Check whether a given point lies inside a rectangle or not
Given four points of a rectangle, and one more point P. Write a function to check whether P lies within the given rectangle or not.
Input : R = [(10, 10), (10, -10), (-10, -10), (-10, 10)] P = (0, 0) Output : yes Illustration :
Input : R = [(10, 10), (10, -10), (-10, -10), (-10, 10)], P = (20, 20) Output : no Illustration :
Prerequisite: Check whether a given point lies inside a triangle or not
Approach : Let the coordinates of four corners be A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). And coordinates of the given point P be (x, y)
1) Calculate area of the given rectangle, i.e., area of the rectangle ABCD as area of triangle ABC + area of triangle ACD.
Area A = [ x1(y2 – y3) + x2(y3 – y1) + x3(y1-y2)]/2 + [ x1(y4 – y3) + x4(y3 – y1) + x3(y1-y4)]/2
2) Calculate area of the triangle PAB as A1.
3) Calculate area of the triangle PBC as A2.
4) Calculate area of the triangle PCD as A3.
5) Calculate area of the triangle PAD as A4.
6) If P lies inside the triangle, then A1 + A2 + A3 + A4 must be equal to A.
Time complexity: O(1)
Auxiliary Space: O(1)
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