Minimize the difference between the largest and smallest elements by decreasing and increasing array elements by 1

It can be useful for C coders to reduce the gap between the maximum and minimum number of elements in an array. This promotes an even dispersion of value across all its elements, potentially leading to multiple benefits in multiple situations. Our current focus is on methods to optimize the balance within an array structure through practical techniques to increase or decrease the size of the array structure.

grammar

Before delving into the details of the algorithm, let us first briefly examine the syntax of the methods used in the illustrative code example -

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

The minimumDifference function takes the array arr and its size n as parameters.

algorithm

In order to reduce the gap between the maximum and minimum values ​​of the array, please follow the following sequential instructions -

• In order to determine the highest and lowest value present in a given element, each value must be determined and compared to each other.

• Calculate the difference between the largest and smallest elements.

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

• Loop through the array and perform the following steps for each element -

• If the element is greater than the average of the largest and smallest elements, subtract midDiff from it.

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

• Our goal requires that we persist in applying the methodology, repeating steps 1 to 4 without interruption until we reach a state where the upper and lower bounds converge or diverge by no more than one unit.

method

Now let us discuss two different ways to minimize the difference between the largest and smallest elements in an array −

Method 1: Naive method

An approach for individuals unfamiliar with this problem might be to try running the algorithm repeatedly until there is only one unit of difference between the largest and smallest elements. Here's how you can implement this solution programmatically -

grammar

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

Explanation

The naive method - also known as method 1 - aims to minimize the difference between items in the array by reducing the difference between the largest and smallest elements. Executing this strategy requires the following steps: first, we determine which item in the original data set serves as the maximum value, and at the same time find which other item represents the minimum value, these data sets are saved in an array structure; next, we calculate these lowest and highest entities distance from a statistically driven data set; the third stage requires access to every element in the data set to update them using specific conditions dictated by the algorithm; based on these conditions, each individual entry is compared to the previously found statistical mean Difference between (mathematical mean) (extreme highest/lowest pairs given in step I) or smaller/larger range of cases that need to be rescaled, decreasing or increasing in different proportions until optimal Equilibrium - i.e. the largest/smallest entities become closest without exceeding each other.

Method 2: Sorting method

Sorting the array in descending order before traversing the array from both ends can be seen as another possible way to solve this problem. By alternately decreasing and increasing the size, we are able to optimize our output strategy. The following implementation demonstrates these steps through code -

grammar

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

Explanation

To minimize the difference between the largest and smallest values ​​in the array, approach 2 - often called sorting - can be used. Following this approach requires first organizing each element in the collection in ascending order. Next, start traversing either end of said set simultaneously, increasing smaller elements while decreasing larger elements, until you reach the midpoint. This will bring the maximum and minimum values ​​closer together to achieve better spatial consistency between the parameters, according to their respective magnitudes, with high accuracy in measuring any newly discovered differences after the operation.

in conclusion

Our goal with this article is to discuss an algorithm-driven approach that focuses on reducing the difference between the highest and lowest values ​​of a range by prioritizing smaller units within the range. In our exploration, we propose two different strategies: the naive strategy and the sorting strategy, and provide readers with real-life use cases on how to best apply both strategies using functional example code, but are not limited to this. By utilizing these strategies, we can effectively manage the number of elements in the array to achieve the best value balance. When implementing, keep in mind that customization for specific project goals is key when performing different configurations

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