##### Short Problem Definition:

Count the number of triangles that can be built from a given set of edges.

##### Link

##### Complexity:

expected worst-case time complexity is O(N^{2});

expected worst-case space complexity is O(1)

##### Execution:

Apply the caterpillar method. We know that in a sorted array every position between Q and R will be bigger than Q and therefore P+Q will be bigger than R. I therefore either increment Q if P+Q is not larger than R or increment R as far as possible.

##### Solution:

def solution(A): A.sort() print A triangle_cnt = 0 for P_idx in xrange(0, len(A)-2): Q_idx = P_idx + 1 R_idx = P_idx + 2 while (R_idx < len(A)): if A[P_idx] + A[Q_idx] > A[R_idx]: triangle_cnt += R_idx - Q_idx R_idx += 1 elif Q_idx < R_idx -1: Q_idx += 1 else: R_idx += 1 Q_idx += 1 return triangle_cnt

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