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[ALGO] Selection Sort

Selection Sort

The algorithm works by selecting the smallest unsorted item and then swapping it with the item in the next position to be filled.

The selection sort works as follows: you look through the entire array for the smallest element, once you find it you swap it (the smallest element) with the first element of the array. Then you look for the smallest element in the remaining array (an array without the first element) and swap it with the second element. Then you look for the smallest element in the remaining array (an array without first and second elements) and swap it with the third element, and so on. Here is an example,

void selectionSort(int[] ar){
   for (int i = 0; i ‹ ar.length-1; i++)
   {
      int min = i;
      for (int j = i+1; j ‹ ar.length; j++)
            if (ar[j] ‹ ar[min]) min = j;
      int temp = ar[i];
      ar[i] = ar[min];
      ar[min] = temp;
} }

Example.

29, 64, 73, 34, 20,
20, 64, 73, 34, 29,
20, 29, 73, 34, 64
20, 29, 34, 73, 64
20, 29, 34, 64, 73

The worst-case runtime complexity is O(n2).

2. The selection sort is a combination of searching and sorting. During each pass, the unsorted element with the smallest (or largest) value is moved to its proper position in the array. The number of times the sort passes through the array is one less than the number of items in the array. In the selection sort, the inner loop finds the next smallest (or largest) value and the outer loop places that value into its proper location.

Selection sort is not difficult to analyze compared to other sorting algorithms since none of the loops depend on the data in the array. Selecting the lowest element requires scanning all n elements (this takesn − 1 comparisons) and then swapping it into the first position. Finding the next lowest element requires scanning the remaining n − 1 elements and so on, for (n − 1) + (n − 2) + … + 2 + 1 = n(n − 1) / 2 ∈ Θ(n2) comparisons. Each of these scans requires one swap for n − 1 elements.

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package com.java2novice.algos;
public class MySelectionSort {
    public static int[] doSelectionSort(int[] arr){
        
        for (int i = 0; i < arr.length - 1; i++)
        {
            int index = i;
            for (int j = i + 1; j < arr.length; j++)
                if (arr[j] < arr[index])
                    index = j;
     
            int smallerNumber = arr[index]; 
            arr[index] = arr[i];
            arr[i] = smallerNumber;
        }
        return arr;
    }
    
    public static void main(String a[]){
        
        int[] arr1 = {10,34,2,56,7,67,88,42};
        int[] arr2 = doSelectionSort(arr1);
        for(int i:arr2){
            System.out.print(i);
            System.out.print(", ");
        }
    }
}
Output:
2, 7, 10, 34, 42, 56, 67, 88,

reference:

http://www.java2novice.com/java-sorting-algorithms/

https://www.cs.cmu.edu/~adamchik/15-121/lectures/Sorting%20Algorithms/sorting.html

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