给定一个整数S ,任务是找到面积为(S / 2)的三角形的坐标。
例子:
Input: S = 4
Output:
(0, 0)
(1000000000, 1)
(999999996, 1)
Input: S = 15
Output:
(0, 0)
(1000000000, 1)
(999999985, 1)
方法:
- 已知坐标为(X1, Y1) , (X2, Y2)和(X3, Y3)的三角形的面积由A = ((X1 * Y2) + (X2 * Y3) + (X3 * Y1) – (X1 * Y3) – (X2 * Y1) – (X3 * Y2)) / 2 。
- 现在将(X1, Y1)固定到(0, 0)给出A = ((X2 * Y3) – (X3 * Y2)) / 2 。
- 假设A = S / 2这意味着S = (X2 * Y3) – (X3 * Y2) 。
- 现在将(X2, Y2)固定为(10 9 , 1) ,方程变为S = 10 9 * Y3 – X3 ,可以通过取一个变量的整数值来求解,该整数值给出了另一个变量的整数值。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
const long MAX = 1000000000;
// Function to find the triangle
// with area = (S / 2)
void findTriangle(long S)
{
// Fix the two pairs of coordinates
long X1 = 0, Y1 = 0;
long X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
cout << "(" << X1 << ", " << Y1 << ")\n";
cout << "(" << X2 << ", " << Y2 << ")\n";
cout << "(" << X3 << ", " << Y3 << ")";
}
// Driver code
int main()
{
long S = 4;
findTriangle(S);
return 0;
}
Java
// Java implementation of the approach
class GFG
{
static final long MAX = 1000000000;
// Function to find the triangle
// with area = (S / 2)
static void findTriangle(long S)
{
// Fix the two pairs of coordinates
long X1 = 0, Y1 = 0;
long X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
System.out.println("(" + X1 +
", " + Y1 + ")");
System.out.println("(" + X2 +
", " + Y2 + ")");
System.out.println("(" + X3 +
", " + Y3 + ")");
}
// Driver code
public static void main (String[] args)
{
long S = 4;
findTriangle(S);
}
}
// This code is contributed by AnkitRai01
Python3
# Python3 implementation of the approach
MAX = 1000000000;
# Function to find the triangle
# with area = (S / 2)
def findTriangle(S) :
# Fix the two pairs of coordinates
X1 = 0; Y1 = 0;
X2 = MAX; Y2 = 1;
# Find (X3, Y3) with integer coordinates
X3 = (MAX - S % MAX) % MAX;
Y3 = (S + X3) / MAX;
print("(", X1, ",", Y1, ")");
print("(", X2, ",", Y2, ")");
print("(", X3, ",", Y3, ")");
# Driver code
if __name__ == "__main__" :
S = 4;
findTriangle(S);
# This code is contributed by kanugargng
C#
// C# implementation of the above approach
using System;
class GFG
{
static readonly long MAX = 1000000000;
// Function to find the triangle
// with area = (S / 2)
static void findTriangle(long S)
{
// Fix the two pairs of coordinates
long X1 = 0, Y1 = 0;
long X2 = MAX, Y2 = 1;
// Find (X3, Y3) with integer coordinates
long X3 = (MAX - S % MAX) % MAX;
long Y3 = (S + X3) / MAX;
Console.WriteLine("(" + X1 +
", " + Y1 + ")");
Console.WriteLine("(" + X2 +
", " + Y2 + ")");
Console.WriteLine("(" + X3 +
", " + Y3 + ")");
}
// Driver code
public static void Main (String[] args)
{
long S = 4;
findTriangle(S);
}
}
// This code is contributed by PrinciRaj1992
Javascript
输出:
(0, 0)
(1000000000, 1)
(999999996, 1)
时间复杂度: O(1)
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