给定二进制字符串str ，任务是构建一个 DFA，如果字符串以“01”开头或以“01”结尾，则该字符串接受该字符串。
Input: str = “010000”
Output: Accepted
Explanation:
The given string starts with “01”.
Input: str = “1100111”
Output: Not Accepted
Explanation:
The given string neither starts with nor ends with “01”.
DFA 或确定性有限自动机是一种有限状态机，如果字符串达到最终状态，则接受字符串(在某些特定条件下)，否则拒绝它。
在DFA中，没有记忆的概念，因此我们必须通过字符来检查字符串的字符，与第0字符开始。问题的输入字符集是 {0, 1}。为了使 DFA 有效，必须为每个状态的输入集的每个符号定义一个转换规则到有效状态。因此，按照以下步骤来设计 DFA：
- 在这种情况下，以 01 开头或以 01 结尾或都以 01 开头和 01 结尾的字符串应该是可以接受的。
- 制作一个初始状态并将其输入字母表，即 0 和 1 转换为两个不同的状态。
- 在每次转换后检查是否接受字符串以忽略错误。
- 首先，为最小长度字符串制作 DfA，然后逐步进行。
- 根据字符串的接受度定义 Final State(s)。
设计 DFA 的分步方法：
- 步骤 1：使初始状态为“A”。最小可能的字符串是 01，这是可以接受的。为此，将 0 从状态“A”转移到状态“B”，然后将 1 从状态“B”转移到状态“C”，并注意这个状态“C”作为最终状态。
- 第二步：现在，我们已经设计了以 01 开头的 DFA。要接受所有以 01 开头的字符串，如 011、010、010000、01111、010101000010001 等，我们需要将 0 和 1 的自循环放入状态“C”。这个自循环包含 0 和 1 的所有组合。
- 第 3 步：现在，我们需要考虑以“01”结尾的字符串。我们已经完成了状态“A”的 0 转换，然后是状态“A”的输入 1。以 01 结尾的最小可能字符串为 101。为此，将状态“A”的输入 1 转换为状态“D”，然后将输入 0 从状态“D”转换为状态“E”，然后然后将输入 1 从状态“E”转换为状态“F”，并注意这个“F”状态是最终状态。
- 第 4 步：还有一种可能是任意数量的 1 以 01 开头然后以 01 结尾。为此，在状态“D”上进行 1 的自循环，并且任意数量的 0 可以出现在 1 中的 1 之前结尾。为此，将自循环设为 0 并设置为“E”。
- 第 5 步：到目前为止，我们已经完成了以 1 开头并以 01 结尾的字符串。现在，我们需要考虑以 0 开头并以 01 结尾的字符串。为此，将输入 0 从状态“转换” B”表示“E”。
- 第 6 步：现在我们只剩下状态“F”的输入字母。将输入 1 从状态“F”转移到状态“D”，然后将输入 0 从状态“F”转移到状态“E”。
上述DFA的Transition表和Transition规则：
| State | Input (0) | Input (1) |
|---|---|---|
| —>A | B | D |
| B | E | C |
| C* | C | C |
| D | E | D |
| E | E | F |
| F* | E | D |
下面是上述方法的实现：
C++
// C++ program to check if a string
// either starts or ends with 01
#include
using namespace std;
void stateA(string);
void stateB(string);
void stateC(string);
void stateD(string);
void stateE(string);
void stateF(string);
// Function for transition
// state A
void checkstateA(string n)
{
// State transition to
// B if the character is
// 0
if(n[0] == '0')
stateB(n.substr(1));
// State transition to
// D if the character is
// 1
else
stateD(n.substr(1));
}
// Function for transition
// state B
void stateB(string n)
{
// Check if the string has
// ended
if (n.length() == 0)
cout << "string not accepted";
else
{
// State transition to C
// if the character is 1
if(n[0] == '1')
stateC(n.substr(1));
// State transition to D
// if the character is 0
else
stateD(n.substr(1));
}
}
// Function for transition
// state C
void stateC(string n)
{
cout << "String accepted";
}
// Function for transition
// state D
void stateD(string n)
{
if (n.length() == 0)
cout << "string not accepted";
else
{
// State transition to D
// if the character is 1
if (n[0] == '1')
stateD(n.substr(1));
// State transition to E
// if the character is 0
else
stateE(n.substr(1));
}
}
// Function for transition
// state E
void stateE(string n)
{
if (n.length() == 0)
cout << "string not accepted";
else
{
// State transition to E
// if the character is 0
if(n[0] == '0')
stateE(n.substr(1));
// State transition to F
// if the character is 1
else
stateF(n.substr(1));
}
}
// Function for transition
// state F
void stateF(string n)
{
if(n.length() == 0)
cout << "string accepred";
else
{
// State transition to D
// if the character is 1
if(n[0] == '1')
stateD(n.substr(1));
// State transition to E
// if the character is 0
else
stateE(n.substr(1));
}
}
// Driver code
int main()
{
string n = "0100101";
checkstateA(n);
return 0;
}
// This code is contributed by chitranayal Java
// Java program to check if a string
// either starts or ends with 01
import java.util.*;
class GFG{
// Function for transition
// state A
static void checkstateA(String n)
{
// State transition to
// B if the character is
// 0
if (n.charAt(0) == '0')
stateB(n.substring(1));
// State transition to
// D if the character is
// 1
else
stateD(n.substring(1));
}
// Function for transition
// state B
static void stateB(String n)
{
// Check if the string has
// ended
if (n.length() == 0)
System.out.println("string not accepted");
else
{
// State transition to C
// if the character is 1
if (n.charAt(0) == '1')
stateC(n.substring(1));
// State transition to D
// if the character is 0
else
stateD(n.substring(1));
}
}
// Function for transition
// state C
static void stateC(String n)
{
System.out.println("String accepted");
}
// Function for transition
// state D
static void stateD(String n)
{
if (n.length() == 0)
System.out.println("string not accepted");
else
{
// State transition to D
