Given a triangle ABC. H horizontal lines from side AB to AC (as shown in fig.) and V vertical lines from vertex A to side BC are drawn, the task is to find the total no. of triangles formed.
Input: H = 2, V = 2
As we see in the image above, total triangles formed are 18.
Input: H = 3, V = 4
Approach: As we see in the images below, we can derive a general formula for above problem:
- If there are only h horizontal lines then total triangles are (h + 1).
- If there are only v vertical lines then total triangles are (v + 1) * (v + 2) / 2..
- So, total triangles are Triangles formed by horizontal lines * Triangles formed by vertical lines i.e. (h + 1) * (( v + 1) * (v + 2) / 2).
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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- Number of Triangles that can be formed given a set of lines in Euclidean Plane
- Number of horizontal or vertical line segments to connect 3 points
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- Number of triangles that can be formed with given N points
- Vertical and Horizontal retrieval (MRT) on Tapes
- Number of triangles formed by joining vertices of n-sided polygon with one side common
- Count of different straight lines with total n points with m collinear
- Number of triangles formed by joining vertices of n-sided polygon with two common sides and no common sides
- Number of triangles after N moves
- Count the number of possible triangles
- Count number of right triangles possible with a given perimeter
- Number of triangles in a plane if no more than two points are collinear
- Number of triangles possible with given lengths of sticks which are powers of 2
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