Given an integer K, and two arrays X[] and Y[] both consisting of N integers, where (X[i], Y[i]) is a coordinate in a plane, the task is to find the total number of pairs of points such that the line passing through them has a slope in the range [-K, K].
Examples:
Input: X[] = {2, 1, 0}, Y[] = {1, 2, 0}, K = 1
Output: 2
Explanation:
The set of pairs satisfying the given condition are [(0, 0), (2, 1)] and [(1, 2), (2, 1)].Input: X[] = {2, 4}, Y[][] = {5, 6}, K = 1
Output: 1
Approach: The idea is to traverse through all pairs of points and check whether their slope lies in the range [-K, K] or not. Follow the steps below to solve the problem:
- Initialize a variable, say ans to 0 to store the resultant count of pairs.
- Now, generate all possible pairs of coordinates and if the slope of the 2 points (X[i], Y[i]) and (X[j], Y[j]) lies in the range [-K, K], then increment ans by 1.
- After completing the above steps, print the value of and as the result.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the number of pairs // of points such that the line passing // through them has a slope in the range[-k, k] void findPairs(vector< int > x, vector< int > y,
int K)
{ int n = x.size();
// Store the result
int ans = 0;
// Traverse through all the
// combination of points
for ( int i = 0; i < n; ++i) {
for ( int j = i + 1; j < n; ++j) {
// If pair satisfies
// the given condition
if (K * abs (x[i] - x[j])
>= abs (y[i] - y[j])) {
// Increment ans by 1
++ans;
}
}
}
// Print the result
cout << ans;
} // Driver Code int main()
{ vector< int > X = { 2, 1, 0 },
Y = { 1, 2, 0 };
int K = 1;
// Function Call
findPairs(X, Y, K);
return 0;
} |
// Java program for the above approach import java.util.*;
class GFG
{ // Function to find the number of pairs // of points such that the line passing // through them has a slope in the range[-k, k] static void findPairs( int [] x, int [] y,
int K)
{ int n = x.length;
// Store the result
int ans = 0 ;
// Traverse through all the
// combination of points
for ( int i = 0 ; i < n; ++i) {
for ( int j = i + 1 ; j < n; ++j) {
// If pair satisfies
// the given condition
if (K * Math.abs(x[i] - x[j])
>= Math.abs(y[i] - y[j])) {
// Increment ans by 1
++ans;
}
}
}
// Print the result
System.out.print(ans);
} // Driven Code public static void main(String[] args)
{ int [] X = { 2 , 1 , 0 };
int [] Y = { 1 , 2 , 0 };
int K = 1 ;
// Function Call
findPairs(X, Y, K);
} } // This code is contributed by sanjoy_62. |
# Python3 program for the above approach # Function to find the number of pairs # of points such that the line passing # through them has a slope in the range[-k, k] def findPairs(x, y, K):
n = len (x)
# Store the result
ans = 0
# Traverse through all the
# combination of points
for i in range (n):
for j in range (i + 1 , n):
# If pair satisfies
# the given condition
if (K * abs (x[i] - x[j]) > = abs (y[i] - y[j])):
# Increment ans by 1
ans + = 1
# Print the result
print (ans)
# Driver Code if __name__ = = '__main__' :
X = [ 2 , 1 , 0 ]
Y = [ 1 , 2 , 0 ]
K = 1
# Function Call
findPairs(X, Y, K)
# This code is contributed by mohit kumar 29.
|
// C# program for the above approach using System;
class GFG{
// Function to find the number of pairs // of points such that the line passing // through them has a slope in the range[-k, k] static void findPairs( int [] x, int [] y,
int K)
{ int n = x.Length;
// Store the result
int ans = 0;
// Traverse through all the
// combination of points
for ( int i = 0; i < n; ++i)
{
for ( int j = i + 1; j < n; ++j)
{
// If pair satisfies
// the given condition
if (K * Math.Abs(x[i] - x[j]) >=
Math.Abs(y[i] - y[j]))
{
// Increment ans by 1
++ans;
}
}
}
// Print the result
Console.WriteLine(ans);
} // Driver Code public static void Main(String []args)
{ int [] X = { 2, 1, 0 };
int [] Y = { 1, 2, 0 };
int K = 1;
// Function Call
findPairs(X, Y, K);
} } // This code is contributed by souravghosh0416 |
<script> // Javascript program for the above approach
// Function to find the number of pairs
// of points such that the line passing
// through them has a slope in the range[-k, k]
function findPairs(x, y, K)
{
let n = x.length;
// Store the result
let ans = 0;
// Traverse through all the
// combination of points
for (let i = 0; i < n; ++i) {
for (let j = i + 1; j < n; ++j) {
// If pair satisfies
// the given condition
if (K * Math.abs(x[i] - x[j])
>= Math.abs(y[i] - y[j])) {
// Increment ans by 1
++ans;
}
}
}
// Print the result
document.write(ans);
}
// Driver code
let X = [ 2, 1, 0 ], Y = [ 1, 2, 0 ];
let K = 1;
// Function Call
findPairs(X, Y, K);
// This code is contributed by divyesh072019.
</script> |
2
Time Complexity: O(N2)
Auxiliary Space: O(1)