CN107292464B - Automatic evaluation method and system based on directed acyclic graph and topological sorting - Google Patents

Automatic evaluation method and system based on directed acyclic graph and topological sorting Download PDF

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CN107292464B
CN107292464B CN201610195271.6A CN201610195271A CN107292464B CN 107292464 B CN107292464 B CN 107292464B CN 201610195271 A CN201610195271 A CN 201610195271A CN 107292464 B CN107292464 B CN 107292464B
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俞昊然
杨博洋
杨斌
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Beijing Judaoyouda Network Technology Co ltd
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Abstract

The invention relates to an automatic evaluation method and system based on directed acyclic graph and topological sorting. The method comprises the steps that a directed acyclic graph is formed by logical nodes and the directional relation between the logical nodes, topological ordering is carried out on the directed acyclic graph, and a solution set is generated; and traversing and comparing the result sequence submitted by the user with the solutions in the solution set to obtain a final result. The system comprises an information generation subsystem, a foreground interaction subsystem and a logic verification subsystem. The user can use the system to generate elements in the process of mathematic proof and deduction, realize large-scale online detection of logical thinking tightness and deductive reasoning ability of the learner, and simultaneously acquire the problems encountered by the learner in the process of deduction. The invention provides a high-efficiency, simple and easy-to-use teaching tool for teaching workers, and simultaneously provides a strong-interactivity and interesting information interaction and learning platform for learners, thereby training the computational thinking of users more effectively.

Description

Automatic evaluation method and system based on directed acyclic graph and topological sorting
Technical Field
The invention relates to the technical field of computer science, deductive reasoning and mathematical proof, in particular to an automatic evaluation method and system based on directed acyclic graph and topological sorting.
Background
With the continuous and rapid popularization of computer science, the learning appeal of people to the science reaches unprecedented intensity. As is well known, computer science has been developed based on mathematical science, and the development of computers in the field of mathematical identification has achieved a certain achievement, and the well-known four-color theorem is identified by using a computer as an auxiliary tool. However, the technology and application of combining computer science with mathematical evidence and applying the combination to teaching are very deficient, and the detection of learners by a teacher usually belongs to repetitive work. In the existing teaching system, the teaching mode for cultivating the deductive reasoning and computational thinking ability of the learner is extremely limited, and large-scale training and evaluation are difficult, so that the design of an automatic evaluation method and system which are suitable for analyzing and detecting the logic thinking tightness and the deductive reasoning ability and can collect relevant behavior data becomes extremely urgent.
Disclosure of Invention
The invention aims to realize an automatic evaluation method and system based on directed acyclic graph and topological sorting, which are used for solving the problem that a teacher cannot train in scale and evaluate the deductive reasoning and computational thinking capability of a learner.
The invention adds corresponding logic modules to be verified aiming at different course design requirements, wherein the logic modules to be verified comprise correct logic nodes and automatically generated logic nodes with interference. And then adding a pointing relationship to the added correct logical node, and in the process, checking whether the pointing relationship between the logical node and the logical node conforms to the definition of the directed acyclic graph. In the effective logic module verification process, all logic nodes of the directed acyclic graph are subjected to topology sequencing, and each sequence after the topology sequencing can be regarded as a group of correct solutions. The system and the method can completely monitor the deduction process of the learner and accurately verify the deduction reasoning ability of the learner.
The logic node refers to the process of deducing individual conclusions by deduction from general preconditions in a propositional demonstration process. For example, given the preconditions of a > b, b > c, and c > d, the conclusion of a > d needs to be proved first, so the process of deriving a > c from the conditions of a > b and b > c is a logical node.
The purpose of the invention is realized by the following technical scheme:
an automatic evaluation method based on directed acyclic graph and topological sorting comprises the following steps:
1) generating and storing logic nodes, relations among the logic nodes and interference items related in the logic proving process;
2) taking the logic nodes as a plurality of vertexes in a graph structure, taking the directional relation among the logic nodes as a plurality of directed edges connecting the vertexes in the graph structure to form a directed acyclic graph, and carrying out topological sorting on the directed acyclic graph to generate at least one correct solution sequence as a solution set;
3) selecting data with certain confusion degree from the stored logic nodes and the corresponding interference items, displaying the data to a user and waiting for the user to submit a sequenced result sequence;
4) and acquiring a result sequence submitted by a user, performing traversal comparison on the result sequence and the solution in the solution set, and then returning a final result.
