Algorithm Analysis Sorting Fall 2013 Carola Wenk Sorting Lets - - PowerPoint PPT Presentation

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Algorithm Analysis Sorting Fall 2013 Carola Wenk Sorting Lets - - PowerPoint PPT Presentation

Feb 22, 2023 142 likes •272 views

Algorithm Analysis Sorting Fall 2013 Carola Wenk Sorting Lets consider the problem of sorting a list of numbers. Sorted List Program List An arbitrary list with A list in ascending comparable items. order. Can we make the

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SLIDE 1

Algorithm Analysis Sorting

Fall 2013 Carola Wenk

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SLIDE 2

Sorting

Let’s consider the problem of sorting a list of numbers.

List Program Sorted List

A list in ascending

  • rder.

Can we make the specifications more concrete?

An arbitrary list with comparable items.

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SLIDE 3

Sorting

Let’s consider the problem of sorting a list of numbers.

List Program Sorted List

How do we sort a list?

L = [2,1,9, ...] L[i] <= L[i+1], for all values of i from 0..n-2.

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SLIDE 4

A Sorting Algorithm

Let’s consider the problem of sorting a list of numbers. What is the running time? Algorithm:

  • 1. Find the minimum element in the

list.

  • 2. Swap it with the first element.
  • 3. Repeat with the rest of the list.
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SLIDE 5

A Sorting Algorithm

Let’s consider the problem of sorting a list of numbers. What is the running time? How many times do we find the minimum? Algorithm:

  • 1. Find the minimum element in the

list.

  • 2. Swap it with the first element.
  • 3. Repeat with the rest of the list.
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SLIDE 6

Algorithm Analysis

Each time we find a minimum, we are reducing the time spent on searching for “future” minima. The list sizes are: The corresponding number of operations is: This approach to sorting a list is often called “selection”

  • sorting. For a list with elements, we perform about
  • perations to find the minimum.
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SLIDE 7

Algorithm Analysis

Each time we find a minimum, we are reducing the time spent on searching for “future” minima. The list sizes are: The corresponding number of operations is: This approach to sorting a list is often called “selection”

  • sorting. For a list with elements, we perform about
  • perations to find the minimum.
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SLIDE 8

Algorithm Analysis

Each time we find a minimum, we are reducing the time spent on searching for “future” minima. The list sizes are: The corresponding number of operations is: This approach to sorting a list is often called “selection”

  • sorting. For a list with elements, we perform about
  • perations to find the minimum.
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SLIDE 9

An Implementation

# find the index of the minimum in L def my_min_index(L): curr_min_index = 0 for i in range(1,len(L)): if (L[i] < L[curr_min_index]): curr_min_index = i return curr_min_index # swap the contents of L[i] and L[j] def swap(L, i, j): temp = L[i]; L[i] = L[j]; L[j] = temp # sort a list in O(n^2) time def selection_sort(L):

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SLIDE 10

An Implementation

# find the index of the minimum in L def my_min_index(L): curr_min_index = 0 for i in range(1,len(L)): if (L[i] < L[curr_min_index]): curr_min_index = i return curr_min_index # swap the contents of L[i] and L[j] def swap(L, i, j): temp = L[i]; L[i] = L[j]; L[j] = temp # sort a list in O(n^2) time def selection_sort(L): n = len(L) for i in range(n):

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SLIDE 11

An Implementation

# find the index of the minimum in L def my_min_index(L): curr_min_index = 0 for i in range(1,len(L)): if (L[i] < L[curr_min_index]): curr_min_index = i return curr_min_index # swap the contents of L[i] and L[j] def swap(L, i, j): temp = L[i]; L[i] = L[j]; L[j] = temp # sort a list in O(n^2) time def selection_sort(L): n = len(L) for i in range(n): j = i + my_min_index(L[i:]) swap(L, i, j) “List Slicing”