"General drinking horse" is a classic geometric problem, and its basic problem is to find the shortest path, so that the general can walk from one side of the river to the other and avoid being discovered by the enemy. Mathematically, this problem is called "shortest path problem" or "shortest path problem".
The basic steps to solve the problem are as follows:
Determine the conditions of the problem:
First, you need to determine all the conditions of the problem. For the problem of "general drinking horses", these conditions may include: the width of the river, the location of two castles (or two points), whether there are other obstacles (such as forests and hills), and whether the general can take a diagonal line.
Define the goal of the problem:
Determine the goal of the problem. In the problem of "drinking horses", the goal is to find the shortest path from the starting point to the end point.
Using mathematical models:
According to the conditions and objectives of the problem, choose the appropriate mathematical model to solve it. For the problem of "generals drinking horses", the commonly used mathematical models are Euclid distance formula and Manhattan distance formula.
Perform calculations:
Calculate according to the selected mathematical model. In the problem of "drinking horses in general", it may be necessary to analyze mathematical tools such as geometry and calculus.
Integrated answer:
According to the calculation results, the shortest path to solve the problem is synthesized.
In addition, there are some commonly used skills and strategies for the problem of "drinking horses in general", such as "symmetry" and "the shortest line segment between two points".
Expand knowledge:
Analytic geometry:
Analytic geometry is a branch of mathematics, which studies the geometric shape of graphics and its position in plane or space. It can help us express geometric elements such as points, lines and surfaces in two-dimensional or three-dimensional space and their relationships.
Calculus:
Calculus is a branch of mathematics that studies functions, limits and infinitesimals. It can help us understand the changing trend of the function and how to find the minimum or maximum value of the function.
Shortest path problem:
In graph theory, the shortest path problem is to find the shortest path from one vertex to another. This kind of problem is widely used in operational research, computer science and network theory.
Dynamic planning:
Dynamic programming is an algorithm design technology, which can be used to solve problems that need to make a series of decisions. When solving the shortest path problem, dynamic programming can help us avoid calculating the same subpath repeatedly, thus improving the efficiency of the algorithm.
Dijkstra algorithm and Bellman-Ford algorithm;
Dijkstra algorithm and Bellman-Ford algorithm are two commonly used algorithms to solve the shortest path problem. Dijkstra algorithm is suitable for graphs without negative weighted edges, while Bellman-Ford algorithm can deal with graphs with negative weighted edges.