87 lines
2.4 KiB
Markdown
Executable File
87 lines
2.4 KiB
Markdown
Executable File
---
|
|
layout: post
|
|
title: HackerRank - Minimum Height Triangle
|
|
date: "2022-11-21 17:19:32 +0800"
|
|
categories: [Code, C]
|
|
tags: [c, hackerrank, math] # TAG names should always be lowercase
|
|
author: devoalda
|
|
math: true
|
|
libraries:
|
|
- mathjax
|
|
---
|
|
|
|
# Introduction
|
|
|
|
Given integers `b` and `a`, find the smallest integer `h`, such that there exists a triangle of height `h`, base `b`, having an area of at least `a`.
|
|
|
|
## Example Input Output
|
|
|
|
```shell
|
|
# Input:
|
|
2 2
|
|
# Output:
|
|
2
|
|
```
|
|
|
|
{: file="Input and Output" }
|
|
|
|
Explanation:
|
|
The task is to find the height of the triangle having base `b = 2` and area `a = 2`. It turns out that the height is `h = 2`.
|
|
|
|
```shell
|
|
# Input:
|
|
17 100
|
|
# Output:
|
|
12
|
|
```
|
|
|
|
{: file="Input and Output" }
|
|
|
|
Explanation:
|
|
The task is to find the height of the triangle having base `b = 17` and area `a = 100`. It turns out that the height is `h = 12` and the triangle has an area of `102`.
|
|
|
|
# Process
|
|
|
|
The area of a triangle is given by the formula:
|
|
|
|
$$
|
|
A = \frac{1}{2}bh
|
|
$$
|
|
|
|
where `b` is the base and `h` is the height of the triangle. Manupulating the formula, we get:
|
|
|
|
$$
|
|
h = \frac{2A}{b}
|
|
$$
|
|
|
|
I knew I needed to use the ceiling function to get the smallest integer `h` that satisfies the condition. So I used the `ceil()` function from the `math.h` library to round the calculated value of the height up to the next integer. The formula can be changed to:
|
|
|
|
$$
|
|
h = \lceil\frac{2A}{b} \rceil
|
|
$$
|
|
|
|
We are able to use this formula to calculate the height of the triangle given the base and area.
|
|
|
|
# Code
|
|
|
|
```c
|
|
int lowestTriangle(int trianglebase, int area) {
|
|
double height = ceil(2 * (double)area / (double)trianglebase);
|
|
return (int)height;
|
|
}
|
|
```
|
|
|
|
{: file="Minimum Height Triangle.c" }
|
|
|
|
# Afterthoughts
|
|
|
|
Upon applying the manipulated formula, I was able to return the minimum height of the triangle, given the base and the area.
|
|
|
|
However, All challenges come with their hurdles and I was met with some when I did this.
|
|
|
|
1. I initially used `int` for the height, but using a calculator to check the results, some results return a decimal value and `int` will truncate the decimal value. So, I changed the type to `double` and used `ceil()` to round up the value.
|
|
2. I needed to typecast the `area` and `trianglebase` to `double` to avoid integer division as the result of the division will be an integer.
|
|
3. The return value of the function is an `int`, so I had to typecast the `height` to `int`.
|
|
|
|
This solution passed all testcases.
|