贪婪算法--- 拓扑排序（The greedy algorithm, topological sorting）.docVIP

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贪婪算法--- 拓扑排序（The greedy algorithm, topological sorting）.doc

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贪婪算法--- 拓扑排序（The greedy algorithm, topological sorting）

贪婪算法--- 拓扑排序（The greedy algorithm, topological sorting） Topological sort A complex project can usually be broken down into a set of small tasks, and the completion of these small tasks means the completion of the whole project. For example, the automobile assembly project can be divided into the following tasks: placing the chassis on the assembly line, installing the axle, placing the seat on the chassis, painting, loading the brakes, loading doors and so on. There are precedence relations between tasks. For example, the bottom plate should be put on the assembly line before loading the axle. The order of tasks can be represented by directed graphs called Activity On Vertex (AOV) networks. The vertices of the directed graph represent the task, and the directed edge (I, J) represents the precedence relationship: the task I must be completed before the task J starts. Figure 1 - 4 shows the six tasks of the project, the edge (1, 4) said the 1 task in task 4 before completion, the same edge (4, 6) said the 4 task in task 6 before completion, edge (1, 4) and (4, 6) together the 1 tasks in the task 6 before the start of the closed system is completed, before and after delivery. It can be seen that the edges (1, 4) are redundant, because sides (1, 3) and (3, 4) have implied this relationship. In many cases, tasks are carried out continuously, such as car assembly problems, or purchases of consumer goods (bicycles, childrens swings, mowers, etc.) that are usually required to be assembled. We can assemble according to the order we suggest. In the directed graph created by the task, the edge (I, J) indicates that in the assembly sequence, the task I is in front of the task J, and the sequence having this property is called the topological sequence (topological, orders, or topological sequences). The process of establishing topological sequences based on the directed graph of a task is called topological sorting (topological, sorting). Figure 1 - 4 of the task has a variety o