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authormo khan <mo.khan@gmail.com>2020-09-26 19:44:29 -0600
committermo khan <mo.khan@gmail.com>2020-09-26 19:44:29 -0600
commit5cb4ce51804e8bc60fef6f3e33ceaee0f05bacc6 (patch)
tree58a88d84a8d826ae89a23d95d74404a1741bd3ba /src/03/08
parentc93020800e852b17f4cf30fb867bccac88d61cbd (diff)
Collapse all questions into a single README
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-Prove that a binary tree with `k` leaves has height at least `log k`.
-
-The proof can be derived with the following.
-Suppose we have a function `h` that takes input `k`
-and returns a tree with `k` leaves.
-
-For each positive natural number we can
-assert that the height of the tree must greater
-than or equal to `log2(k)`.
-
-```plaintext
-for each positive natural number
- assert(height(h(k)) >= log2(k))
-```
-
-An example test is provided in `btree_test.c` that
-asserts that this holds true for the first
-500 positive integers.
-
-```c
-for (int k = 0; k < 500; ++k)
- assert_that(btree_height(btree_generate(k)) >= log2(k), is_equal_to(true));
-```