# Rearrange a string to maximize the minimum distance between any pair of vowels

In this article, we're going to unravel an interesting problem from the domain of string manipulation: "Rearrange a string to maximize the minimum distance between any pair of vowels". This problem challenges us to manipulate the arrangement of characters in a string to ensure the maximum possible minimum distance between any two vowel characters. We'll discuss the problem in detail, provide a C++ code implementation, and illustrate with an example.

## Understanding the Problem Statement

Given a string, the task is to rearrange the characters in the string in such a way that the minimum distance between any pair of vowels is maximized. In other words, we want to place the vowels as far apart as possible from each other.

The vowels in the English language are 'a', 'e', 'i', 'o', 'u', and their uppercase versions.

## Approach

To solve this problem, we'll take a two-step approach −

First, count the number of vowels in the string and store their positions in an array.

Next, sort this array and calculate the maximum difference between any two consecutive elements. This difference represents the maximum minimum distance between any pair of vowels.

### Example

Let's implement this strategy in C++ −

#include <bits/stdc++.h>
using namespace std;

// Function to check if a character is a vowel
bool isVowel(char c) {
return c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u' ||
c == 'A' || c == 'E' || c == 'I' || c == 'O' || c == 'U';
}

// Function to find maximum minimum distance between vowels
int maxMinDist(string s) {
vector<int> pos;
for (int i = 0; i < s.size(); i++) {
if (isVowel(s[i])) pos.push_back(i);
}
sort(pos.begin(), pos.end());
int maxDist = 0;
for (int i = 1; i < pos.size(); i++) {
maxDist = max(maxDist, pos[i] - pos[i-1]);
}
return maxDist;
}

int main() {
string s = "programming";
cout << "Max minimum distance between vowels: " << maxMinDist(s);
return 0;
}


### Output

Max minimum distance between vowels: 3


This code first finds the positions of all vowels in the string and stores them in a vector. It then sorts this vector and finds the maximum difference between consecutive elements. This difference represents the maximum minimum distance between any pair of vowels.

## Test Case

Let's consider the string "programming". The positions of the vowels 'o', 'a', and 'i' are 1, 4, and 7 respectively. Therefore, the maximum minimum distance between any pair of vowels is 3.

## Conclusion

This article provided a step-by-step approach to solving the problem of maximizing the minimum distance between any pair of vowels in a given string. The solution involved counting the vowels, storing their positions, and then finding the maximum difference between these positions. Although the problem may seem complex at first glance, it simplifies considerably when broken down into these steps.

Updated on: 18-May-2023

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