设计一个确定性有限自动机 (DFA) 来接受语言
用于为语言 L = {a n b m | 创建 DFA n+m=odd} 使用初等数学表示-
odd + even = odd, and
even+odd = odd 例子：
Input: a a b b b
Output: ACCEPTED
// n = 2, m = 3, 2 + 3 = 5 (odd)
Input: a a a b b b
Output: NOT ACCEPTED
// n = 3, m = 3, 3 + 3 = 6 (even)
Input: a a a a b b b
Output: ACCEPTED
// n = 4, m = 3, 4 + 3 = 7 (odd)
方法：
有两种情况会导致接受字符串：
- 如果 n 为奇数且 m 为偶数，则它们的总和将为奇数
- 如果 n 是偶数且 m 是奇数，那么它们的总和将为奇数
任何其他组合结果都是拒绝输入字符串。
描述：
鉴于 DFA 有 2 个部分。第一部分由状态 0、1、5 和 6 组成，其中 n 是奇数，m 是偶数。第二部分由状态 2、3 和 4 组成，因为 n 是偶数，m 是奇数。
DFA 状态转换图：
让我们看看演示的代码：
C/C++
// C program to implement DFS that accepts
// all string which follow the language
// L = { a^n b^m ; n+m=odd }
#include
#include
// dfa tells the number associated
// string end in which state.
int dfa = 0;
// This function is for
// the starting state (Q0)of DFA
void start(char c)
{
if (c == 'a') {
dfa = 1;
}
else if (c == 'b') {
dfa = 2;
}
// -1 is used to check for any invalid symbol
else {
dfa = -1;
}
}
// This function is for the first state (Q1) of DFA
void state1(char c)
{
if (c == 'a') {
dfa = 0;
}
else if (c == 'b') {
dfa = 5;
}
else {
dfa = -1;
}
}
// This function is for the second state (Q2) of DFA
void state2(char c)
{
if (c == 'b') {
dfa = 3;
}
else {
dfa = -1;
}
}
// This function is for the third state (Q3)of DFA
void state3(char c)
{
if (c == 'b') {
dfa = 4;
}
else {
dfa = -1;
}
}
// This function is for the fourth state (Q4) of DFA
void state4(char c)
{
if (c == 'b') {
dfa = 3;
}
else {
dfa = -1;
}
}
// This function is for the fifth state (Q5) of DFA
void state5(char c)
{
if (c == 'b') {
dfa = 6;
}
else {
dfa = -1;
}
}
// This function is for the sixth state (Q6) of DFA
void state6(char c)
{
if (c == 'b') {
dfa = 5;
}
else {
dfa = -1;
}
}
int isAccepted(char str[])
{
// store length of string
int i, len = strlen(str);
for (i = 0; i < len; i++) {
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 2 || dfa == 4 || dfa == 6 || dfa == 1)
return 1;
else
return 0;
}
// driver code
int main()
{
char str[] = "aaaabbbbb";
if (isAccepted(str))
printf("ACCEPTED");
else
printf("NOT ACCEPTED");
return 0;
} Java
// Java program to implement DFS that accepts
// all string which follow the language
// L = { a^n b^m ; n+m=odd }
class GFG
{
// dfa tells the number associated
// string end in which state.
static int dfa = 0;
// This function is for
// the starting state (Q0)of DFA
static void start(char c)
{
if (c == 'a')
{
dfa = 1;
}
else if (c == 'b')
{
dfa = 2;
}
// -1 is used to check for any invalid symbol
else
{
dfa = -1;
}
}
// This function is for
// the first state (Q1) of DFA
static void state1(char c)
{
if (c == 'a')
{
dfa = 0;
}
else if (c == 'b')
{
dfa = 5;
}
else
{
dfa = -1;
}
}
// This function is for the
// second state (Q2) of DFA
static void state2(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// third state (Q3)of DFA
static void state3(char c)
{
if (c == 'b')
{
dfa = 4;
}
else
{
dfa = -1;
}
}
// This function is for the
// fourth state (Q4) of DFA
static void state4(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// fifth state (Q5) of DFA
static void state5(char c)
{
if (c == 'b')
{
dfa = 6;
}
else
{
dfa = -1;
}
}
// This function is for the
// sixth state (Q6) of DFA
static void state6(char c)
{
if (c == 'b')
{
dfa = 5;
}
else
{
dfa = -1;
}
}
static int isAccepted(char str[])
{
// store length of string
int i, len = str.length;
for (i = 0; i < len; i++)
{
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 2 || dfa == 4 ||
dfa == 6 || dfa == 1)
return 1;
else
return 0;
}
// Driver code
public static void main(String[] args)
{
char str[] = "aaaabbbbb".toCharArray();
if (isAccepted(str) == 1)
System.out.println("ACCEPTED");
else
System.out.println("NOT ACCEPTED");
}
}
