https://slides.com/georgelee/ics141-algorithms-2/live
We go through each item in the array. If we find it, we return the index. Else, we return -1.
def search(value, numbers):
for index, num in enumerate(numbers):
if num == value:
return index
return -1Assume the array is sorted. We look at the middle value of the array.
If it matches the value we're looking for, yay!
If the value is larger than the one we're searching for, we look in the first half.
Else, we look in the other half of the array.
Array [1 3 6 7 9], Find 9
Iteration 1:
Start: 0, End: 4, Middle: 2 -> [1 3 6 7 9] -> [1 3 6 7 9]
Iteration 2:
Start: 3, End: 4, Middle: 3 -> [1 3 6 7 9] -> [1 3 6 7 9]
Iteration 3:
Start 4, End: 4, Middle: 4 -> [1 3 6 7 9]
Result = 4
Array [1 3 6 7 9], Find 2
Iteration 1:
Start: 0, End: 4, Middle: 2 -> [1 3 6 7 9] -> [1 3 6 7 9]
Iteration 2:
Start: 0, End: 1, Middle: 0 -> [1 3 6 7 9] -> [1 3 6 7 9]
Iteration 3:
Start 1, End: 1 -> [1 3 6 7 9]
Start 1, End: 0 -> -1
Given an array, we iterate from left to right. We compare numbers adjacent to each other. If the one on the left is bigger than the one on the right, we swap them.
The largest number "bubbles" to the end of the array. We iterate again to find the next biggest number.
Keep going until the array is sorted.
Sort the array [1, 4, 7, 2, 6]
Iteration 1:
[1 4 7 2 6] -> [1 4 7 2 6] -> [1 4 2 7 6] -> [1 4 2 6 7]
Iteration 2:
[1 4 2 6 7] -> [1 2 4 6 7] -> [1 2 4 6 7]
Iteration 3:
[1 4 2 6 7] -> [1 2 4 6 7]
Iteration 4:
[1 2 4 6 7]
def bubble_sort(array):
for i in range(0, len(array) - 1):
for j in range(0, len(array) - i - 1):
if array[j] > array[j + 1]:
array[j], array[j + 1] = array[j + 1], array[j]
return arraySplit the array into a sorted and unsorted. Take the first unsorted value and "insert" it into the sorted array. Keep going until the entire array is sorted. Think about being dealt cards.
When inserting, the book goes from left to right.
My implementation will go from right to left.
Sort the array [3 1 7 4 2]
Iteration 1:
[3 1 7 4 2] -> [1 3 7 4 2] -> [1 3 7 4 2]
Iteration 2:
[1 3 7 4 2] -> [1 3 7 4 2]
Iteration 3:
[1 3 7 4 2] -> [1 3 4 7 2] -> [1 3 4 7 2]
Iteration 4:
[1 3 4 7 2] -> [1 3 4 2 7] -> [1 3 2 4 7] -> [1 2 3 4 7] -> [1 2 3 4 7]
def insertion_sort(array):
# Assume first element is "sorted"
for i in range(1, len(array)):
value = array[i]
position = i
for j in range(i, -1, -1):
if array[j - 1] <= value:
break
array[j] = array[j - 1]
array[j] = value
return arrayThe idea is that whenever we are faced with a choice, we take the best one. We typically use these algorithms to solve optimization problems.
* Making Change
* The "Knapsack" problem