Check whether a straight line can be formed using N co-ordinate points

Given an array arr[] of N co-ordinate points, the task is to check wheather a straight line can be formed using these co-ordinate points.

Input: arr[] = {{0, 0}, {1, 1}, {2, 2}}
Output: Yes
Explanation:
Slope of every two points is same. That is 1.
Therefore, a straight line can be formed using these points.

Input: arr[] = {{0, 1}, {2, 0}}
Output: Yes
Explanation:
Two points in co-ordinate system always forms a straight line.

Approach: The idea is to find the slope of line between every pair of points in the array and if the slope of every pair of point is same, then these points together forms a straight line.

// Slope of line formed by 
// two points (y2, y1), (x2, x1)

Slope of Line = y2 - y1
               ---------
                x2 - x1

Below is the implementation of the above approach:

C++



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// C++ implementation to check 
// if a straight line
// can be formed using N points
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to check if a straight line
// can be formed using N points
bool isStraightLinePossible(
     vector<pair<int, int> > arr, int n)
{
    // First pair of point (x0, y0)
    int x0 = arr[0].first;
    int y0 = arr[0].second;
  
    // Second pair of point (x1, y1)
    int x1 = arr[1].first;
    int y1 = arr[1].second;
  
    int dx = x1 - x0, dy = y1 - y0;
      
    // Loop to iterate over the points
    for (int i = 0; i < n; i++) {
        int x = arr[i].first, y = arr[i].second;
        if (dx * (y - y1) != dy * (x - x1)){
            cout << "NO";
            return false;
        }
    }
    cout << "YES";
    return true;
}
  
// Driver Code
int main()
{
    // Array of points
    vector<pair<int, int> > arr = 
      { { 0, 0 }, { 1, 1 }, { 3, 3 }, { 2, 2 } };
    int n = 4;
      
    // Function Call
    isStraightLinePossible(arr, n);
    return 0;
}

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Output:

YES

Time Complexity: O(N)

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