Algorithmes de Recherche et de Tri en Informatique

Algorithms of Searching and Sorting

In the realm of computer science, algorithms of searching and sorting play a crucial role in organizing data efficiently. These algorithms help us find specific elements within a dataset and arrange them in a particular order based on certain criteria. In this article, we will explore three popular algorithms: binary search, bubble sort, and selection sort.

Binary Search

Binary search is a highly efficient algorithm used for finding a specific element in a sorted array or linked list. It works by repeatedly dividing the search interval in half until the desired item is found. This halving process continues until the target value is either located or it becomes clear that the element does not exist in the array.

Here are the steps involved in binary search:

1. Begin at the middle of the array.
2. Compare the middle element with the target value.
3. If they match, return the index of the matched element.
4. If the target value is greater than the middle element, discard all elements before the middle index.
5. Otherwise, if the target value is less than the middle element, discard all elements after the middle index.
6. Repeat steps 1-5 until the target value is found or the search space is empty.

Binary search is faster than linear search because it reduces the search space by half with each comparison. However, it requires the input list to be already sorted.

Bubble Sort

Bubble sort is one of the simplest sorting algorithms out there. It involves comparing adjacent elements in an array and swapping their positions if they are in the wrong order. This process is repeated until the entire array is sorted. Here is how it works:

1. Iterate through the array from left to right.
2. For each pair of adjacent elements, compare them.
3. Swap their positions if they are in the wrong order (larger first, smaller second).
4. Continue iterating until the end of the array.
5. Decrease the range of the iteration by '1' in each pass.

The animation below demonstrates the functioning of bubble sort:

start                              start
1   2    3  4    5            1   2   3 4  5
|-------------------------------|---| |--------------|---|
| compare                <      |     swap            |
1  -> 2       <- 1: is max       2-> 1      3<- 2
    |--- next step
          swap
1  -> 3        <- 2
         |--- next step
           swap
1  -> 2        <- 3
           |--- last step
|-------------------------------|
end                               end
1   2    3  4    5

While bubble sort is simple to implement and understand, it has some drawbacks. Its time complexity is O(n^2), meaning its efficiency decreases significantly for large datasets. Therefore, it is recommended to use more advanced sorting algorithms like quicksort for larger sets of data.

Selection Sort

Selection sort is another basic sorting algorithm that focuses on finding the smallest value in the unsorted part of an array and swapping it with the smallest element found so far. This process continues until the end of the array is reached. Here are the steps involved:

1. Find the minimum element in the unsorted portion of the array (the rest of the array).
2. Swap this minimum element with the first item in the unsorted region.
3. Remove the first item from the unsorted region, since it has been sorted. Now, the remaining subarray becomes the new unsorted region (n-1 elements).
4. Repeat steps 1-3 for the updated unsorted region.
5. Continue this process until no more swaps occur or all elements have been processed.

Unlike bubble sort, selection sort guarantees that at least one swap occurs during each pass through the array. However, its time complexity is also O(n^2), making it less efficient than other advanced sorting algorithms like quicksort.

In conclusion, while binary search is a powerful tool for finding specific values within a sorted dataset, bubble sort and selection sort are basic algorithms used to sort data. These simple approaches can be useful when the input list is small or when the primary goal is to understand the underlying principles of sorting algorithms. For larger datasets, however, more sophisticated sorting methods such as quicksort should be considered.