text: ### Chapter 8 Selection and Sorting
  
  ```Chapter 8:
  Searching and
  Sorting Arrays
  8.1
  Introduction to Search Algorithms
  Introduction to Search
  Algorithms
  • Search: locate an item in a list of
  information
  • Two algorithms we will examine:
  – Linear search
  – Binary search
  Linear Search
  • Also called the sequential search
  • Starting at the first element, this algorithm
  sequentially steps through an array
  examining each element until it locates the
  value it is searching for.
  Linear Search - Example
  • Array numlist contains:
  17
  23
  5
  11
  2
  29
  3
  • Searching for the the value 11, linear search
  examines 17, 23, 5, and 11
  • Searching for the the value 7, linear search
  examines 17, 23, 5, 11, 2, 29, and 3
  Linear Search
  • Algorithm:
  set found to false; set position to –1; set index to 0
  while index < number of elts. and found is false
  if list[index] is equal to search value
  found = true
  position = index
  end if
  end while
  return position
  A Linear Search Function
  int searchList(int list[], int numElems, int value)
  {
  int index = 0;
  // Used as a subscript to search array
  int position = -1; // To record position of search value
  bool found = false; // Flag to indicate if value was found
  while (index < numElems && !found)
  {
  if (list[index] == value) // If the value is found
  {
  found = true; // Set the flag
  position = index; // Record the value's subscript
  }
  index++; // Go to the next element
  }
  return position; // Return the position, or -1
  }
  • Benefits:
  – Easy algorithm to understand
  – Array can be in any order
  – Inefficient (slow): for array of N elements,
  examines N/2 elements on average for value
  in array, N elements for value not in array
  Binary Search
  Requires array elements to be in order
  1. Divides the array into three sections:
  – middle element
  – elements on one side of the middle element
  – elements on the other side of the middle element
  2. If the middle element is the correct value, done.
  Otherwise, go to step 1. using only the half of the
  array that may contain the correct value.
  3. Continue steps 1. and 2. until either the value is
  found or there are no more elements to examine
  Binary Search - Example
  • Array numlist2 contains:
  2
  3
  5
  11
  17
  23
  29
  • Searching for the the value 11, binary
  search examines 11 and stops
  • Searching for the the value 7, linear
  search examines 11, 3, 5, and stops
  Binary Search
  Set first index to 0.
  Set last index to the last subscript in the array.
  Set found to false.
  Set position to -1.
  While found is not true and first is less than or equal to last
  Set middle to the subscript half-way between array[first] and array[last].
  If array[middle] equals the desired value
  Set found to true.
  Set position to middle.
  Else If array[middle] is greater than the desired value
  Set last to middle - 1.
  Else
  Set first to middle + 1.
  End If.
  End While.
  Return position.
  A Binary Search Function
  int binarySearch(int array[],
  {
  int first = 0,
  last = size - 1,
  middle,
  position = -1;
  bool found = false;
  int size, int value)
  //
  //
  //
  //
  //
  First array element
  Last array element
  Mid point of search
  Position of search value
  Flag
  while (!found && first <= last)
  {
  middle = (first + last) / 2;
  if (array[middle] == value)
  {
  found = true;
  position = middle;
  }
  else if (array[middle] > value)
  last = middle - 1;
  else
  first = middle + 1;
  }
  return position;
  }
  // Calculate mid point
  // If value is found at mid
  // If value is in lower half
  // If value is in upper half
  • Benefits:
  – Much more efficient than linear search. For
  array of N elements, performs at most log2N
  comparisons
  – Requires that array elements be sorted
  8.3
  Introduction to Sorting Algorithms
  Introduction to Sorting
  Algorithms
  • Sort: arrange values into an order:
  – Alphabetical
  – Ascending numeric
  – Descending numeric
  • The sorting algorithms considered here:
  – Selection sort
  Selection Sort
  • Concept for sort in ascending order:
  – Locate smallest element in array. Exchange it
  with element in position 0
  – Locate next smallest element in array.
  Exchange it with element in position 1.
  – Continue until all elements are arranged in
  order
  Selection Sort - Example
  Array numlist contains:
  11
  2
  29
  3
  1. Smallest element is 2. Exchange 2 with
  element in 1st position in array:
  2
  11
  29
  3
  Example (Continued)
  2. Next smallest element is 3. Exchange 3 with
  element in 2nd position in array:
  2
  3
  29
  11
  3. Next smallest element is 11. Exchange 11
  with element in 3rd position in array:
  2
  3
  11
  29
  A Selection Sort Function –
  From Program 8-5
  35 void selectionSort(int array[], int size)
  36 {
  37
  int startScan, minIndex, minValue;
  38
  39
  for (startScan = 0; startScan < (size - 1); startScan++)
  40
  {
  41
  minIndex = startScan;
  42
  minValue = array[startScan];
  43
  for(int index = startScan + 1; index < size; index++)
  44
  {
  45
  if (array[index] < minValue)
  46
  {
  47
  minValue = array[index];
  48
  minIndex = index;
  49
  }
  50
  }
  51
  array[minIndex] = array[startScan];
  52
  array[startScan] = minValue;
  53
  }
  54 }