先决条件：有限自动机
给定一个由字符a ， b和c组成的字符串str ，请检查该字符串中任何字符的出现次数是否为3的倍数。
例子：
Input: str = bc
Output: ACCEPTED
Explanation: The string consists 0 a’s and 3 * 0 = 0.
Input: str = abccc
Output: ACCEPTED
Explanation: The string consists 3 c’s.
Input: str = abc
Output: NOT ACCEPTED
方法：
NFA或非确定性有限自动机与DFA非常相似。它是一个有限状态机，如果达到最终状态，则它会接受字符串(在某些特定条件下)，否则将其拒绝。 NFA具有的其他功能是：
- 空移是允许的，即它可以不读取符号而向前移动。
- 能够针对特定输入传输到任意数量的状态。
NFA机器，接受所有出现至少一个字符为3的倍数的字符串：
对于以上问题陈述，我们必须首先构建NFA计算机。 NFA机器类似于具有各种状态和转换的流程图。与上述问题相对应的NFA机器如下图所示，Q3，Q4和Q8为最终状态：
该NFA机器如何工作：
机器的工作取决于检查字符串是否具有a或b或c的3倍。
- 情况1：a的数目是三的倍数：
- 为了检查字符串中a的数目是否为三的倍数，定义了一组单独的状态。定义为Q2，Q3，Q4的状态检查a的数量是否为3的倍数。如果在任何情况下这种情况都达到了最终状态Q2，则a的数量是3的倍数。
- 情况2：b的数目是三的倍数：
- 为了检查字符串中b的数目是否为三的倍数，定义了一组单独的状态。定义为Q5，Q6，Q7的状态检查b的数目是否为3的倍数。如果这种情况在任何时候都达到了最终状态Q5，则b的数目是三的倍数。
- 情况3：c的数目是三的倍数：
- 为了检查字符串中c的数目是否为三的倍数，定义了一组单独的状态。定义为Q8，Q9，Q10的状态检查c的数量是否为3的倍数。如果这种情况在任何时候都达到了最终状态Q8，则c的数量是三的倍数。
如果上述状态中的任何一个达到了最终状态Q2，Q5或Q8；然后字符串满足条件
下面是上述方法的实现：
C++
// C++ implementation of the above approach
#include
// NFA variable that keeps track of
// the state while transaction.
int nfa = 1;
// This checks for invalid input.
int flag = 0;
using namespace std;
// Function for the state Q2
void state1(char c)
{
// State transitions
// 'a' takes to Q4, and
// 'b' and 'c' remain at Q2
if (c == 'a')
nfa = 2;
else if (c == 'b' || c == 'c')
nfa = 1;
else
flag = 1;
}
// Function for the state Q3
void state2(char c)
{
// State transitions
// 'a' takes to Q3, and
// 'b' and 'c' remain at Q4
if (c == 'a')
nfa = 3;
else if (c == 'b' || c == 'c')
nfa = 2;
else
flag = 1;
}
// Function for the state Q4
void state3(char c)
{
// State transitions
// 'a' takes to Q2, and
// 'b' and 'c' remain at Q3
if (c == 'a')
nfa = 1;
else if (c == 'b' || c == 'c')
nfa = 3;
else
flag = 1;
}
// Function for the state Q5
void state4(char c)
{
// State transitions
// 'b' takes to Q6, and
// 'a' and 'c' remain at Q5
if (c == 'b')
nfa = 5;
else if (c == 'a' || c == 'c')
nfa = 4;
else
flag = 1;
}
// Function for the state Q6
void state5(char c)
{
// State transitions
// 'b' takes to Q7, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 6;
else if (c == 'a' || c == 'c')
nfa = 5;
else
flag = 1;
}
// Function for the state Q7
void state6(char c)
{
// State transitions
// 'b' takes to Q5, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 4;
else if (c == 'a' || c == 'c')
nfa = 6;
else
flag = 1;
}
// Function for the state Q8
void state7(char c)
{
// State transitions
// 'c' takes to Q9, and
// 'a' and 'b' remain at Q8
if (c == 'c')
nfa = 8;
else if (c == 'b' || c == 'a')
nfa = 7;
else
flag = 1;
}
// Function for the state Q9
void state8(char c)
{
// State transitions
// 'c' takes to Q10, and
// 'a' and 'b' remain at Q9
if (c == 'c')
nfa = 9;
else if (c == 'b' || c == 'a')
nfa = 8;
else
flag = 1;
}
// Function for the state Q10
void state9(char c)
{
// State transitions
// 'c' takes to Q8, and
// 'a' and 'b' remain at Q10
if (c == 'c')
nfa = 7;
else if (c == 'b' || c == 'a')
nfa = 9;
else
flag = 1;
}
// Function to check for 3 a's
bool checkA(string s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 1)
state1(s[i]);
else if (nfa == 2)
state2(s[i]);
else if (nfa == 3)
state3(s[i]);
}
if (nfa == 1) {
return true;
}
else {
nfa = 4;
}
}
// Function to check for 3 b's
bool checkB(string s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 4)
state4(s[i]);
else if (nfa == 5)
state5(s[i]);
else if (nfa == 6)
state6(s[i]);
}
if (nfa == 4) {
return true;
}
else {
nfa = 7;
}
}
// Function to check for 3 c's
bool checkC(string s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 7)
state7(s[i]);
else if (nfa == 8)
state8(s[i]);
else if (nfa == 9)
state9(s[i]);
}
if (nfa == 7) {
return true;
}
}
// Driver Code
int main()
{
string s = "bbbca";