// This code is contributed by PrinciRaj1992Python3
# Python3 program to implement DFS that accepts
# all Stringing which follow the language
# L = a ^ n b ^ m n + m = odd
# This function is for the dfa = starting
# dfa = state (zeroth) of DFA
def start(c):
if (c == 'a'):
dfa = 1
elif (c == 'b'):
dfa = 2
# -1 is used to check for any
# invalid symbol
else:
dfa = -1
return dfa
# This function is for the first
# dfa = state of DFA
def state1(c):
if (c == 'a'):
dfa = 0
elif (c == 'b'):
dfa = 5
else:
dfa = -1
return dfa
# This function is for the second
# dfa = state of DFA
def state2(c):
if (c == 'b'):
dfa = 3
else:
dfa = -1
return dfa
# This function is for the third
# dfa = state of DFA
def state3(c):
if (c == 'b'):
dfa = 4
else:
dfa = -1
return dfa
# This function is for the fourth
# dfa = state of DFA
def state4(c):
if (c == 'b'):
dfa = 3
else:
dfa = -1
return dfa
# This function is for the fifth
# dfa = state of DFA
def state5(c):
if (c == 'b'):
dfa = 6
else:
dfa = -1
return dfa
# This function is for the sixth
# dfa = state of DFA
def state6(c):
if (c == 'b'):
dfa = 5
else:
dfa = -1
return dfa
def isAccepted(String):
# store length of Stringing
l = len(String)
# dfa tells the number associated
# with the present dfa = state
dfa = 0
for i in range(l):
if (dfa == 0):
dfa = start(String[i])
elif (dfa == 1):
dfa = state1(String[i])
elif (dfa == 2) :
dfa = state2(String[i])
elif (dfa == 3) :
dfa = state3(String[i])
elif (dfa == 4) :
dfa = state4(String[i])
elif (dfa == 5) :
dfa = state5(String[i])
elif (dfa == 6):
dfa = state6(String[i])
else:
return 0
if(dfa == 1 or dfa == 2 or dfa == 4 or dfa == 6) :
return 1
else:
return 0
# Driver code
if __name__ == "__main__" :
String = "aaaabbbbb"
if (isAccepted(String)) :
print("ACCEPTED")
else:
print("NOT ACCEPTED")C#
// C# program to implement DFS that accepts
// all string which follow the language
// L = { a^n b^m ; n+m=odd }
using System;
class GFG
{
// dfa tells the number associated
// string end in which state.
static int dfa = 0;
// This function is for
// the starting state (Q0)of DFA
static void start(char c)
{
if (c == 'a')
{
dfa = 1;
}
else if (c == 'b')
{
dfa = 2;
}
// -1 is used to check for any invalid symbol
else
{
dfa = -1;
}
}
// This function is for
// the first state (Q1) of DFA
static void state1(char c)
{
if (c == 'a')
{
dfa = 0;
}
else if (c == 'b')
{
dfa = 5;
}
else
{
dfa = -1;
}
}
// This function is for the
// second state (Q2) of DFA
static void state2(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// third state (Q3)of DFA
static void state3(char c)
{
if (c == 'b')
{
dfa = 4;
}
else
{
dfa = -1;
}
}
// This function is for the
// fourth state (Q4) of DFA
static void state4(char c)
{
if (c == 'b')
{
dfa = 3;
}
else
{
dfa = -1;
}
}
// This function is for the
// fifth state (Q5) of DFA
static void state5(char c)
{
if (c == 'b')
{
dfa = 6;
}
else
{
dfa = -1;
}
}
// This function is for the
// sixth state (Q6) of DFA
static void state6(char c)
{
if (c == 'b')
{
dfa = 5;
}
else
{
dfa = -1;
}
}
static int isAccepted(char []str)
{
// store length of string
int i, len = str.Length;
for (i = 0; i < len; i++)
{
if (dfa == 0)
start(str[i]);
else if (dfa == 1)
state1(str[i]);
else if (dfa == 2)
state2(str[i]);
else if (dfa == 3)
state3(str[i]);
else if (dfa == 4)
state4(str[i]);
else if (dfa == 5)
state5(str[i]);
else if (dfa == 6)
state6(str[i]);
else
return 0;
}
if (dfa == 2 || dfa == 4 ||
dfa == 6 || dfa == 1)
return 1;
else
return 0;
}
// Driver code
public static void Main(String[] args)
{
char []str = "aaaabbbbb".ToCharArray();
if (isAccepted(str) == 1)
Console.WriteLine("ACCEPTED");
else
Console.WriteLine("NOT ACCEPTED");
}
}
// This code contributed by Rajput-JiPHP
输出：
ACCEPTED