// if the character is 1
if (n.charAt(0) == '1')
stateD(n.substring(1));
// State transition to E
// if the character is 0
else
stateE(n.substring(1));
}
}
// Function for transition
// state E
static void stateE(String n)
{
if (n.length() == 0)
System.out.println("string not accepted");
else
{
// State transition to E
// if the character is 0
if(n.charAt(0) == '0')
stateE(n.substring(1));
// State transition to F
// if the character is 1
else
stateF(n.substring(1));
}
}
// Function for transition
// state F
static void stateF(String n)
{
if (n.length() == 0)
System.out.println("string accepred");
else
{
// State transition to D
// if the character is 1
if (n.charAt(0) == '1')
stateD(n.substring(1));
// State transition to E
// if the character is 0
else
stateE(n.substring(1));
}
}
// Driver Code
public static void main(String args[])
{
String n = "0100101";
checkstateA(n);
}
}
// This code is contributed by jyoti369Python3
# Python3 program to check if
# a string either starts or
# ends with 01
# Function for transition
# state A
def checkstateA(n):
# State transition to
# B if the character is
# 0
if(n[0]=='0'):
stateB(n[1:])
# State transition to
# D if the character is
# 1
else:
stateD(n[1:])
# Function for transition
# state B
def stateB(n):
# Check if the string has
# ended
if (len(n)== 0):
print("string not accepted")
else:
# State transition to C
# if the character is 1
if(n[0]=='1'):
stateC(n[1:])
# State transition to D
# if the character is 0
else:
stateD(n[1:])
# Function for transition
# state C
def stateC(n):
print("String accepted")
# Function for transition
# state D
def stateD(n):
if (len(n)== 0):
print("string not accepted")
else:
# State transition to D
# if the character is 1
if (n[0]=='1'):
stateD(n[1:])
# State transition to E
# if the character is 0
else:
stateE(n[1:])
# Function for transition
# state E
def stateE(n):
if (len(n)== 0):
print("string not accepted")
else:
# State transition to E
# if the character is 0
if(n[0]=='0'):
stateE(n[1:])
# State transition to F
# if the character is 1
else:
stateF(n[1:])
# Function for transition
# state F
def stateF(n):
if(len(n)== 0):
print("string accepred")
else:
# State transition to D
# if the character is 1
if(n[0]=='1'):
stateD(n[1:])
# State transition to E
# if the character is 0
else:
stateE(n[1:])
# Driver code
if __name__ == "__main__":
n = "0100101"
checkstateA(n)C#
// C# program to check if
// a string either starts
// or ends with 01
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
// Function for transition
// state A
static void checkstateA(string n)
{
// State transition to
// B if the character is
// 0
if(n[0] == '0')
stateB(n.Substring(1));
// State transition to
// D if the character is
// 1
else
stateD(n.Substring(1));
}
// Function for transition
// state B
static void stateB(string n)
{
// Check if the string has
// ended
if (n.Length == 0)
{
Console.Write("string not accepted");
}
else
{
// State transition to C
// if the character is 1
if(n[0] == '1')
stateC(n.Substring(1));
// State transition to D
// if the character is 0
else
stateD(n.Substring(1));
}
}
// Function for transition
// state C
static void stateC(string n)
{
Console.Write("string accepted");
}
// Function for transition
// state D
static void stateD(string n)
{
if (n.Length == 0)
Console.Write("string not accepted");
else
{
// State transition to D
// if the character is 1
if (n[0] == '1')
stateD(n.Substring(1));
// State transition to E
// if the character is 0
else
stateE(n.Substring(1));
}
}
// Function for transition
// state E
static void stateE(string n)
{
if (n.Length == 0)
Console.Write("string not accepted");
else
{
// State transition to E
// if the character is 0
if(n[0] == '0')
stateE(n.Substring(1));
// State transition to F
// if the character is 1
else
stateF(n.Substring(1));
}
}
// Function for transition
// state F
static void stateF(string n)
{
if(n.Length == 0)
Console.Write("string accepted");
else
{
// State transition to D
// if the character is 1
if(n[0] == '1')
stateD(n.Substring(1));
// State transition to E
// if the character is 0
else
stateE(n.Substring(1));
}
}
// Driver code
public static void Main(string []args)
{
string n = "0100101";
checkstateA(n);
}
}
// This code is contributed by rutvik_56Javascript
输出：
String accepted如果您想与行业专家一起参加直播课程，请参阅Geeks Classes Live