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Write a sequential search algorithm that returns true if an item is included in a list and false otherwise. |
The sequential search algorithm iterates over every element in a list to see if an item is included in the list. ```
def sequential_search(list, item)
list.each do |i|
return true if i == item
end
false
end
puts sequential_search([1, 5, 9], 9) # => true
puts sequential_search([1, 5, 9], 44) # => false
``` |

What is the Big O notation for the |
The |

Write a method that uses the binary search algorithm to determine if an item is in a list. |
Here is an overview of the binary search algorithm from Wikipedia: "The binary search algorithm begins by comparing the target value to the value of the middle element of the sorted array. If the target value is equal to the middle element's value, then the position is returned and the search is finished. If the target value is less than the middle element's value, then the search continues on the lower half of the array; or if the target value is greater than the middle element's value, then the search continues on the upper half of the array. This process continues, eliminating half of the elements, and comparing the target value to the value of the middle element of the remaining elements - until the target value is either found (and its associated element position is returned), or until the entire array has been searched (and "not found" is returned)." ```
def binary_search(list, item)
first = 0
last = list.length - 1
while first <= last
midpoint = (first + last) / 2
if list[midpoint] == item
return true
else
if item < list[midpoint]
last = midpoint-1
else
first = midpoint+1
end
end
end
false
end
testlist = [0, 1, 2, 8, 13, 17, 19, 32, 42]
binary_search(testlist, 13) # => true
binary_search(testlist, 15) # => false
``` |

Write the binary search algorithm recursively. |
```
def binary_search(list, item)
return false if list.length == 0
midpoint = list.length / 2
return true if list[midpoint] == item
if item < list[midpoint]
binary_search(list[0...midpoint],item)
else
binary_search(list[midpoint+1...-1],item)
end
end
testlist = [0, 1, 2, 8, 13, 17, 19, 32, 42]
binary_search(testlist, 3) # => false
binary_search(testlist, 13) # => true
``` |

What is the Big O performance of the binary search algorithm. |
See this section for a detailed description of how to compute the performance of this algorithm. In short, the list is cut in half each iteration and this results in |