int x = 5;
// If any of the states is true, that is, if either
// the number of a's or number of b's or number of c's
// is a multiple of three, then the string is accepted
if (checkA(s, x) || checkB(s, x) || checkC(s, x)) {
cout << "ACCEPTED";
}
else {
if (flag == 0) {
cout << "NOT ACCEPTED";
return 0;
}
else {
cout << "INPUT OUT OF DICTIONARY.";
return 0;
}
}
} Java
// Java implementation of the above approach
class GFG {
// NFA variable that keeps track of
// the state while transaction.
static int nfa = 1;
// This checks for invalid input.
static int flag = 0;
// Function for the state Q2
static void state1(char c)
{
// State transitions
// 'a' takes to Q4, and
// 'b' and 'c' remain at Q2
if (c == 'a')
nfa = 2;
else if (c == 'b' || c == 'c')
nfa = 1;
else
flag = 1;
}
// Function for the state Q3
static void state2(char c)
{
// State transitions
// 'a' takes to Q3, and
// 'b' and 'c' remain at Q4
if (c == 'a')
nfa = 3;
else if (c == 'b' || c == 'c')
nfa = 2;
else
flag = 1;
}
// Function for the state Q4
static void state3(char c)
{
// State transitions
// 'a' takes to Q2, and
// 'b' and 'c' remain at Q3
if (c == 'a')
nfa = 1;
else if (c == 'b' || c == 'c')
nfa = 3;
else
flag = 1;
}
// Function for the state Q5
static void state4(char c)
{
// State transitions
// 'b' takes to Q6, and
// 'a' and 'c' remain at Q5
if (c == 'b')
nfa = 5;
else if (c == 'a' || c == 'c')
nfa = 4;
else
flag = 1;
}
// Function for the state Q6
static void state5(char c)
{
// State transitions
// 'b' takes to Q7, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 6;
else if (c == 'a' || c == 'c')
nfa = 5;
else
flag = 1;
}
// Function for the state Q7
static void state6(char c)
{
// State transitions
// 'b' takes to Q5, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 4;
else if (c == 'a' || c == 'c')
nfa = 6;
else
flag = 1;
}
// Function for the state Q8
static void state7(char c)
{
// State transitions
// 'c' takes to Q9, and
// 'a' and 'b' remain at Q8
if (c == 'c')
nfa = 8;
else if (c == 'b' || c == 'a')
nfa = 7;
else
flag = 1;
}
// Function for the state Q9
static void state8(char c)
{
// State transitions
// 'c' takes to Q10, and
// 'a' and 'b' remain at Q9
if (c == 'c')
nfa = 9;
else if (c == 'b' || c == 'a')
nfa = 8;
else
flag = 1;
}
// Function for the state Q10
static void state9(char c)
{
// State transitions
// 'c' takes to Q8, and
// 'a' and 'b' remain at Q10
if (c == 'c')
nfa = 7;
else if (c == 'b' || c == 'a')
nfa = 9;
else
flag = 1;
}
// Function to check for 3 a's
static boolean checkA(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 1)
state1(s.charAt(i));
else if (nfa == 2)
state2(s.charAt(i));
else if (nfa == 3)
state3(s.charAt(i));
}
if (nfa == 1) {
return true;
}
else {
nfa = 4;
}
return false;
}
// Function to check for 3 b's
static boolean checkB(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 4)
state4(s.charAt(i));
else if (nfa == 5)
state5(s.charAt(i));
else if (nfa == 6)
state6(s.charAt(i));
}
if (nfa == 4) {
return true;
}
else {
nfa = 7;
}
return false;
}
// Function to check for 3 c's
static boolean checkC(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 7)
state7(s.charAt(i));
else if (nfa == 8)
state8(s.charAt(i));
else if (nfa == 9)
state9(s.charAt(i));
}
if (nfa == 7) {
return true;
}
return false;
}
// Driver Code
public static void main (String[] args)
{
String s = "bbbca";
int x = 5;
// If any of the states is true, that is, if either
// the number of a's or number of b's or number of c's
// is a multiple of three, then the string is accepted
if (checkA(s, x) || checkB(s, x) || checkC(s, x)) {
System.out.println("ACCEPTED");
}
else {
if (flag == 0) {
System.out.println("NOT ACCEPTED");
}
else {
System.out.println("INPUT OUT OF DICTIONARY.");
