already be taken care of.

# Longest Balanced Substring Problem Statement

Find the longest balanced substring in a given string of letters. A string is balanced if every letter in the string appears in both uppercase and lowercase.

## Example One

``````{
}
``````

Output:

``````"GOogleLE"
``````

## Example Two

``````{
"s": "aPPle",
}
``````

Output:

``````""
``````

## Notes

• The input string consists of uppercase and lowercase english letters.
• Return any longest balanced substring of the given input string. If no such string is possible, return an empty string.

Constraints: 1 <= size of the input string <= 105

## Code For Longest Balanced Substring Solution: Divide And Conquer

``````/*
Asymptotic complexity in terms of the length of string \`s\` ( = \`n\`):
* Time: O(n).
* Auxiliary space: O(n).
* Total space: O(n).
*/

string longest_balanced_substring(string s) {
if (s.size() < 2) {
return "";
}

vector<bool> is_upper_present(26, false), is_lower_present(26, false);
for (char c: s) {
if (isupper(c)) {
is_upper_present[c - 'A'] = true;
} else {
is_lower_present[c - 'a'] = true;
}
}

// split_indices will store indices of characters that appear only in either uppercase or lowercase,
// and then split the string by these characters.
vector<int> split_indices;
split_indices.push_back(-1);
for (int i = 0; i < s.size(); i++) {
int char_index = toupper(s[i]) - 'A';
if (!is_upper_present[char_index] or !is_lower_present[char_index]) {
split_indices.push_back(i);
}
}
if (split_indices.size() == 1) {
return s;
}
split_indices.push_back(s.size());

string result = "";
for (int i = 0; i < split_indices.size() - 1; i++) {
string substring = s.substr(split_indices[i] + 1, split_indices[i + 1] - split_indices[i] - 1);
string balanced_substring = longest_balanced_substring(substring);
if (balanced_substring.size() > result.size()) {
result = balanced_substring;
}
}
return result;
}

string find_longest_balanced_substring(string &s) {
return longest_balanced_substring(s);
}

``````

We hope that these solutions to the longest balanced substring problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart’s FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

‍To learn more, register for the FREE webinar.

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