Given three non-collinear points whose co-ordinates are P(p1, p2), Q(q1, q2) and R(r1, r2) in the X-Y plane. Find the number ofintegral / lattice points strictly inside the triangle formed by these points.
Note - A point in X-Y plane is said to be integral / lattice point if both its co-ordinates are integral.
Example 1:
Input:
p = (0,0)
q = (0,5)
r = (5,0)
Output: 6
Explanation:
There are 6 integral points in the
triangle formed by p, q and r.
Example 2:
Input:
p = (62,-3)
q = (5,-45)
r = (-19,-23)
Output: 1129
Explanation:
There are 1129 integral points in the
triangle formed by p, q and r.
Your Task:
You don't need to read input or print anything. Your task is to complete the function InternalCount() which takes the three points p, q and r as input parameters and returns the number of integral points contained within the triangle formed by p, q and r.
Expected Time Complexity: O(Log2109) Expected Auxillary Space: O(1)
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Avoid using static/global variables in coding problems as your code is tested
against multiple test cases and these tend to retain their previous values.
Passing the Sample/Custom Test cases in coding problems does not guarantee the
correctness of code. On submission, your code is tested against multiple test cases
consisting of all possible corner cases and stress constraints.
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