Using the StateGraph shown in figure 1, describe the order in which vertices would be visited, predecessor of each vertex, and the distance from the source using breadth-first search algorithm. Also, describe the order in which vertices would be visited, the order in which the vertices are marked, predecessor of each vertex, and the distance from the source using the depth- first search algorithm.

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Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to solve the problem. Test and mistake, rule of thumb, or an educated estimate are all examples of heuristics. These methods are sufficient for achieving an immediate, brief aim. When a heuristic is used in practice, it works as predicted. It can, however, produce systematic errors. Trial and error is an important heuristic that may be used in a variety of situations, from cross-linking nuts and bolts to determining the values of given input variables in mathematical puzzles. Additional hypotheses, visual illustrations, simplification, and forward or backward reasoning are all common heuristics in mathematics.