Published at Sep 19 2019
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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.

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.

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.

Wikipedia http://en.wikipedia.org/wiki/Binary_search_algorithm

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

```
#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();
}
```

```
#include "binary_search.h"
const int*
binary_search(int value, const int *arr, size_t length)
{
if (length == 0) {
return NULL;
}
return search_recursive(value, arr, 0, length-1);
}
const int*
search_recursive (int value, const int *arr, size_t min, size_t max)
{
size_t mid = (min+max)/2;
if (arr[mid] == value) {
return &arr[mid];
}
if (min == max) {
return NULL;
}
if (value < arr[mid]) {
return search_recursive(value, arr, min, mid-1);
} else {
return search_recursive(value, arr, mid+1, max);
}
}
```

```
#ifndef BINARY_SEARCH_H
#define BINARY_SEARCH_H
#include <stddef.h>
const int* binary_search(int value, const int *arr, size_t length);
const int* search_recursive (int value, const int *arr, size_t min, size_t max);
#endif
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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