最大化给定半径的半圆的值-yiteyi-C++库

我们得到了一个机会半圆半径 R 我们可以取圆周上的任意一点 P 从那时起 P 在直径的两边画两条线。别管台词了 PQ 和附言 . 任务是找到表达式的最大值 附言 ^2. +PQ 在一定的时间内 R

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semi-circle

例如：

Input : R = 1 Output : 4.25  (4*1^2 + 0.25) = 4.25Input : R = 2Output : 16.25 (4 * 2^2 + 0.25)= 16.25

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

设F=PS^2+PQ。我们知道QS=2R（半圆的直径） -> 我们也知道 三角形PQS 永远都是 直角三角形 不考虑点P在圆周上的位置

1.)QS^2 = PQ^2 + PS^2 (Pythagorean Theorem)2.) Adding and Subtracting PQ on the RHS     QS^2 = PQ^2 + PS^2 + PQ - PQ3.) Since QS = 2R   4*R^2 + PQ - PQ^2 = PS^2 + PQ => 4*R^2 + PQ - PQ^2 = F4.) Using the concept of maxima and minima differentiating F with respect to PQ and equating it to 0 to get the point of maxima for F i.e.   1 - 2 * PQ = 0 => PQ = 0.55.) Now F will be maximum at F = 4*R^2 + 0.25

C++

                         // C++ program to find                       
                         // the maximum value of F                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find the                       
                         // maximum value of F                       
                         double                                     maximumValueOfF (                                     int                                     R)                       
                         {                       
                                                 // using the formula derived for                       
                                                 // getting the maximum value of F                       
                                                 return                                     4 * R * R + 0.25;                       
                         }                       
                                   
                         // Drivers code                       
                         int                                     main()                       
                         {                       
                                                 int                                     R = 3;                       
                                                 printf                                     (                                     "%.2f"                                     , maximumValueOfF(R));                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // JAVA program to find                       
                         // the maximum value of F                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
                                   
                                                 // Function to find the                       
                                                 // maximum value of F                       
                                                 static                                     double                                     maximumValueOfF (                                     int                                     R)                       
                                                 {                       
                                   
                                                 // using the formula derived for                       
                                                 // getting the maximum value of F                       
                                                 return                                     4                                     * R * R +                                     0.25                                     ;                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     R =                                     3                                     ;                       
                                                 System.out.println(maximumValueOfF(R));                       
                                                 }                       
                                   
                         }                       
           
                         // This code is contributed                       
                         // by anuj_67.                       

Python3

                         # python program to find                       
                         # the maximum value of F                       
           
                         # Function to find the                       
                         # maximum value of F                       
                         def                                     maximumValueOfF (R):                       
                                   
                                                 # using the formula derived for                       
                                                 # getting the maximum value of F                       
                                                 return                                     4                                     *                                     R                                     *                                     R                                     +                                     0.25                       
           
                                   
                         # Drivers code                       
                         R                                     =                                     3                       
                         print                                     (maximumValueOfF(R))                       
           
                         # This code is contributed by Sam007.                       

C#

                         // C# program to find the                       
                         // maximum value of F                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
                                   
                                                 // Function to find the                       
                                                 // maximum value of F                       
                                                 static                                     double                                     maximumValueOfF (                                     int                                     R)                       
                                                 {                       
                                   
                                                 // using the formula derived for                       
                                                 // getting the maximum value of F                       
                                                 return                                     4 * R * R + 0.25;                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     R = 3;                       
                                                 Console.WriteLine(maximumValueOfF(R));                       
                                                 }                       
                                   
                         }                       
           
                         // This code is contributed by Sam007.                       

PHP

                         <?php                       
                         // PHP program to find the                       
                         // maximum value of F                       
           
                         // Function to find the                       
                         // maximum value of F                       
                         function                                     maximumValueOfF (                                     $R                                     )                       
                         {                       
                                   
                                                 // using the formula derived                       
                                                 // for getting the maximum                       
                                                 // value of F                       
                                                 return                                     4 *                                     $R                                     *                                     $R                                     + 0.25;                       
                         }                       
                                   
                         // Drivers code                       
                         $R                                     = 3;                       
                         echo                                     maximumValueOfF(                                     $R                                     );                       
           
                         // This code is contributed                       
                         // by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
                         // javascript program to find the                       
                         // maximum value of F                       
           
                                                 // Function to find the                       
                                                 // maximum value of F                       
                                   
                                                 function                                     maximumValueOfF(R) {                       
                                   
                                                 // using the formula derived for                       
                                                 // getting the maximum value of F                       
                                   
                                                 return                                     4 * R * R + 0.25;                       
                                                 }                       
                                   
                                                 // Driver code                       
           
                                                 var                                     R = 3;                       
                                                 document.write(maximumValueOfF(R));                       
           
                         // This code is contributed by bunnyram19.                       
                         </script>                       

输出：

36.25

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