检查给定的圆是否完全位于两个同心圆形成的环内
原文:https://www . geesforgeks . org/check-given-circle-lies-完全在环内-形成-两个同心圆/
给定半径为 R 和 R 的两个圆，它们的中心都在原点。现在，给定另一个半径为 r1 且圆心在(x1，y1)的圆。检查第三个圆(半径为 r1 的圆)是否完全位于半径为 r 和 r 的两个圆形成的环内。 示例:
Input : r = 8 R = 4
r1 = 2 x1 = 6 y1 = 0
Output : yes
Input : r = 8 R = 4
r1 = 2 x1 = 5 y1 = 0
Output : no
重要提示:同心圆是那些圆心相同的圆。位于两个同心圆之间的区域称为环或圆环。
例: 有两个同心圆，圆心在原点(0，0)，半径为 r = 8，R = 4。 1。)圆圈 1 和 2 位于环内。 2。)圈 3 和圈 4 在圈外。 完整的图形如下所示:
方法: 这个问题可以用 勾股定理 来解决。用毕达哥拉斯定理计算圆心和原点之间的距离，假设用“dis”表示。 计算完距离后，只需检查(dis–R1)>= r 和(dis + r1) < = R 的值。如果这两个条件都成立，则圆完全位于环内。
C++
// CPP code to check if a circle
// lies in the ring
#include <bits/stdc++.h>
using namespace std;
// Function to check if circle
// lies in the ring
bool checkcircle(int r, int R, int r1,
int x1, int y1)
{
// distance between center of circle
// center of concentric circles(origin)
// using Pythagoras theorem
int dis = sqrt(x1*x1+y1*y1);
// Condition to check if circle is
// strictly inside the ring
return (dis-r1 >= R && dis+r1 <= r);
}
// Driver Code
int main()
{
// Both circle with radius 'r'
// and 'R' have center (0,0)
int r = 8, R = 4, r1 = 2, x1 = 6, y1 = 0;
if (checkcircle(r, R, r1, x1, y1))
cout << "yes" << endl;
else
cout << "no" << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java code to check if a
// circle lies in the ring
import java.io.*;
class ring
{
// Function to check if circle
// lies in the ring
public static boolean checkcircle(int r, int R,
int r1, int x1, int y1)
{
// distance between center of circle
// center of concentric circles(origin)
// using Pythagoras theorem
int dis = (int)Math.sqrt(x1 * x1 +
y1 * y1);
// Condition to check if circle
// is strictly inside the ring
return (dis - r1 >= R && dis + r1 <= r);
}
// Driver Code
public static void main(String args[])
{
// Both circle with radius 'r'
// and 'R' have center (0,0)
int r = 8, R = 4, r1 = 2, x1 = 6, y1 = 0;
if (checkcircle(r, R, r1, x1, y1))
System.out.println("yes");
else
System.out.println("no");
}
}
Python 3
# Python3 code to check if
# a circle lies in the ring
import math
# Function to check if circle
# lies in the ring
def checkcircle(r, R, r1, x1, y1):
# distance between center of circle
# center of concentric circles(origin)
# using Pythagoras theorem
dis = int(math.sqrt(x1 * x1 + y1 * y1))
# Condition to check if circle is
# strictly inside the ring
return (dis-r1 >= R and dis+r1 <= r)
# Driver Code
# Both circle with radius 'r'
# and 'R' have center (0,0)
r = 8; R = 4; r1 = 2; x1 = 6; y1 = 0
if (checkcircle(r, R, r1, x1, y1)):
print("yes")
else:
print("no")
# This code is contributed by Smitha Dinesh Semwal.
C
// C# code to check if a
// circle lies in the ring
using System;
class ring {
// Function to check if circle
// lies in the ring
public static bool checkcircle(int r, int R,
int r1, int x1, int y1)
{
// distance between center of circle
// center of concentric circles(origin)
// using Pythagoras theorem
int dis = (int)Math.Sqrt(x1 * x1 + y1 * y1);
// Condition to check if circle
// is strictly inside the ring
return (dis - r1 >= R && dis + r1 <= r);
}
// Driver Code
public static void Main()
{
// Both circle with radius 'r'
// and 'R' have center (0, 0)
int r = 8, R = 4, r1 = 2, x1 = 6, y1 = 0;
if (checkcircle(r, R, r1, x1, y1))
Console.WriteLine("yes");
else
Console.WriteLine("no");
}
}
// This code is contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP code to check if a circle
// lies in the ring
// Function to check if circle
// lies in the ring
function checkcircle($r, $R, $r1,
$x1, $y1)
{
// distance between center of circle
// center of concentric circles(origin)
// using Pythagoras theorem
$dis = sqrt($x1 * $x1 + $y1 * $y1);
// Condition to check if circle is
// strictly inside the ring
return ($dis-$r1 >= $R && $dis + $r1 <= $r);
}
// Driver Code
// Both circle with radius 'r'
// and 'R' have center (0,0)
$r = 8; $R = 4;
$r1 = 2; $x1 = 6;
$y1 = 0;
if (checkcircle($r, $R, $r1, $x1, $y1))
echo "yes" ,"\n";
else
echo "no" ,"\n";
// This code is contributed by ajit.
?>
java 描述语言
<script>
// JavaScript program code to check if a
// circle lies in the ring
// Function to check if circle
// lies in the ring
function checkcircle(r, R, r1, x1, y1)
{
// distance between center of circle
// center of concentric circles(origin)
// using Pythagoras theorem
let dis = Math.sqrt(x1 * x1 +
y1 * y1);
// Condition to check if circle
// is strictly inside the ring
return (dis - r1 >= R && dis + r1 <= r);
}
// Driver Code
// Both circle with radius 'r'
// and 'R' have center (0,0)
let r = 8, R = 4, r1 = 2, x1 = 6, y1 = 0;
if (checkcircle(r, R, r1, x1, y1))
document.write("yes");
else
document.write("no");
// This code is contributed by splevel62.
</script>
Output:
yes
时间复杂度: O(1)
辅助空间: O(1)
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