DSC 40B – Theoretical Foundations of Data Science II


Problems tagged with "loop invariants"

Problem #062

Tags: loop invariants, binary search

Consider the iterative implementation of binary search shown below:


import math

def iterative_binary_search(arr, target):

    start = 0
    stop = len(arr)

    while (stop - start) > 0:
        print(arr[start])
        middle = math.floor((start + stop) / 2)
        if arr[middle] == target:
            return middle
        elif arr[middle] > target:
            stop = middle
        else:
            start = middle + 1

    return None

Which of the following loop invariants is true, assuming that arr is sorted and non-empty, and target is not in the array? Select all that apply.

Solution

The first option is correct.

Problem #074

Tags: loop invariants, binary search

Consider iterative_binary_search below and note the print statement in the while-loop:



import math

def iterative_binary_search(arr, target):

    start = 0
    stop = len(arr)

    while (stop - start) > 0:
        print(arr[start])
        middle = math.floor((start + stop) / 2)
        if arr[middle] == target:
            return middle
        elif arr[middle] > target:
            stop = middle
        else:
            start = middle + 1

    return None

Suppose iterative_binary_search is run on the array:


[-202, -201, -200, -50, -20, -10, -4, -3, 0, 1, 3, 5, 6, 7, 9, 10, 12, 15, 22]

with target 11.

What will be the last value of arr[start] printed?

Solution

10

Problem #075

Tags: loop invariants, quickselect

Recall the partition operation from quickselect. Which of the following arrays could have been partitioned at least once? Select all that apply.

Solution

The second, third, and last all should be selected.