Further, the method for generating the interference term in step 1) mainly includes five methods: the first method is digital fluctuation, and digital content in a logic node is adjusted within a certain range; the second method is that the operation symbol fluctuates, and the operation symbol content in the logic node is adjusted; the third method is predicate logic change, and according to the content in the logic node, any logic condition is adjusted to be a logic condition, or the logic condition is adjusted to be any logic condition; the fourth method is negative logic change, and the content of the original logic node is adjusted to negative logic; the fifth method is a reverse propositional logic change, which replaces the conditions and the conclusions in the original logic node content and adjusts the conditions into the logic of deducing the conditions according to the conclusions. In this manner, one or more methods are used to generate interference terms for selection by the user.
Further, step 3) comprises the following sub-steps:
a) acquiring information such as the logical nodes, interference items and the pointing relationships among the logical nodes generated in the step 1), and grouping and arranging the information for the following steps;
b) when receiving the result sequence information submitted by the user, simply analyzing the information contained in the sequence, and if the sequence contains the elements of the interference item grouping in the step a), regarding the sequence as an error solution and returning error information; otherwise, continuously detecting whether the result sequence is a correct solution;
c) traversing and matching the result sequence in the step b) with the solution set in the step 2), and if the result sequence exists in the solution set, namely the result sequence is a correct solution, returning correct prompt information; otherwise, returning wrong prompt information.
An automatic evaluation system based on directed acyclic graph and topological sorting by adopting the method comprises the following steps:
the information generation subsystem is used for generating the logic nodes, the relation among the logic nodes and the interference items related in the logic proving process, carrying out validity verification on the generated information and sending the information to the foreground interaction subsystem;
the foreground interaction subsystem receives and responds to a result sequence generated by a user in the interaction process, sends the result sequence to the logic verification subsystem and displays feedback information of the logic verification subsystem;
and the logic verification subsystem analyzes the relation between the logic nodes generated by the information generation subsystem, generates a set of effective solutions as a solution set, matches and verifies whether the result sequence is an effective solution according to the result sequence submitted by the foreground interaction subsystem, and then returns the detection result to the foreground interaction subsystem.
Further, the information generation subsystem includes:
the logic node generating module is used for adding information in the logic nodes and sending all the generated logic nodes to the interference item generating module, the logic node relation generating module and the logic node screening module of the foreground interaction subsystem;
the interference item generation module is used for acquiring the information in the logic node generation module and automatically generating a series of interference items for a user to select according to the information; the user can also directly add a new interference item and then send the information of the interference item which is determined to be generated to a logic node screening module of the foreground interaction subsystem;
the logical node relation generating module is used for adding a pointing relation to the logical nodes generated in the logical node generating module and sending the pointing relation to the logical node and node relation checking module;
and the logical node and node relation checking module is used for regarding the logical nodes as vertexes in the graph structure and regarding the logical node relation as a directed edge in the graph structure according to the information generated by the logical node generating module and the logical node relation generating module, and then checking whether the graph meets the condition of the directed acyclic graph.
Furthermore, the method for generating the interference item used by the interference item generation module mainly comprises five methods, wherein the first method is digital fluctuation and adjusts the digital content in the logic node within a certain range; the second method is that the operation symbol fluctuates, and the operation symbol content in the logic node is adjusted; the third method is predicate logic change, and according to the content in the logic node, any logic condition is adjusted to be a logic condition, or the logic condition is adjusted to be any logic condition; the fourth method is negative logic change, and the content of the original logic node is adjusted to negative logic; the fifth method is a reverse propositional logic change, which replaces the conditions and the conclusions in the original logic node content and adjusts the conditions into the logic of deducing the conditions according to the conclusions. In this manner, one or more methods are used to generate interference terms for selection by the user.
Further, the foreground interaction subsystem includes:
the logic node screening module is used for screening out information with a certain confusion degree from the stored logic nodes and the corresponding interference items, returning the screened information to the interface display module and displaying the information in a to-be-selected area (the to-be-selected area refers to an area selected by a user);
the interface display module is used for displaying information (such as a draggable logic node item, a draggable interference item, a reset button, a submission button and the like) operated by a user in a to-be-selected area, sending the information submitted by the user to the information analysis and submission module according to the interactive behavior of the user in the to-be-answered area (the to-be-answered area refers to the area answered by the user), and giving corresponding display behavior feedback to the user; giving corresponding prompt information to the user according to the information returned by the information response module;
the information response module processes the information sent by the result detection module of the logic verification subsystem and feeds the processed information back to the interface display module of the foreground interaction subsystem;
and the information analysis and submission module is used for sorting the information of the to-be-answered region in the interface display module into a list according to the sequence and sending the list to the logic verification subsystem.
Further, the logic verification subsystem includes:
the information monitoring module receives the information sent by the information analysis and submission module in the foreground interaction subsystem, acquires a result sequence submitted by a user, and sends the result sequence to the result detection module;
the logic analysis and sequencing module is used for acquiring result information generated in the logic node generation module and the logic node relation generation module, organizing the logic nodes and the logic node pointing relations into a directed acyclic graph, then carrying out topological sequencing on the directed acyclic graph, and sending all sequenced results serving as a solution set to the result detection module;
the result detection module receives a result sequence submitted by a user from the information monitoring module, compares the result sequence with a solution set generated by the logic analysis and the topology sequencing in the sequencing module, if the result sequence exists in the solution set, the result sequence is considered to be a correct solution, and sends correct prompt information to an information response module of the foreground interaction subsystem; and if the result sequence does not exist in the solution set, the result sequence is considered not to be a correct solution, and wrong prompt information and the specific reason of the error are sent to an information response module of the foreground interaction subsystem.
The automatic evaluation method and system based on the directed acyclic graph and the topological sorting can realize the training and evaluation of the online automatic mathematical identification and the logic derivation capability of large-scale crowds. The invention provides a friendly interactive form for users, and provides a high-efficiency and highly-interesting learning and testing platform for students and teachers in computer major and mathematics major from the generation process of logic nodes and relations in the background to the selection process of logic nodes and relations in the foreground users from the to-be-selected area and adding the selected logic nodes to the to-be-answered area in a dragging mode.
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FIG. 1 is a general flowchart of an automated evaluation method based on directed acyclic graph and topological sorting in an embodiment;
FIG. 2 is a flow diagram of an information generation subsystem in an embodiment;
FIG. 3 is a flow diagram of a logic verification subsystem in an embodiment;
FIG. 4 is a schematic diagram of a logical node relationship generation module of the information generation subsystem in an embodiment;
FIG. 5 is a schematic diagram of an interface display module of the foreground interaction subsystem in the embodiment.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
FIG. 1 is a schematic general flow diagram of the process of the present invention. As shown in fig. 1, this embodiment mainly includes the following steps:
step 11, the information generation subsystem provides the data source and the interference information for the user, and checks the validity of the data source.
Fig. 2 is a schematic flow chart of the information generation subsystem of this embodiment, and as shown in fig. 2, the method includes the following sub-steps:
step 111, the logic node generation module analyzes the content input by the user, judges whether the content is legal content, compares the legal content with the existing logic node content, and prompts error information if the content is legal content; otherwise, inserting a new element into the logic node list;
in step 112, when there are multiple logical nodes in the database, the logical node relationship generation module allows the user to add the pointing relationship to these logical nodes. The user can start from any node and point to another node, so as to generate a directed edge, as shown in fig. 4;
in step 113, when the behavior of adding directed edges by the user is finished, the logical node and node relation checking module will check the validity of the behavior. Considering that in the derivation process of the mathematical identification, each initial condition can be regarded as a node with zero in degree in a directed graph, the derived intermediate conclusion is taken as a node with non-zero in degree and non-zero out degree in the directed graph, and the final conclusion is taken as a node with zero out degree in the directed graph, which conforms to the definition of the directed acyclic graph. The logical node and node relation checking module detects whether the directed edge added by the user can cause the directed graph to become a cyclic graph, namely, the directed graph has the condition that the directed graph returns to the node from a certain node through a plurality of edges, if the directed edge appears, the user is considered to add wrong logical node pointing relation, error information is prompted, and the pointing relation is removed; otherwise, addition may continue; as shown in fig. 4;
step 114, the interference item generation module performs automatic confusion according to the existing logic node content, and returns the confused result to the user, and the user can select the interference item which is considered to be valuable from the confused result, and can also add the interference item manually;
step 115, when the user adds all the information, the information can be saved, and the information generation subsystem will send the saved information to the foreground interaction subsystem and the logic verification subsystem.
Step 12, the foreground interaction subsystem displays the acquired logic nodes and interference items, and feeds back and prompts the interaction behavior of the user in time, and the method comprises the following substeps:
step 121, the logical node screening module selects all effective logical node information in the database, simultaneously randomly selects a plurality of interference items corresponding to the logical nodes, and displays the selected information in the area to be selected of the interface display module, as shown in the left side of fig. 5;
step 122, the user selects an element from the to-be-selected area of the interface display module and drags the element to the to-be-answered area, as shown in the right side of fig. 5; during the period, the user can reorder the contents of the to-be-answered region until submission;
and step 123, when the information analysis and submission module detects the submission behavior of the user, acquiring the content of the to-be-answered region of the interface display module, arranging the content according to the serial number of each element, and sending an arranged result sequence to the logic verification subsystem.
