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Program to find number of possible BSTs can be generated using n distinct nodes in Python
Suppose we have a number n. If we have numbers like [1,2,...,n] we have to count number ofpossible BSTs can be formed using these n values. If the answer is too large, then mod the result by 10^9+7.
So, if the input is like n = 3, then the output will be 14,
To solve this, we will follow these steps
- a := a list with values [0, 1]
- m := 10^9+7
- max_n := 1000
- for k in range 2 to max_n + 1, do
- insert (1 + sum of all elements of the list (a[i] * a[k - i] for all i in range(1, k))) mod m at the end of a
- return (a[n + 1] - 1) mod m
Example
Let us see the following implementation to get better understanding −
def solve(n): a = [0, 1] m = 10**9+7 max_n = 1000 for k in range(2, max_n + 2): a.append((1 + sum(a[i] * a[k - i] for i in range(1, k))) % m) return ((a[n + 1] - 1) % m) n = 3 print(solve(n))
Input
3
Output
14
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