yugantarjain / Optimal-BST-quadratic-time

Algorithmic solution of Optimal Binary Search Tree in Quadratic Time. Reduces time complexity from O(n^3) to O(n^2).

Optimal BST (Quadratic-Time implementation)

Special implementation of Dynamic Programming based Optimal Binary Search Tree algorithm. Uses Knuth's Theorem to achieve Quadratic Time complexity.

Time complexity chart:

This Implementation(Highy Efficient)	Usual DP based implementation	Naive Implementation
Theta(n^2)	Theta(n^3)	Theta(n^4)

Knuth's Theorem:

There are always roots of optimal subtrees such that root[i,j-1] <= root[i,j] <= root[i+1,j] for all 1<=i<j<=n.

Sample Input/Output

Input

Keys Probability = 0.15, 0.10, 0.05, 0.10, 0.20
Dummy Keys Probablity = 0.05, 0.10, 0.05, 0.05, 0.05, 0.10

Output

Reference

Introduction to Algorithms
by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein