Question

fill in the blank so that the resulting statement is true.
a method that determines the solution to the traveling salesperson problem involves listing all hamilton circuits and selecting the circuit with the maximum sum of weights. this method is called the _____ method.
a method that determines the solution to the traveling salesperson problem involves listing all hamilton circuits and selecting the circuit with the minimum sum of weights. this method is called the _____ method.

Explanation:

The traveling salesperson problem (TSP) is a well - known problem in graph theory. The brute - force method for solving the TSP involves checking all possible Hamilton circuits (a circuit that visits each vertex exactly once and returns to the starting vertex). By calculating the sum of the weights (edge lengths) for each Hamilton circuit and then selecting the circuit with the minimum sum of weights, we can find the optimal solution. This is a basic and straightforward (albeit computationally expensive for large graphs) approach to solving the TSP.

Answer:

Brute - Force