Binary Search Algorithm

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Questions and Answers

What is the primary purpose of the binarySearch function?

To sort an array of integers.
To calculate the average of values in an array.
To find the middle index of an array.
To determine if a target value is contained within a specified range of an array. (correct)

Under what condition will the binarySearch function immediately return `false`?

When the `first` index is greater than the `last` index. (correct)
When the `target` value is negative.
When the target value is equal to the value at the midpoint.
When array `values` is empty.

In the provided binarySearch function, what condition causes the function to return `true`?

When the `target` value is greater than the value at the midpoint.
When the `target` value is equal to the value at the midpoint. (correct)
When the `target` value is less than the value at the midpoint.
When the `first` index equals the `last` index.

What is the significance of the `midpoint` variable in the binarySearch function?

It represents the index of the middle element (or an approximation thereof) in the current search range. (C) Signup and view all the answers

If `target` is greater than `values[midpoint]`, what range is searched in the subsequent recursive call to binarySearch?

From <code>midpoint + 1</code> to <code>last</code>. (A) Signup and view all the answers

If `target` is less than `values[midpoint]`, which part of the array is searched in the next recursive call?

The search continues from <code>first</code> to <code>midpoint - 1</code>. (A) Signup and view all the answers

What must be true about the array `values` for binarySearch to function correctly?

The array must be sorted in ascending order. (A) Signup and view all the answers

Given the array `values = {2, 4, 6, 8, 10}`, what would be the initial value of `midpoint` when searching for the `target` 6, with `first = 0` and `last = 4`?

2 (A) Signup and view all the answers

Suppose `values = {3, 7, 9, 12, 15}` and we call `binarySearch(10, 0, 4)`. What happens in the next recursive call?

binarySearch<code>(10, 2, 4)</code> will be called. (B) Signup and view all the answers

Consider the array `values = {1, 3, 5, 7, 9}`. What will `binarySearch(2, 0, 4)` return?

false (A) Signup and view all the answers

Given `values = {2, 4, 6, 8, 10}` and a call to `binarySearch(4, 0, 4)`, how many times is the `values` array accessed before the function returns?

1 (B) Signup and view all the answers

If `binarySearch` is called with `first` and `last` having the same value, what does this imply about the search?

The search is focused on a single element. (A) Signup and view all the answers

What is the space complexity of the given recursive `binarySearch` function?

O(log n) (C) Signup and view all the answers

How would you modify the `binarySearch` algorithm to find the first occurrence of a `target` value in `values` if duplicates are allowed?

Continue searching the lower half after finding the target. (A) Signup and view all the answers

If the values array does not contain the target value, what is the maximum number of times the 'values' array will be accessed, in terms of the array length n?

log₂(n) (B) Signup and view all the answers

When should you choose binary search over a linear search?

When the array is large and sorted. (C) Signup and view all the answers

What is a potential issue with calculating `midpoint` as `(first + last) / 2` in some programming languages?

It may lead to an integer overflow if <code>first + last</code> is too large. (D) Signup and view all the answers

In the context of the binarySearch function given, what does the term 'precondition' refer to?

Conditions that must be true before the function is executed. (C) Signup and view all the answers

How does the binarySearch function handle the case where the target value is smaller than the first element in the array?

It recursively calls itself with adjusted parameters, eventually returning false. (B) Signup and view all the answers

What would happen if the line `int midpoint = (first + last) / 2;` was replaced with `int midpoint = first + (last - first) / 2;`?

The function might avoid integer overflow issues. (C) Signup and view all the answers

Flashcards

Binary Search

An algorithm that searches for a target within a sorted array by repeatedly dividing the search interval in half.

Midpoint (Binary Search)

The index of the element in the middle of the current search range in a binary search.

Binary Search Precondition

Condition that must be true for binary search to function correctly.

Binary Search Success

Return 'true' if the target value is found within the searched range.

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Binary Search Failure

Return 'false' if the target value is not found within the searched range.

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Base Case (Binary Search)

The condition when the 'first' index becomes greater than the 'last' index during binary search.

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Study Notes

The code defines a binarySearch function that searches for a target value within a specified range of indices in a sorted array.
The function takes three integer arguments: target (the value to search for), first (the starting index of the search range), and last (the ending index of the search range).
It includes a precondition that first and last must be legal indices within an array called values.
The goal is to return true if the target is found within the array slice values[first...last], and false otherwise.

How the Search Works

A variable midpoint is calculated as the average of first and last, effectively finding the middle index of the current search range.
If first is greater than last, it means the search range is empty, so the function returns false, indicating value isn't there.
If the value at values[midpoint] is equal to the target, the function returns true, indicating the value has been found.
If the target is greater than the value at values[midpoint], the function recursively calls itself with a new search range from midpoint + 1 to last, effectively searching the right half of the array.
If the target is less than the value at values[midpoint], the function recursively calls itself with a new search range from first to midpoint - 1, effectively searching the left half of the array.

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Podcast

Questions and Answers

What is the primary purpose of the binarySearch function?

Under what condition will the binarySearch function immediately return `false`?

In the provided binarySearch function, what condition causes the function to return `true`?

What is the significance of the `midpoint` variable in the binarySearch function?

If `target` is greater than `values[midpoint]`, what range is searched in the subsequent recursive call to binarySearch?

If `target` is less than `values[midpoint]`, which part of the array is searched in the next recursive call?

What must be true about the array `values` for binarySearch to function correctly?

Given the array `values = {2, 4, 6, 8, 10}`, what would be the initial value of `midpoint` when searching for the `target` 6, with `first = 0` and `last = 4`?

Suppose `values = {3, 7, 9, 12, 15}` and we call `binarySearch(10, 0, 4)`. What happens in the next recursive call?

Consider the array `values = {1, 3, 5, 7, 9}`. What will `binarySearch(2, 0, 4)` return?

Given `values = {2, 4, 6, 8, 10}` and a call to `binarySearch(4, 0, 4)`, how many times is the `values` array accessed before the function returns?

If `binarySearch` is called with `first` and `last` having the same value, what does this imply about the search?

What is the space complexity of the given recursive `binarySearch` function?

How would you modify the `binarySearch` algorithm to find the first occurrence of a `target` value in `values` if duplicates are allowed?

If the values array does not contain the target value, what is the maximum number of times the 'values' array will be accessed, in terms of the array length n?

When should you choose binary search over a linear search?

What is a potential issue with calculating `midpoint` as `(first + last) / 2` in some programming languages?

In the context of the binarySearch function given, what does the term 'precondition' refer to?

How does the binarySearch function handle the case where the target value is smaller than the first element in the array?

What would happen if the line `int midpoint = (first + last) / 2;` was replaced with `int midpoint = first + (last - first) / 2;`?