}
}
}
}
// This code is contributed by AnkitRai01Python3
# Python3 implementation of the above approach
# NFA variable that keeps track of
# the state while transaction.
nfa = 1
# This checks for invalid input.
flag = 0
# Function for the state Q2
def state1(c):
global nfa,flag
# State transitions
# 'a' takes to Q4, and
# 'b' and 'c' remain at Q2
if (c == 'a'):
nfa = 2
elif (c == 'b' or c == 'c'):
nfa = 1
else:
flag = 1
# Function for the state Q3
def state2(c):
global nfa,flag
# State transitions
# 'a' takes to Q3, and
# 'b' and 'c' remain at Q4
if (c == 'a'):
nfa = 3
elif (c == 'b' or c == 'c'):
nfa = 2
else:
flag = 1
# Function for the state Q4
def state3(c):
global nfa,flag
# State transitions
# 'a' takes to Q2, and
# 'b' and 'c' remain at Q3
if (c == 'a'):
nfa = 1
elif (c == 'b' or c == 'c'):
nfa = 3
else:
flag = 1
# Function for the state Q5
def state4(c):
global nfa,flag
# State transitions
# 'b' takes to Q6, and
# 'a' and 'c' remain at Q5
if (c == 'b'):
nfa = 5
elif (c == 'a' or c == 'c'):
nfa = 4
else:
flag = 1
# Function for the state Q6
def state5(c):
global nfa, flag
# State transitions
# 'b' takes to Q7, and
# 'a' and 'c' remain at Q7
if (c == 'b'):
nfa = 6
elif (c == 'a' or c == 'c'):
nfa = 5
else:
flag = 1
# Function for the state Q7
def state6(c):
global nfa,flag
# State transitions
# 'b' takes to Q5, and
# 'a' and 'c' remain at Q7
if (c == 'b'):
nfa = 4
elif (c == 'a' or c == 'c'):
nfa = 6
else:
flag = 1
# Function for the state Q8
def state7(c):
global nfa,flag
# State transitions
# 'c' takes to Q9, and
# 'a' and 'b' remain at Q8
if (c == 'c'):
nfa = 8
elif (c == 'b' or c == 'a'):
nfa = 7
else:
flag = 1
# Function for the state Q9
def state8(c):
global nfa,flag
# State transitions
# 'c' takes to Q10, and
# 'a' and 'b' remain at Q9
if (c == 'c'):
nfa = 9
elif (c == 'b' or c == 'a'):
nfa = 8
else:
flag = 1
# Function for the state Q10
def state9(c):
global nfa,flag
# State transitions
# 'c' takes to Q8, and
# 'a' and 'b' remain at Q10
if (c == 'c'):
nfa = 7
elif (c == 'b' or c == 'a'):
nfa = 9
else:
flag = 1
# Function to check for 3 a's
def checkA(s, x):
global nfa,flag
for i in range(x):
if (nfa == 1):
state1(s[i])
elif (nfa == 2):
state2(s[i])
elif (nfa == 3):
state3(s[i])
if (nfa == 1):
return True
else:
nfa = 4
# Function to check for 3 b's
def checkB(s, x):
global nfa,flag
for i in range(x):
if (nfa == 4):
state4(s[i])
elif (nfa == 5):
state5(s[i])
elif (nfa == 6):
state6(s[i])
if (nfa == 4):
return True
else:
nfa = 7
# Function to check for 3 c's
def checkC(s, x):
global nfa, flag
for i in range(x):
if (nfa == 7):
state7(s[i])
elif (nfa == 8):
state8(s[i])
elif (nfa == 9):
state9(s[i])
if (nfa == 7):
return True
# Driver Code
s = "bbbca"
x = 5
# If any of the states is True, that is, if either
# the number of a's or number of b's or number of c's
# is a multiple of three, then the is accepted
if (checkA(s, x) or checkB(s, x) or checkC(s, x)):
print("ACCEPTED")
else:
if (flag == 0):
print("NOT ACCEPTED")
else:
print("INPUT OUT OF DICTIONARY.")
