Update README.md

add A* algorithm

Author: MASTERDAMMU

README.md

@@ -21,4 +21,7 @@ The algorithm is named after Robert W. Floyd, who was credited with its inventio
 The key insight in the algorithm is as follows. If there is a cycle, then, for any integers i ≥ μ and k ≥ 0, xi = xi + kλ, where λ is the length of the loop to be found and μ is the index of the first element of the cycle. Based on this, it can then be shown that i = kλ ≥ μ for some k if and only if xi = x2i. Thus, the algorithm only needs to check for repeated values of this special form, one twice as far from the start of the sequence as the other, to find a period ν of a repetition that is a multiple of λ. Once ν is found, the algorithm retraces the sequence from its start to find the first repeated value xμ in the sequence, using the fact that λ divides ν and therefore that xμ = xμ + v. Finally, once the value of μ is known it is trivial to find the length λ of the shortest repeating cycle, by searching for the first position μ + λ for which xμ + λ = xμ.
 
 The algorithm thus maintains two pointers into the given sequence, one (the tortoise) at xi, and the other (the hare) at x2i. At each step of the algorithm, it increases i by one, moving the tortoise one step forward and the hare two steps forward in the sequence, and then compares the sequence values at these two pointers. The smallest value of i > 0 for which the tortoise and hare point to equal values is the desired value ν.
+## A* Algorithm
+A* algorithm is used to find the shortest path in a grapg/tree. As it uses an heuristic to guide the search. The algorithm starts from an initial start node, expands neighbors and updates the full path cost of each neighbor. It selects the neighbor with the lowest cost and continues until it finds a goal node, this can be implemented with a priority queue or by sorting the list of open nodes in ascending order. It is important to select a good heuristic to make A* fast in searches, a good heuristic should be close to the actual cost but should not be higher than the actual cost.
 
+A* is complete and optimal, it will find the shortest path to the goal. A good heuristic can make the search very fast, but it may take a long time and consume a lot of memory in a large search space. The time complexity is O(n) in a grid and O(b^d) in a graph/tree with a branching factor (b) and a depth (d). The branching factor is the average number of neighbor nodes that can be expanded from each node and the depth is the average number of levels in a graph/tree.