And step 13, after the logic verification subsystem receives a result sequence submitted by the user and sent by the foreground interaction subsystem, analyzing and comparing the information and returning a result.
Fig. 3 is a schematic flow chart of the logic verification subsystem of this embodiment, and as shown in fig. 3, the logic verification subsystem includes the following sub-steps:
step 131, after receiving the result sequence submitted by the user, the information monitoring module detects whether the number of elements in the sequence is equal to the number of valid logical nodes existing in the current database, and if so, continues to detect the result sequence; otherwise, returning error information and prompting the user to resubmit;
step 132, the information monitoring module continues to detect the result sequence passed by the detection in the step 131, and if the result sequence does not have the sequence number of the interference item, all the logical nodes and the pointing relationships between the nodes stored in the database are obtained; otherwise, returning error information and prompting the user to resubmit;
step 133, considering that the precondition for performing topology ranking is that the graph is a directed acyclic graph, the logic analysis and ranking module organizes the obtained pointing relationships between the logic nodes and the nodes into a directed acyclic graph, and if the graph can not return to the node from any node in the graph through a plurality of edges, the graph is a directed acyclic graph; otherwise, returning error information and prompting the user to resubmit;
134, the logic analyzing and sorting module takes the logic nodes and the directional relations among the nodes as the nodes and the edges in the directed acyclic graph respectively, and arranges all the nodes in the directed acyclic graph into a linear sequence, so that the directed edges (u, v) connecting the nodes u to the nodes v arbitrarily in the graph are formed, and in the final sorting result, the nodes u are always in front of the nodes v, that is, the directed acyclic graph is subjected to topological sorting; after sorting, a plurality of different linear sequence sets are obtained;
step 135, the result detection module receives the linear sequence set obtained in step 134, and performs traversal search on the set, and if the result sequence submitted by the user obtained in step 132 exists, sends a correct prompt message to the information response module of the foreground interaction subsystem; otherwise, returning error information and prompting the user to resubmit.
The above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person skilled in the art can modify the technical solution of the present invention or substitute the same without departing from the spirit and scope of the present invention, and the scope of the present invention should be determined by the claims.

Claims (7)

1. An automatic evaluation method based on directed acyclic graph and topological sorting is characterized by comprising the following steps:
1) generating and storing logic nodes, relations among the logic nodes and interference items related in the logic proving process;
2) taking the logic nodes as a plurality of vertexes in a graph structure, taking the directional relation among the logic nodes as a plurality of directed edges connecting the vertexes in the graph structure to form a directed acyclic graph, and carrying out topological sorting on the directed acyclic graph to generate at least one correct solution sequence as a solution set;
3) selecting data with certain confusion degree from the stored logic nodes and the corresponding interference items, displaying the data to a user and waiting for the user to submit a sequenced result sequence;
4) acquiring a result sequence submitted by a user, performing traversal comparison on the result sequence and a solution in a solution set, and returning a final result;
wherein step 1) generates the interference term using one or more of the following methods: the first method is digital fluctuation, and digital content in a logic node is adjusted within a certain range; the second method is that the operation symbol fluctuates, and the operation symbol content in the logic node is adjusted; the third method is predicate logic change, and according to the content in the logic node, any logic condition is adjusted to be a logic condition, or the logic condition is adjusted to be any logic condition; the fourth method is negative logic change, and the content of the original logic node is adjusted to negative logic; the fifth method is a reverse propositional logic change, which replaces the conditions and the conclusions in the original logic node content and adjusts the conditions into the logic of deducing the conditions according to the conclusions;
wherein, the step 4) comprises the following substeps:
a) acquiring the logical nodes, the relation among the logical nodes and the interference items generated in the step 1), and grouping and sorting the logical nodes and the relation among the logical nodes and the interference items for the use of the following steps;
b) when receiving the result sequence information submitted by the user, simply analyzing the information contained in the sequence, and if the sequence contains the elements of the interference item grouping in the step a), regarding the sequence as an error solution and returning error information; otherwise, continuously detecting whether the result sequence is a correct solution;
c) traversing and matching the result sequence in the step b) with the solution set in the step 2), and if the result sequence exists in the solution set, namely the result sequence is a correct solution, returning correct prompt information; otherwise, returning wrong prompt information.
