1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
| #include <iostream>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <iomanip>
#include <algorithm>
using namespace std;
vector<string> generateRandomMinterms(int numMinterms, int numVariables) {
vector<string> minterms;
set<string> uniqueMinterms;
srand(static_cast<unsigned>(time(0)));
while (minterms.size() < numMinterms) {
string minterm = "";
for (int j = 0; j < numVariables; ++j) {
minterm += (rand() % 2) ? '1' : '0';
}
if (uniqueMinterms.find(minterm) == uniqueMinterms.end()) {
minterms.push_back(minterm);
uniqueMinterms.insert(minterm);
}
}
return minterms;
}
void printQuineMatrix(const vector<string>& minterms) {
vector<string> sortedMinterms = minterms;
sort(sortedMinterms.begin(), sortedMinterms.end());
size_t numVariables = sortedMinterms[0].size();
cout << "Quine Matrix:" << endl;
for (const auto& minterm : sortedMinterms) {
cout << "+";
for (int i = 0; i < numVariables; ++i) {
cout << "---+";
}
cout << endl;
cout << "| ";
for (char c : minterm) {
cout << c << " | ";
}
cout << endl;
}
cout << "+";
for (int i = 0; i < numVariables; ++i) {
cout << "---+";
}
cout << endl;
}
map<int, vector<string>> formGroups(const vector<string>& minterms) {
map<int, vector<string>> groups;
for (const string& minterm : minterms) {
int ones = count(minterm.begin(), minterm.end(), '1');
groups[ones].push_back(minterm);
}
return groups;
}
bool canCombine(const string& a, const string& b, string& result) {
int diffCount = 0;
result = "";
for (size_t i = 0; i < a.size(); i++) {
if (a[i] != b[i]) {
if (++diffCount > 1) return false;
result += "-";
}
else {
result += a[i];
}
}
return diffCount == 1;
}
set<string> performCombinations(map<int, vector<string>>& groups) {
set<string> newImplicants;
map<int, vector<string>> newGroups;
bool merged = true;
set<string> mergedImplicants;
while (merged) {
merged = false;
for (auto it = groups.begin(); it != groups.end(); ++it) {
auto next_it = it;
++next_it;
if (next_it != groups.end()) {
int next_group = next_it->first;
for (const string& term1 : it->second) {
for (const string& term2 : next_it->second) {
string combined;
if (canCombine(term1, term2, combined)) {
merged = true;
if (mergedImplicants.find(combined) == mergedImplicants.end()) {
newGroups[it->first].push_back(combined);
newImplicants.insert(combined);
}
else {
newImplicants.erase(combined);
}
mergedImplicants.insert(combined);
merged = true;
}
}
}
}
}
if (merged) {
groups = std::move(newGroups);
newGroups.clear();
}
}
return newImplicants;
}
map<string, vector<string>> createImplicantMatrix(const vector<string>& minterms, const set<string>& implicants) {
map<string, vector<string>> matrix;
for (const string& implicant : implicants) {
vector<string> covers;
for (const string& minterm : minterms) {
bool coversMinterm = true;
for (size_t i = 0; i < minterm.size(); i++) {
if (implicant[i] != '-' && implicant[i] != minterm[i]) {
coversMinterm = false;
break;
}
}
if (coversMinterm) {
covers.push_back(minterm);
}
}
matrix[implicant] = covers;
}
return matrix;
}
vector<string> findEssentialImplicants(const map<string, vector<string>>& matrix) {
map<string, int> mintermCount;
map<string, set<string>> mintermToImplicants;
for (const auto& pair : matrix) {
const vector<string>& minterms = pair.second;
for (const string& minterm : minterms) {
mintermCount[minterm]++;
mintermToImplicants[minterm].insert(pair.first);
}
}
vector<string> essential;
set<string> coveredMinterms;
set<string> usedImplicants;
for (const auto& count : mintermCount) {
const string& minterm = count.first;
if (count.second == 1) {
const string& essentialImplicant = *mintermToImplicants[minterm].begin();
if (usedImplicants.insert(essentialImplicant).second) {
essential.push_back(essentialImplicant);
for (const string& mintermCovered : matrix.at(essentialImplicant)) {
coveredMinterms.insert(mintermCovered);
}
}
}
}
return essential;
}
string combineImplicants(const vector<string>& implicants) {
string result = "";
for (const string& implicant : implicants) {
if (!result.empty()) {
result += " + ";
}
for (size_t i = 0; i < implicant.size(); i++) {
if (implicant[i] == '0') {
result += char('a' + i) + "'";
}
else if (implicant[i] == '1') {
result += char('a' + i);
}
}
}
return result;
}
string buildTerm(const string& implicant) {
string term;
for (size_t i = 0; i < implicant.size(); ++i) {
if (implicant[i] == '0' || implicant[i] == '1') {
if (!term.empty()) term += " AND ";
term += "X" + to_string(i + 1);
if (implicant[i] == '0') term += "!";
}
}
return term;
}
void printMDNF(const vector<string>& essentialImplicants) {
cout << "MDNF = ";
for (size_t i = 0; i < essentialImplicants.size(); ++i) {
if (i > 0) cout << " OR ";
cout << "(" << buildTerm(essentialImplicants[i]) << ")";
}
cout << endl;
}
void prettyPrintMatrix(const map<string, vector<string>>& matrix, const vector<string>& minterms) {
const int columnWidth = 10;
// Print header with minterms
cout << left << setw(columnWidth) << "MINTERM-> |";
for (const auto& minterm : minterms) {
cout << setw(columnWidth) << minterm;
}
cout << "\nImplicant |";
cout << "\n";
// Print line separating header from data
cout << setw(columnWidth) << setfill('-') << "+" << setfill('-');
for (size_t i = 0; i < minterms.size(); i++) {
cout << setw(columnWidth) << "-";
}
cout << "\n" << setfill(' ');
for (const auto& pair : matrix) {
cout << left << setw(columnWidth) << pair.first << "|";
set<string> coveredMinterms(pair.second.begin(), pair.second.end());
for (const auto& minterm : minterms) {
if (coveredMinterms.count(minterm)) {
cout << setw(columnWidth) << "X";
}
else {
cout << setw(columnWidth) << " ";
}
}
cout << "\n";
}
}
int main() {
int numMinterms, numVariables;
cout << "Enter the number of minterms: ";
cin >> numMinterms;
cout << "Enter the number of variables: ";
cin >> numVariables;
vector<string> minterms = generateRandomMinterms(numMinterms, numVariables);
// Формирование групп
map<int, vector<string>> groups = formGroups(minterms);
cout << "Initial Grouping by number of 1s:" << endl;
for (const auto& group : groups) {
cout << "Group " << group.first << ": ";
for (const auto& minterm : group.second) {
cout << minterm << " ";
}
cout << endl;
}
// Выполнение комбинаций
set<string> newImplicants = performCombinations(groups);
cout << "New Implicants after combination:" << endl;
for (const auto& implicant : newImplicants) {
cout << implicant << endl;
}
// Составление импликантной матрицы
map<string, vector<string>> implicantMatrix = createImplicantMatrix(minterms, newImplicants);
cout << "Implicant Matrix:" << endl;
prettyPrintMatrix(implicantMatrix, minterms);
// Поиск существенных импликантов
vector<string> essentialImplicants = findEssentialImplicants(implicantMatrix);
cout << "Essential Implicants:" << endl;
for (const auto& essential : essentialImplicants) {
cout << essential << endl;
}
printMDNF(essentialImplicants);
return 0;
} |
(
Сообщение от olljlk
