可以内接半圆的最大矩形
给定一个半径为 r 的半圆，我们必须找到半圆中可以内接的最大矩形，底部位于直径上。 例:
Input : r = 4
Output : 16
Input : r = 5
Output :25
设 r 为半圆半径， x 为矩形底边的一半， y 为矩形高度。我们希望面积最大化，A = 2xy。 所以从图中我们有， y = √(r^2–x^2) 所以，a = 2x(√(r^2–x^2)】，或者da/dx = 2√(r^2–x^2)-2x^2/√(r^2–x^2) 设置这个导数等于 0 并求解为 x， dA/dx = 0 或者， 2√(r^2–x^2)–2x^2/√(r^2–x^2)= 0 2r^2–4x^2 = 0 x = r/√2 这是面积的最大值 as， t30】da/dx>0 当x>r/√2t34】和， dA/dx < 0 当时 所以，区a=r^2t53】
C++
// C++ Program to find the
// the biggest rectangle
// which can be inscribed
// within the semicircle
#include <bits/stdc++.h>
using namespace std;
// Function to find the area
// of the biggest rectangle
float rectanglearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the rectangle
float a = r * r;
return a;
}
// Driver code
int main()
{
float r = 5;
cout << rectanglearea(r) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find the
// the biggest rectangle
// which can be inscribed
// within the semicircle
class GFG
{
// Function to find the area
// of the biggest rectangle
static float rectanglearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the rectangle
float a = r * r;
return a;
}
// Driver code
public static void main(String[] args)
{
float r = 5;
System.out.println((int)rectanglearea(r));
}
}
// This code is contributed
// by ChitraNayal
Python 3
# Python 3 Program to find the
# the biggest rectangle
# which can be inscribed
# within the semicircle
# Function to find the area
# of the biggest rectangle
def rectanglearea(r) :
# the radius cannot
# be negative
if r < 0 :
return -1
# area of the rectangle
a = r * r
return a
# Driver Code
if __name__ == "__main__" :
r = 5
# function calling
print(rectanglearea(r))
# This code is contributed
# by ANKITRAI1
C
// C# Program to find the
// the biggest rectangle
// which can be inscribed
// within the semicircle
using System;
class GFG
{
// Function to find the area
// of the biggest rectangle
static float rectanglearea(float r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the rectangle
float a = r * r;
return a;
}
// Driver code
public static void Main()
{
float r = 5;
Console.Write((int)rectanglearea(r));
}
}
// This code is contributed
// by ChitraNayal
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the
// the biggest rectangle
// which can be inscribed
// within the semicircle
// Function to find the area
// of the biggest rectangle
function rectanglearea($r)
{
// the radius cannot
// be negative
if ($r < 0)
return -1;
// area of the rectangle
$a = $r * $r;
return $a;
}
// Driver code
$r = 5;
echo rectanglearea($r)."\n";
// This code is contributed
// by ChitraNayal
?>
java 描述语言
<script>
// javascript Program to find the
// the biggest rectangle
// which can be inscribed
// within the semicircle
// Function to find the area
// of the biggest rectangle
function rectanglearea(r)
{
// the radius cannot be negative
if (r < 0)
return -1;
// area of the rectangle
var a = r * r;
return a;
}
// Driver code
var r = 5;
document.write(parseInt(rectanglearea(r)));
// This code is contributed by Amit Katiyar
</script>
输出:
25
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