Lecture Notes on 23 Sep 2020

* Sequential Search
Efficiency: O(n)
Input: a is a list and x is an element to be found
Output: the index of the first occurence of x or
        -1 if x is not in the list
def sequential_search (a, x):
  for i in range (len(a)):
    if (a[i] == x):
      return i
  return -1

* Binary Search
Efficiency: O(log n), log base 2
Pre-condition: list a is sorted in ascending order
Input: a is a list and x is an element to be found
Output: the index of the first occurence of x or
        -1 if x is not in the list
def binary_search (a, x):
  lo = 0
  hi = len(a) - 1
  while (lo <= hi):
    mid = (lo + hi) // 2
    if (x > a[mid]):
      lo = mid + 1
    elif (x < a[mid]):
      hi = mid - 1
    else:
      return mid
  return -1

* Selection Sort
Efficiency: O(n^2)
Input: a is a list
Output: function does not return anything but a is sorted in place
def selection_sort (a):
  for i in range (len(a) - 1):
    # find the minimum
    min_val = a[i]
    min_idx = i

    for j in range (i + 1, len(a)):
      if (a[j] < min_val):
        min_val = a[j]
	    min_idx = j

    # Swap the minimum element with the element at the ith place
    a[min_idx] = a[i]
    a[i] = min_val

* Merging
Efficiency: O(n)
Pre-condition: a and b are sorted lists in ascending order
Input: a and b are sorted lists
Output: returns c that is the merged list in ascending order
def merge (a, b):
  c = []
  idxA = 0
  idxB = 0

  while ((idxA < len(a)) and (idxB < len(b))):
    if (a[idxA] < b[idxB]):
      c.append (a[idxA])
      idxA = idxA + 1
    else:
      c.append (b[idxB])
      idxB = idxB + 1

  # if a is not empty write out the remaining elements
  while (idxA < len(a)):
    c.append (a[idxA])
    idxA = idxA + 1

  # if b is not empty write out the remaining elements
  while (idxB < len(b)):
    c.append (b[idxB])
    idxB = idxB + 1

  return c