Merge pull request #286 from neha030/dev8

Collinearity of three points added

Author: smv1999

Dynamic Programming/Collinearity_of_three_points.cpp

@@ -0,0 +1,65 @@
+/*
+Problem Statement
+Given 3 co-ordinates , find if they are collinear or not .
+Three or more points are said to be collinear if they all lie on the same straight line.
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+struct Point {
+    int x;
+    int y;
+};
+
+/*
+We can calculate the area formed by the three points, and if the area is
+zero then they lie on a same line. 
+*/
+bool check_collinear(Point a, Point b, Point c) {
+    int area = 0;
+
+    /*
+    The Area of a Triangle formed by three points (x1, y1), (x2, y2), (x3, y3)
+    is determined by the following formula
+    
+    Area = (1/2) * {x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)}     
+    */
+    area = a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y);
+
+    if (area == 0)
+        return true;
+    else
+        return false;
+}
+
+int main() {
+    int x, y;
+    Point a, b, c;
+    cout << "\nEnter the first co-ordinates:  ";
+    cin >> a.x >> a.y;
+    cout << "Enter the second co-ordinates: ";
+    cin >> b.x >> b.y;
+    cout << "Enter the third co-ordinates:  ";
+    cin >> c.x >> c.y;
+
+    if (check_collinear(a, b, c)) {
+        cout << "\nThe given points are collinear" << endl;
+    } else {
+        cout << "\nThe given points are not collinear" << endl;
+    }
+    return 0;
+}
+
+/*
+Time Complexity: O(1)
+Space Complexity: O(1)
+
+SAMPLE INPUT AND OUTPUT
+
+Enter the first co-ordinates:  1 1
+Enter the second co-ordinates: 2 2
+Enter the third co-ordinates:  3 3
+
+The given points are collinear
+*/