Selection Sort

Last translate with upstream: ade5838(on Jul 14, 2021)

This article will briefly introduce selection sort.

Introduction

Selection sort is a simple and straightforward sorting algorithm. The principle is to find the i -th smallest element (that is, the smallest element in A_{i..n} ) each time, and then swap this element with the element at position i of the array.

An animated example of selection sort

Properties

Stability

Because of the operation of swapping two elements, the selection sort is an unstable sort.

Time Complexity

The worst-case, average-case and best-case time complexity are all O(n^2) .

Code Implementations

Pseudocode

\begin{array}{ll} 1 & \textbf{Input. } \text{An array } A \text{ consisting of }n\text{ elements.} \\ 2 & \textbf{Output. } A\text{ will be sorted in nondecreasing order.} \\ 3 & \textbf{Method. } \\ 4 & \textbf{for } i\gets 1\textbf{ to }n-1\\ 5 & \qquad ith\gets i\\ 6 & \qquad \textbf{for }j\gets i+1\textbf{ to }n\\ 7 & \qquad\qquad\textbf{if }A[j]<A[ith]\\ 8 & \qquad\qquad\qquad ith\gets j\\ 9 & \qquad \text{swap }A[i]\text{ and }A[ith]\\ \end{array}

C++ code

void selection_sort(int* a, int n) {
  for (int i = 1; i < n; ++i) {
    int ith = i;
    for (int j = i + 1; j <= n; ++j) {
      if (a[j] < a[ith]) {
        ith = j;
      }
    }
    int t = a[i];
    a[i] = a[ith];
    a[ith] = t;
  }
}

Python

# Python Version
def selection_sort(a, n):
    for i in range(1, n):
        ith = i
        for j in range(i + 1, n + 1):
            if a[j] < a[ith]:
                ith = j
        a[i], a[ith] = a[ith], a[i]
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