Our goal is to organize the keys in a binary search tree so that the average time it takes to locate a key is minimized. In general, we cannot find an optimal binary search tree by considering all bin
Consider the multiplication of the following four matrices. $$A \quad\times\quad B \quad\times\quad C \quad\times\quad D \\(20\times2) \ (2\times30) \ (30\times12) \ (12\times8)$$ A(B(CD)) (30×12×8)
The principle of optimality is said to apply in a problem if an optimal solution to an instance of a problem always contains optimal solutions to all substances. If the principle of optimality applies
A common problem encountered by air travelers is the determination of the shortest way to fly from one city to another when a direct flight does not exist. Next we develop an algorithm that solves thi
$$\begin{align}{n \choose k} &= \frac{n!}{k!(n-k)!} \quad for \ 0 \leq k \leq n&. \\{n \choose k} &=\begin{cases} {n-1 \choose k-1} + {n-1 \choose k} &\text{0 < $k$ < $n$} \\
The divide and conquer algorithm works in problems such as Mergesort, where the smaller instances are unrelated. However, in problems such as nth Fibonacci term, the smaller instances are related. For