 # qxp's solution

## to Collatz Conjecture in the C Track

Published at Sep 10 2019 · 0 comments
Instructions
Test suite
Solution

#### Note:

This exercise has changed since this solution was written.

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.

## Examples

Starting with n = 12, the steps would be as follows:

1. 12
2. 6
3. 3
4. 10
5. 5
6. 16
7. 8
8. 4
9. 2
10. 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

## 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.

## Source

An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

## Submitting Incomplete Solutions

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

### test_collatz_conjecture.c

``````#include "../src/collatz_conjecture.h"

#include "vendor/unity.h"

static void test_zero_steps_for_one(void)
{
TEST_ASSERT_EQUAL(0, steps(1));
}

static void test_divide_if_even(void)
{
TEST_ASSERT_EQUAL(4, steps(16));
}

static void test_even_and_odd_steps(void)
{
TEST_ASSERT_EQUAL(9, steps(12));
}

static void test_large_number_of_even_and_odd_steps(void)
{
TEST_ASSERT_EQUAL(152, steps(1000000));
}

static void test_zero_is_an_error(void)
{
TEST_ASSERT_EQUAL(ERROR_VALUE, steps(0));
}

static void test_negative_value_is_an_error(void)
{
TEST_ASSERT_EQUAL(ERROR_VALUE, steps(-15));
}

int main(void)
{
UnityBegin("collatz_conjecture.c");

RUN_TEST(test_zero_steps_for_one);
RUN_TEST(test_divide_if_even);
RUN_TEST(test_even_and_odd_steps);
RUN_TEST(test_large_number_of_even_and_odd_steps);
RUN_TEST(test_zero_is_an_error);
RUN_TEST(test_negative_value_is_an_error);

return UnityEnd();
}``````
``````#include "collatz_conjecture.h"

int steps(int start)
{
if (start < 1)
return ERROR_VALUE;

int steps = 0;
for (int n = start; n > 1; ++steps)
{
n = n % 2 == 0 ? n / 2 : 3 * n + 1;
}

return steps;
}``````