# This code is contributed by shubhamsingh10C#
// C# implementation of the above approach
using System;
class GFG {
// NFA variable that keeps track of
// the state while transaction.
static int nfa = 1;
// This checks for invalid input.
static int flag = 0;
// Function for the state Q2
static void state1(char c)
{
// State transitions
// 'a' takes to Q4, and
// 'b' and 'c' remain at Q2
if (c == 'a')
nfa = 2;
else if (c == 'b' || c == 'c')
nfa = 1;
else
flag = 1;
}
// Function for the state Q3
static void state2(char c)
{
// State transitions
// 'a' takes to Q3, and
// 'b' and 'c' remain at Q4
if (c == 'a')
nfa = 3;
else if (c == 'b' || c == 'c')
nfa = 2;
else
flag = 1;
}
// Function for the state Q4
static void state3(char c)
{
// State transitions
// 'a' takes to Q2, and
// 'b' and 'c' remain at Q3
if (c == 'a')
nfa = 1;
else if (c == 'b' || c == 'c')
nfa = 3;
else
flag = 1;
}
// Function for the state Q5
static void state4(char c)
{
// State transitions
// 'b' takes to Q6, and
// 'a' and 'c' remain at Q5
if (c == 'b')
nfa = 5;
else if (c == 'a' || c == 'c')
nfa = 4;
else
flag = 1;
}
// Function for the state Q6
static void state5(char c)
{
// State transitions
// 'b' takes to Q7, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 6;
else if (c == 'a' || c == 'c')
nfa = 5;
else
flag = 1;
}
// Function for the state Q7
static void state6(char c)
{
// State transitions
// 'b' takes to Q5, and
// 'a' and 'c' remain at Q7
if (c == 'b')
nfa = 4;
else if (c == 'a' || c == 'c')
nfa = 6;
else
flag = 1;
}
// Function for the state Q8
static void state7(char c)
{
// State transitions
// 'c' takes to Q9, and
// 'a' and 'b' remain at Q8
if (c == 'c')
nfa = 8;
else if (c == 'b' || c == 'a')
nfa = 7;
else
flag = 1;
}
// Function for the state Q9
static void state8(char c)
{
// State transitions
// 'c' takes to Q10, and
// 'a' and 'b' remain at Q9
if (c == 'c')
nfa = 9;
else if (c == 'b' || c == 'a')
nfa = 8;
else
flag = 1;
}
// Function for the state Q10
static void state9(char c)
{
// State transitions
// 'c' takes to Q8, and
// 'a' and 'b' remain at Q10
if (c == 'c')
nfa = 7;
else if (c == 'b' || c == 'a')
nfa = 9;
else
flag = 1;
}
// Function to check for 3 a's
static bool checkA(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 1)
state1(s[i]);
else if (nfa == 2)
state2(s[i]);
else if (nfa == 3)
state3(s[i]);
}
if (nfa == 1) {
return true;
}
else {
nfa = 4;
}
return false;
}
// Function to check for 3 b's
static bool checkB(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 4)
state4(s[i]);
else if (nfa == 5)
state5(s[i]);
else if (nfa == 6)
state6(s[i]);
}
if (nfa == 4) {
return true;
}
else {
nfa = 7;
}
return false;
}
// Function to check for 3 c's
static bool checkC(String s, int x)
{
for (int i = 0; i < x; i++) {
if (nfa == 7)
state7(s[i]);
else if (nfa == 8)
state8(s[i]);
else if (nfa == 9)
state9(s[i]);
}
if (nfa == 7) {
return true;
}
return false;
}
// Driver Code
public static void Main(String[] args)
{
String s = "bbbca";
int x = 5;
// If any of the states is true, that is, if either
// the number of a's or number of b's or number of c's
// is a multiple of three, then the string is accepted
if (checkA(s, x) || checkB(s, x) || checkC(s, x)) {
Console.WriteLine("ACCEPTED");
}
else {
if (flag == 0) {
Console.WriteLine("NOT ACCEPTED");
}
else {
Console.WriteLine("INPUT OUT OF DICTIONARY.");
}
}
}
}
// This code is contributed by 29AjayKumar输出：
ACCEPTED