2. An automated evaluation system based on directed acyclic graph and topological sort using the method of claim 1, comprising an information generation subsystem, a foreground interaction subsystem and a logic verification subsystem; the information generation subsystem generates logical nodes, relations among the logical nodes and interference items related in the logical proving process, performs validity check on the generated information and sends the information to the foreground interaction subsystem; the foreground interaction subsystem receives and responds to a result sequence generated by a user in an interaction process, sends the result sequence to the logic verification subsystem and displays feedback information of the logic verification subsystem; the logic verification subsystem analyzes the relation between the logic nodes generated by the information generation subsystem and generates a set of effective solutions as a solution set, then matches and verifies whether the result sequence is an effective solution according to the result sequence submitted by the foreground interaction subsystem, and then returns the detection result to the foreground interaction subsystem.
3. The system of claim 2, wherein the information generation subsystem comprises:
the logic node generating module is used for adding information in the logic nodes and sending all the generated logic nodes to the interference item generating module, the logic node relation generating module and the logic node screening module of the foreground interaction subsystem;
the interference item generation module is used for acquiring the information in the logic node generation module and automatically generating a series of interference items for a user to select according to the information; or the user directly adds a new interference item; then sending the interference item information to a logic node screening module of a foreground interaction subsystem;
the logical node relation generating module is used for adding a pointing relation to the logical nodes generated in the logical node generating module and sending the pointing relation to the logical node and node relation checking module;
and the logical node and node relation checking module is used for regarding the logical nodes as vertexes in the graph structure and regarding the logical node relation as a directed edge in the graph structure according to the information generated by the logical node generating module and the logical node relation generating module, and then checking whether the graph meets the condition of the directed acyclic graph.
4. The system of claim 3, wherein the interference term generation module generates the interference term using one or more of the following methods: the first method is digital fluctuation, and digital content in a logic node is adjusted within a certain range; the second method is that the operation symbol fluctuates, and the operation symbol content in the logic node is adjusted; the third method is predicate logic change, and according to the content in the logic node, any logic condition is adjusted to be a logic condition, or the logic condition is adjusted to be any logic condition; the fourth method is negative logic change, and the content of the original logic node is adjusted to negative logic; the fifth method is a reverse propositional logic change, which replaces the conditions and the conclusions in the original logic node content and adjusts the conditions into the logic of deducing the conditions according to the conclusions.
5. The system of claim 3 or 4, wherein the foreground interaction subsystem comprises:
the logic node screening module is used for screening out information with a certain confusion degree from the stored logic nodes and the corresponding interference items, returning the screened information to the interface display module and displaying the information in a region to be selected;
the interface display module is used for displaying information operated by a user in the area to be selected, sending the information submitted by the user to the information analysis and submission module according to the interactive behavior of the user in the area to be answered, and simultaneously giving corresponding display behavior feedback to the user; giving corresponding prompt information to the user according to the information returned by the information response module;
the information response module processes the information sent by the result detection module of the logic verification subsystem and feeds the processed information back to the interface display module of the foreground interaction subsystem;
and the information analysis and submission module is used for sorting the information of the to-be-answered region in the interface display module into a list according to the sequence and sending the list to the logic verification subsystem.
6. The system of claim 5, wherein the information for user manipulation comprises: draggable logical node items, draggable interference items, reset buttons, submit buttons.
7. The system of claim 5, wherein the logic verification subsystem comprises:
the information monitoring module receives the information sent by the information analysis and submission module in the foreground interaction subsystem, acquires a result sequence submitted by a user, and sends the result sequence to the result detection module;
the logic analysis and sequencing module is used for acquiring result information generated in the logic node generation module and the logic node relation generation module, organizing the logic nodes and the logic node pointing relations into a directed acyclic graph, then carrying out topological sequencing on the directed acyclic graph, and sending all sequenced results serving as a solution set to the result detection module;
the result detection module receives a result sequence submitted by a user from the information monitoring module, compares the result sequence with a solution set generated by the logic analysis and the topology sequencing in the sequencing module, if the result sequence exists in the solution set, the result sequence is considered to be a correct solution, and sends correct prompt information to an information response module of the foreground interaction subsystem; and if the result sequence does not exist in the solution set, the result sequence is considered not to be a correct solution, and wrong prompt information and the specific reason of the error are sent to an information response module of the foreground interaction subsystem.
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