给定需要建造塔的四个坐标A，B，C和D ，任务是检查是否出现视塔问题。
Tower of sight issue occurs if the towers at A or C lies in the line joining B and D or vice versa.
例子：
Input: A = (0, 0), B = (0, -2), C = (2, 0), D = (0, 2)
Output: Yes
Explanation:
Tower A lies in the line joining B and D.
Input: A = (0, 0), B = (0, -2), C = (2, 0), D = (0, -5)
Output: No
Explanation:
No intersection occurs.
方法：
- 如果A和C平行于X轴，请检查B或D的y坐标是否等于A和C的y坐标，以及x坐标是否介于A和C的坐标之间。
- 如果A和C平行于Y轴，请检查B或D的x坐标是否等于A和C的x坐标，以及y坐标在A和C的Y坐标之间。
- 否则，检查B或D是否满足A和C的线方程。
- 同样，按照上述三个步骤检查A或C是否位于B或D之间。
下面的代码是上述方法的实现：
C++
// C++ program to check if tower
// of sight issue occurs or not
#include
using namespace std;
// Function to check if point p lies in
// between the line joining p1 and p2
int checkIntersection(pair p1,
pair p2,
pair p)
{
int val;
// If parallel to X-axis
if (p1.second == p2.second
&& p1.second == p.second) {
if (p.first <= max(p1.first, p2.first)
&& (p.first >= min(p1.first, p2.first)))
// Point p lies between p1 and p2
return 1;
}
// If parallel to Y-axis
if (p1.first == p2.first
&& p1.first == p.first) {
if (p.second <= max(p1.second, p2.second)
&& (p.second >= min(p1.second, p2.second)))
// Point p lies between p1 and p2
return 1;
}
// If point p satisfies the equation
// of line joining p1 and p2
else {
val = (p.second - p1.second)
* (p2.first - p1.first)
- (p.first - p1.first)
* (p2.second - p1.second);
if (val == 0)
if ((p.first <= max(p1.first, p2.first)
&& (p.first >= min(p1.first, p2.first)))
&& (p.second <= max(p1.second, p2.second)
&& (p.second >= min(p1.second, p2.second))))
return 1;
}
return 0;
}
// Function to check if tower
// of sight issue occurred
void towerOfSight(pair a,
pair b,
pair c,
pair d)
{
int flag = 0;
if (checkIntersection(a, c, b))
// B lies between AC
flag = 1;
else if (checkIntersection(a, c, d))
// D lies between AC
flag = 1;
else if (checkIntersection(b, d, a))
// A lies between BD
flag = 1;
else if (checkIntersection(b, d, c))
// C lies between BD
flag = 1;
flag ? cout << "Yes\n"
: cout << "No\n";
}
// Driver code
int main()
{
// Point A
pair a = { 0, 0 };
// Point B
pair b = { 0, -2 };
// Point C
pair c = { 2, 0 };
// Point D
pair d = { 0, 2 };
towerOfSight(a, b, c, d);
return 0;
} Java
// Java program to check if tower
// of sight issue occurs or not
class GFG{
static class pair
{
int first, second;
public pair(int first, int second)
{
this.first = first;
this.second = second;
}
}
// Function to check if point p lies in
// between the line joining p1 and p2
static int checkIntersection(pair p1,
pair p2,
pair p)
{
int val;
// If parallel to X-axis
if (p1.second == p2.second
&& p1.second == p.second) {
if (p.first <= Math.max(p1.first, p2.first)
&& (p.first >= Math.min(p1.first, p2.first)))
// Point p lies between p1 and p2
return 1;
}
// If parallel to Y-axis
if (p1.first == p2.first
&& p1.first == p.first) {
if (p.second <= Math.max(p1.second, p2.second)
&& (p.second >= Math.min(p1.second, p2.second)))
// Point p lies between p1 and p2
return 1;
}
// If point p satisfies the equation
// of line joining p1 and p2
else {
val = (p.second - p1.second)
* (p2.first - p1.first)
- (p.first - p1.first)
* (p2.second - p1.second);
if (val == 0)
if ((p.first <= Math.max(p1.first, p2.first)
&& (p.first >= Math.min(p1.first, p2.first)))
&& (p.second <= Math.max(p1.second, p2.second)
&& (p.second >= Math.min(p1.second, p2.second))))
return 1;
}
return 0;
}
// Function to check if tower
// of sight issue occurred
static void towerOfSight(pair a,
pair b,
pair c,
pair d)
{
int flag = 0;
if (checkIntersection(a, c, b) == 1)
// B lies between AC
flag = 1;
else if (checkIntersection(a, c, d) == 1)
// D lies between AC
flag = 1;
else if (checkIntersection(b, d, a) == 1)
// A lies between BD
flag = 1;
