"算法导论第三版答案.pdf中的SELECTION-SORT算法详解"

The given algorithm is a solution to Exercise 2.2-2 in the book "Introduction to Algorithms, 3rd edition". The purpose of the algorithm is to sort an array A of length n using the selection sort method. The algorithm works by maintaining a loop invariant that at the start of each iteration of the outer for loop, the subarray A[1:j-1] consists of the j-1 smallest elements in the array A[1:n], and this subarray is in sorted order. The algorithm starts by initializing a variable `smallest` to `j`. Then, for each iteration of the outer loop, it finds the smallest element in the subarray A[j:n] and stores its index in the `smallest` variable. After finding the smallest element, it swaps the elements A[j] and A[smallest]. By maintaining the loop invariant, the algorithm ensures that after the first n-1 elements, the subarray A[1:n-1] contains the smallest n-1 elements, sorted. Therefore, after the entire array is processed, the array A is sorted in non-decreasing order. This algorithm is based on the selection sort method, which repeatedly selects the smallest element from the unsorted portion of the array and places it at the beginning of the sorted portion. It has a time complexity of O(n^2) and is not the most efficient sorting algorithm for large datasets, but it is simple and easy to implement. In conclusion, the algorithm provided in the "Algorithm Introduction, Third Edition" solution manual is a straightforward implementation of the selection sort method for sorting an array. It maintains a loop invariant that ensures the correctness of the sorting process and has a time complexity of O(n^2). While not the most efficient algorithm for large datasets, it is a useful and instructive example of sorting algorithms.