Editorial for TLE '17 Contest 7 P1 - Stargazing

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Author: leonchen0613

Use two arrays to keep track of the X and Y coordinates for every planet. Let the first planet be located at the origin (0, 0). For each other planet, calculate its X and Y coordinates relative to the first planet, using the X and Y coordinates of a previously located planet:

x[i] = x[P_i] + X_i

y[i] = y[P_i] + Y_i

After that, there are two main ways to count the number of distinct pairs of coordinates:

  1. Insert all the pairs of coordinates into a set. The size of the set will be your answer. Time Complexity: O(N \log N)

  2. For each planet, loop through all previous planets to check if their coordinates match. If that new planet is unique so far, increment your answer by one. Time Complexity: O(N^2)


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