else if (checkIntersection(b, d, c) == 1)
// C lies between BD
flag = 1;
System.out.print(flag==1?"Yes\n":"No\n");
}
// Driver code
public static void main(String[] args)
{
// Point A
pair a = new pair( 0, 0 );
// Point B
pair b = new pair( 0, -2 );
// Point C
pair c = new pair( 2, 0 );
// Point D
pair d = new pair( 0, 2 );
towerOfSight(a, b, c, d);
}
}
// This code is contributed by Rajput-JiPython3
# Python 3 program to check if tower
# of sight issue occurs or not
# Function to check if point p lies in
# between the line joining p1 and p2
def checkIntersection(p1,p2,p):
# If parallel to X-axis
if (p1[1] == p2[1]
and p1[1] == p[1]):
if (p[0] <= max(p1[0], p2[0])
and (p[0] >= min(p1[0], p2[0]))):
# Point p lies between p1 and p2
return 1
# If parallel to Y-axis
if (p1[0] == p2[0]
and p1[0] == p[0]):
if (p[1] <= max(p1[1], p2[1])
and (p[1] >= min(p1[1], p2[1]))):
# Point p lies between p1 and p2
return 1
# If point p satisfies the equation
# of line joining p1 and p2
else :
val = ((p[1] - p1[1])*(p2[0] - p1[0])
- (p[0] - p1[0])
* (p2[1] - p1[1]))
if (val == 0):
if ((p[0] <= max(p1[0], p2[0])
and (p[0] >= min(p1[0], p2[0])))
and (p[1] <= max(p1[1], p2[1])
and (p[1] >= min(p1[1], p2[1])))):
return 1
return 0
# Function to check if tower
# of sight issue occurred
def towerOfSight(a, b, c, d):
flag = 0
if (checkIntersection(a, c, b)):
# B lies between AC
flag = 1
elif (checkIntersection(a, c, d)):
# D lies between AC
flag = 1
elif (checkIntersection(b, d, a)):
# A lies between BD
flag = 1
elif (checkIntersection(b, d, c)):
# C lies between BD
flag = 1
if(flag):
print("Yes")
else:
print("No")
# Driver code
if __name__ == "__main__":
# Point A
a = [ 0, 0 ]
# Point B
b = [ 0, -2 ]
# Point C
c = [ 2, 0 ]
# Point D
d = [ 0, 2 ]
towerOfSight(a, b, c, d)
# This code is contributed by chitranayalC#
// C# program to check if tower
// of sight issue occurs or not
using System;
class GFG{
class pair
{
public int first, second;
public pair(int first, int second)
{
this.first = first;
this.second = second;
}
}
// Function to check if point p lies in
// between the line joining p1 and p2
static int checkIntersection(pair p1,
pair p2,
pair p)
{
int val;
// If parallel to X-axis
if (p1.second == p2.second
&& p1.second == p.second) {
if (p.first <= Math.Max(p1.first, p2.first)
&& (p.first >= Math.Min(p1.first, p2.first)))
// Point p lies between p1 and p2
return 1;
}
// If parallel to Y-axis
if (p1.first == p2.first
&& p1.first == p.first) {
if (p.second <= Math.Max(p1.second, p2.second)
&& (p.second >= Math.Min(p1.second, p2.second)))
// Point p lies between p1 and p2
return 1;
}
// If point p satisfies the equation
// of line joining p1 and p2
else {
val = (p.second - p1.second)
* (p2.first - p1.first)
- (p.first - p1.first)
* (p2.second - p1.second);
if (val == 0)
if ((p.first <= Math.Max(p1.first, p2.first)
&& (p.first >= Math.Min(p1.first, p2.first)))
&& (p.second <= Math.Max(p1.second, p2.second)
&& (p.second >= Math.Min(p1.second, p2.second))))
return 1;
}
return 0;
}
// Function to check if tower
// of sight issue occurred
static void towerOfSight(pair a,
pair b,
pair c,
pair d)
{
int flag = 0;
if (checkIntersection(a, c, b) == 1)
// B lies between AC
flag = 1;
else if (checkIntersection(a, c, d) == 1)
// D lies between AC
flag = 1;
else if (checkIntersection(b, d, a) == 1)
// A lies between BD
flag = 1;
else if (checkIntersection(b, d, c) == 1)
// C lies between BD
flag = 1;
Console.Write(flag==1?"Yes\n":"No\n");
}
// Driver code
public static void Main(String[] args)
{
// Point A
pair a = new pair( 0, 0 );
// Point B
pair b = new pair( 0, -2 );
// Point C
pair c = new pair( 2, 0 );
// Point D
pair d = new pair( 0, 2 );
towerOfSight(a, b, c, d);
}
}
// This code is contributed by Princi Singh输出：
Yes