#### Uniform Cost Search, Bidirectional Search and Flood Fill Algorithm

Uniform Cost Search (UCS):

The Uniform-cost search expands the least-cost leaf node initially. It is complete and dissimilar; breadth-first search is optimal even when operators contain differing costs. Its time complexity and space are similar as for BFS.

BFS determines the shallowest goal state; however this might not always be the least-cost solution for a general path cost function. UCS always alters BFS by expanding the lowest-cost node on the fringe.

Iterative Depending Search:

Iterative deepening search calls depth-limited search with rising limits until a goal is found. This is complete and optimal, and consists of time complexity of O(b^d)

IDS is a strategy which sidesteps the issue of selecting the best depth limit by trying all possible depth limits: first depth 0, then depth 1, then depth 2, and so forth. In effect, IDS joins the benefits of BFS and DFS.

Bidirectional Search:

Bidirectional search can extremely decrease the time complexity, however is not always applicable. Its memory needs might be impractical.

BDS concurrently search both forward form the initial state and backward from the goal, and stop whenever the two searches meet in the middle, though search similar to this is not always possible.

Informed Search:

Dissimilar to uninformed Search, Informed Search recognizes some information which can be employed to enhance the path selection. Illustrations of Informed Search: Best First Search, IHeuristic Search like A*.

Best First Search:

We define a function f(n) = g(n) where g(n) is the predicted value from node 'n' to goal. This search is "informed" since we do a computation to estimate g(n).

A* Search:

f(n) = h(n) + g(n), identical to Best First Search, it employs g(n), however as well uses h(n), the total cost incurred up to now. The best search to consider when you know how to calculate g(n).

Flood Fill Algorithm:

Flood fill can be performed in three fundamental ways: depth-first, breadth-first, and breadth-first scanning. The fundamental idea is to find some node that has not been assigned to a component and to compute the component which contains. The question is how to evaluate the component.

In depth-first formulation, the algorithm looks at each and every step via all of the neighbors of the current node, and, for such that have not been allocated to a component yet, assigns them to this component and recurses on them.

In breadth-first formulation, rather than recursing on the newly allocated nodes, they are added up to a queue.

In breadth-first scanning formulation, each and every node has two values: component and visited. Whenever calculating the component, the algorithm goes via all of the nodes which have been assigned to that component however not visited yet, and allocates their neighbors to the current component.

The depth-first formulation is the simplest to code and debug, however can need a stack as big as the original graph. For explicit graphs, this is not so terrible, however for implicit graphs, like the problem presented has; the numbers of nodes can be much large.

The breadth-formulation does a little enhanced, since the queue is much more proficient than the run-time stack is, however can still run into similar problem. Both depth-first and breadth-first formulations run in N + M time, where M is the number of edges and N is the number of vertices.

The breadth-first scanning formulation, though, needs very little extra space. However, being a little tricky, it needs no extra space. Though, it is slower, requiring up to N*N + M time, where N is the number of vertices in graph.

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