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

In this article, we will unravel an interesting problem from the field of string manipulation: "Rearrange strings 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 largest possible minimum distance between any two vowel characters. We will discuss this problem in detail, provide a C code implementation, and illustrate it with examples.

Understanding the problem statement

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

The vowels in English are "a", "e", "i", "o", "u" and their capitalized versions.

method

To solve this problem, we will take a two-step approach -

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

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

Test Case

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

in conclusion

This article provides 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 involves counting the vowels, storing their positions, and then finding the maximum difference between those positions. Although the problem may seem complex at first glance, it is greatly simplified when broken down into these steps.

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