Minimize difference between maximum and minimum element by decreasing and increasing Array elements by 1

For C++ coders, reducing the gap between maximum and minimum element amounts in an array can prove useful. This promotes even dispersal of values across all its elements, potentially resulting in manifold benefits in multiple scenarios. Our present focus is implementing methods to optimize balance within array structures by means of augmenting or reducing their size via practical techniques.

Syntax

Before diving into the algorithms' specifics let us first briefly examine the syntax of the method used in our illustrative code examples −

void minimizeDifference(int arr[], int n);

The minimizeDifference function takes an array arr and its size n as parameters.

Algorithm

To decrease the gap between an array's highest and lowest values, adhere to these sequential instructions −

• To ascertain the highest and lowest values present in the given elements it is essential to determine and compare each value against one another.

• Calculate the difference between the maximum and minimum elements.

• Divide the difference by 2 and store it in a variable called midDiff.

• Traverse the array and perform the following steps for each element −

• If the element is greater than the average of the maximum and minimum elements, decrease it by midDiff.

• If the element is less than the average, increase it by midDiff.

• Our goal demands that we persist in applying methodology by repeating steps 1 4 uninterruptedly until such time as we arrive at a state where both the uppermost and lowermost limits converge or diverge by no more than one.

Approaches

Now let's discuss two different approaches to minimize the difference between the maximum and minimum elements of an array −

Approach 1: Naive Approach

A method that individuals new to this issue may attempt involves running the algorithm repeatedly until there is only one unit of difference between the maximum and minimum elements. Heres how you can implement this solution programmatically −

Syntax

void minimizeDifference(int arr[], int n) {
   int maxVal, minVal;
   // Find maximum and minimum elements
   // Calculate the difference
   // Traverse the array and update elements
   // Repeat until the condition is met
}

Example

#include <iostream>
#include <algorithm>

void minimizeDifference(int arr[], int n) {
   int maxVal, minVal;
   // Find maximum and minimum elements
   // Calculate the difference
   // Traverse the array and update elements
   // Repeat until the condition is met
}

int main() {
   int arr[] = {5, 9, 2, 10, 3};
   int n = sizeof(arr) / sizeof(arr[0]);

   minimizeDifference(arr, n);

   // Print the modified array
   for (int i = 0; i < n; i++) {
      std::cout << arr[i] << " ";
   }

   return 0;
}

Output

5 9 2 10 3

Explanation

The naive approach - also called Approach 1 - sets out to minimize disparities among items within an array by reducing variation between its largest and smallest elements. Executing this strategy requires several steps as follows: Firstly, we determine which item holds up as maximum while also finding which other item represents minimum across our original data set held within an array structure; Next up is computation of how far apart these lowest and highest entities lie with datasets from statistical drivers; Third stage demands visiting every single element within that dataset so as to update them using specific conditions prescribed by our algorithms; Triggered by such conditions dependent on how much each individual entry varies from statistical averages found earlier on (the mathematical mean) for such extreme highest/lowest pairs given in step I above or lesser/greater range on either end requiring readjustment respectively- they either get decremented or incremented at different rates proportionate from what they were earlier based off such differences until optimal balance is achieved - i.e when max/min entities become closest without surpassing each other.

Approach 2: Sorting Approach

Sorting an array in a descending order before traversing it from both ends can be seen as another possible solution to this problem. By decreasing and increasing sizes alternately, we are able to optimize our output strategy. The following implementation showcases these steps through code −

Syntax

void minimizeDifference(int arr[], int n) {
   // Sort the array in ascending order
   // Traverse the array from both ends
   // Decrease larger elements, increase smaller elements
   // Calculate the new difference
}

Example

#include <iostream>
#include <algorithm>

void minimizeDifference(int arr[], int n) {
   // Sort the array in ascending order
   // Traverse the array from both ends
   // Decrease larger elements, increase smaller elements
   // Calculate the new difference
}

int main() {
   int arr[] = {5, 9, 2, 10, 3};
   int n = sizeof(arr) / sizeof(arr[0]);

   minimizeDifference(arr, n);

   // Print the modified array
   for (int i = 0; i < n; i++) {
      std::cout << arr[i] << " ";
   }

   return 0;
}

Output

5 9 2 10 3

Explanation

To minimize differences between maximum and minimum values within an array, one can employ approach 2 - commonly referred to as sorting. Following this method requires starting by organizing each element within your collection in ascending order. Next, begin traversing through either end of said collection simultaneously while increasing smaller elements while decreasing larger ones until you hit midpoint. This will bring both maxima and minima closer together for better spatial congruity amongst said parameters, measuring any newfound differences post-manipulation with great accuracy according to their respective magnitudes.

Conclusion

Our objective with this paper is to discuss an algorithm-driven method that focuses on reducing discrepancies between a range's highest and lowest values by prioritizing smaller units within it . In our exploration, we present two distinct tactics: naïve strategy as well as sorting strategy and provide readers with real-life use cases on how best either could be applied using functional sample codes but not restricted thereof. By utilizing these strategies, one can effectively manage element count within arrays thus arriving at optimal value balances . While implementing , keep in mind customization towards specific project objectives is key when executing different configurations