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# kruschk's solution

## to Binary Search in the C Track

Published at Jul 24 2020 · 0 comments
Instructions
Test suite
Solution

Implement a binary search algorithm.

Searching a sorted collection is a common task. A dictionary is a sorted list of word definitions. Given a word, one can find its definition. A telephone book is a sorted list of people's names, addresses, and telephone numbers. Knowing someone's name allows one to quickly find their telephone number and address.

If the list to be searched contains more than a few items (a dozen, say) a binary search will require far fewer comparisons than a linear search, but it imposes the requirement that the list be sorted.

In computer science, a binary search or half-interval search algorithm finds the position of a specified input value (the search "key") within an array sorted by key value.

In each step, the algorithm compares the search key value with the key value of the middle element of the array.

If the keys match, then a matching element has been found and its index, or position, is returned.

Otherwise, if the search key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right.

If the remaining array to be searched is empty, then the key cannot be found in the array and a special "not found" indication is returned.

A binary search halves the number of items to check with each iteration, so locating an item (or determining its absence) takes logarithmic time. A binary search is a dichotomic divide and conquer search algorithm.

## Getting Started

Make sure you have read the "Guides" section of the C track on the Exercism site. This covers the basic information on setting up the development environment expected by the exercises.

## Passing the Tests

Get the first test compiling, linking and passing by following the three rules of test-driven development.

The included makefile can be used to create and run the tests using the `test` task.

``````make test
``````

Create just the functions you need to satisfy any compiler errors and get the test to fail. Then write just enough code to get the test to pass. Once you've done that, move onto the next test.

As you progress through the tests, take the time to refactor your implementation for readability and expressiveness and then go on to the next test.

Try to use standard C99 facilities in preference to writing your own low-level algorithms or facilities by hand.

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### test_binary_search.c

``````#include "vendor/unity.h"
#include "../src/binary_search.h"

void setUp(void)
{
}

void tearDown(void)
{
}

static void test_single_element(void)
{
int arr[] = { 6 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[0] == binary_search(6, arr, length));
}

static void test_value_in_middle(void)
{
TEST_IGNORE();               // delete this line to run test
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[3] == binary_search(6, arr, length));
}

static void test_value_at_beginning(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[0] == binary_search(1, arr, length));
}

static void test_value_at_end(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[6] == binary_search(11, arr, length));
}

static void test_find_value_with_odd_length(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 634 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[9] == binary_search(144, arr, length));
}

static void test_find_value_with_even_length(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(&arr[5] == binary_search(21, arr, length));
}

static void test_identify_missing_value(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(NULL == binary_search(7, arr, length));
}

static void test_value_smaller_than_everything(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(NULL == binary_search(0, arr, length));
}

static void test_value_larger_than_everything(void)
{
TEST_IGNORE();
int arr[] = { 1, 3, 4, 6, 8, 9, 11 };
size_t length = sizeof(arr) / sizeof(arr[0]);
TEST_ASSERT(NULL == binary_search(13, arr, length));
}

static void test_empty_array(void)
{
TEST_IGNORE();
int *arr = NULL;
size_t length = 0;
TEST_ASSERT(NULL == binary_search(1, arr, length));
}

static void test_zero_length_array(void)
{
TEST_IGNORE();
int arr[] = { 1 };
size_t length = 0;
TEST_ASSERT(NULL == binary_search(1, arr, length));
}

int main(void)
{
UnityBegin("test/test_binary_search.c");

RUN_TEST(test_single_element);
RUN_TEST(test_value_in_middle);
RUN_TEST(test_value_at_beginning);
RUN_TEST(test_value_at_end);
RUN_TEST(test_find_value_with_odd_length);
RUN_TEST(test_find_value_with_even_length);
RUN_TEST(test_identify_missing_value);
RUN_TEST(test_value_smaller_than_everything);
RUN_TEST(test_value_larger_than_everything);
RUN_TEST(test_empty_array);
RUN_TEST(test_zero_length_array);

return UnityEnd();
}``````

### src/binary_search.c

``````#include "binary_search.h"

// Return the middle value of the range [low, high) such that the intervals
// [low, mid) and [mid, high) are of equal lengths, or that of [low, mid) is
// one greater than [mid, high), depending on whether the original length is
// even or odd.
static size_t middle(const size_t low, const size_t high) {
return (low + high)/2;
}

// Return a pointer to the element of `array` (an array sorted into
// increasing order) whose value is equivalent to `value`, if one exists;
// otherwise, return `NULL`.
int *binary_search(const int value, int *const array, const size_t length) {
// Guard against null-arrays.
if (NULL == array) {
return NULL;
}
// Implement a binary search.
size_t low = 0, high = length;
size_t mid = middle(low, high);
while (low < high) {
if (value < array[mid]) {
high = mid;
mid = middle(low, high);
} else if (value > array[mid]) {
low = mid + 1;
mid = middle(low, high);
} else {
return &array[mid];
}
}
return NULL;
}``````

### src/binary_search.h

``````#ifndef BINARY_SEARCH_H
#define BINARY_SEARCH_H

#include <stddef.h>

// Return a pointer to the element of `array` (an array sorted into
// increasing order) whose value is equivalent to `value`, if one exists;
// otherwise, return `NULL`.
int *binary_search(const int value, int *const array, const size_t length);

#endif``````