## BdOI 2013 National Problem 5

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bristy1588
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Joined:Sun Jun 19, 2011 10:31 am
BdOI 2013 National Problem 5
You are given a stick of length \$N\$. You want to break it in three pieces such that it can form a
triangle. How many distinct triangles can you make? Two triangles are equal if all the side
lengths are same when sorted in ascending order of length. So \$(1, 3, 2)\$ is same to \$(3, 1, 2)\$
because their side lengths are same if we sort them, which is \$(1, 2, 3)\$. But \$(1, 3, 4) \$is not
same with \$(1, 2, 3)\$. Suppose the lengths of three pieces are \$ X, Y, Z (X <= Y <= Z) \$ respectively.
Following constraints should be maintained:
\$
1. X, Y, Z > 0. \$
\$2. X, Y, Z \$ is an integer.
\$3. X + Y >= Z\$
\$4. X + Y + Z = N
\$

For example if \$ N = 14 \$, then there are \$7\$ triangles: \$(1, 6, 7), (2, 5, 7), (2, 6, 6), (3, 4, 7), (3, 5, 6),
(4, 4, 6), (4, 5, 5)\$.

INPUT
First line will give you the number of test cases,\$ T (T<=100) \$. Then each line will have an
integer \$ N (0< N <= 300000) \$

OUTPUT
For each test case, print the test case number starting from \$1\$ and an integer denoting the
number of distinct triangles possible.

SAMPLE INPUT
SAMPLE OUTPUT
Bristy Sikder

sagor78
Posts:1
Joined:Fri Sep 02, 2022 9:44 pm

### Re: BdOI 2013 National Problem 5

is this probelm editorial available here?