Given an equilateral triangle, the task is to compute the total number of triangles after performing the following operation N times.
For every operation, the uncolored triangles are taken and divided into 4 equal equilateral triangles. Every inverted triangle formed is colored. Refer to the below figure for more details.
For N=1 the triangle formed is:
For N=2 the triangle formed is:
Input :N = 10
Output : 118097
Input : N = 2
Output : 17
At every operation, 3 uncolored triangles, 1 colored triangle and the triangle itself is formed On writing the above statement mathematically; count of triangles at Nth move = 3 * count of triangles at (N-1)th move + 2 Therefore, initializing a variable curr = 1 and tri_count = 0 Next, a loop is iterated from 1 to N For every iteration, the operation mentioned above is performed. Finally, the tri_count is returned
Below is the implementation of the above approach:
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Improved By : 29AjayKumar