dfs卡诺图最简算法

gray.h

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#ifndef __GRAY_H__
#define __GRAY_H__

#include <iostream>
#include <string>

#ifdef __cplusplus
extern "C" {
#endif

class Gray {
private:
  int gray_num;
  int max_num;

public:
  Gray(int num, int max_num);
  ~Gray();
  void add(int num);
  int result();
  std::string to_bin();
};

#ifdef __cplusplus
}
#endif

#endif // !__GRAY_H__

gray.cpp

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#include <gray.h>
#include <math.h>

Gray::Gray(int num, int max_num) {
  this->gray_num = num;
  this->max_num = max_num;
}

Gray::~Gray() {}

int Gray::result() { return this->gray_num; }

void Gray::add(int num) {
  int tmp = this->gray_num;
  int max_num = pow(2, this->max_num);
  tmp ^= tmp >> 16;
  tmp ^= tmp >> 8;
  tmp ^= tmp >> 4;
  tmp ^= tmp >> 2;
  tmp ^= tmp >> 1;
  tmp += num;
  if (tmp >= max_num)
    tmp %= max_num;
  if (tmp < 0)
    tmp += max_num;
  tmp ^= tmp >> 1;
  this->gray_num = tmp;
}

std::string Gray::to_bin() {
  std::string ret;
  for (int i = this->max_num - 1; i >= 0; i--)
    ret += ((this->gray_num >> i) & 0x1) + '0';
  return ret;
}

karnaugh_map.h

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#ifndef __KarnaughMap_H__
#define __KarnaughMap_H__

#include <iostream>
#include <set>
#include <string>
#include <unordered_map>
#include <vector>

#ifdef __cplusplus
extern "C" {
#endif

typedef std::string krt_elem;
typedef std::vector<krt_elem> krt_map;
typedef krt_map krt_equ;
typedef std::set<krt_map> krt_circle;
typedef std::vector<krt_circle> krt_ways;
typedef std::unordered_map<krt_elem, krt_circle> krt_table;

class KarnaughMap {
private:
  krt_table create_table(krt_map *map);
  krt_circle get_max_circle(krt_map *map, krt_elem elem);
  krt_map get_circle(krt_elem src, krt_elem dst);
  bool circle_is_valid(krt_map *map, krt_map *circle);
  void delete_circle(krt_map *map, krt_map *circle);
  krt_equ resolv_ways(krt_ways *ways);
  bool verity_map(krt_map *map);
  void dfs(krt_map *map, krt_table *table, int num, int *min_num,
           krt_ways *ways, krt_circle record_way);

public:
  KarnaughMap();
  ~KarnaughMap();
  bool get_simplest(krt_equ *equ, krt_map *map);
};

#ifdef __cplusplus
}
#endif

#endif // !__KarnaughMap_H__

karnaugh_map.cpp

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#include <algorithm>
#include <gray.h>
#include <karnaugh_map.h>
#include <math.h>
#include <stdint.h>

using namespace std;

KarnaughMap::KarnaughMap() {}

KarnaughMap::~KarnaughMap() {}

krt_equ KarnaughMap::resolv_ways(krt_ways *ways) {
  krt_equ ret;
  for (krt_circle it0 : *ways) {
    std::string tmp0 = "";
    for (krt_map it1 : it0) {
      std::string tmp1 = "";
      int len = it1[0].size();
      for (int i = 0; i < len; i++) {
        bool flag = true;
        char ch = it1[0][i];
        for (krt_elem it2 : it1) {
          if (it2[i] != ch) {
            flag = false;
            break;
          }
        }
        if (!flag)
          continue;
        tmp1 += i + '0' + 17;
        if (ch == '0')
          tmp1 += "'";
      }
      if (tmp1 != "") {
        tmp0 += " + " + tmp1;
      }
    }
    if (tmp0.size() == 0)
      continue;
    tmp0 = tmp0.substr(3, tmp0.size() - 3);
    ret.push_back(tmp0);
  }
  return ret;
}

bool KarnaughMap::verity_map(krt_map *map) {
  int size;
  if (map->size() == 0)
    return false;

  size = (*map)[0].size();
  for (krt_elem item : *map) {
    if (item.size() != size)
      return false;
    for (char ch : item) {
      if (ch != '0' && ch != '1')
        return false;
    }
  }
  return true;
}

bool KarnaughMap::get_simplest(krt_equ *equ, krt_map *map) {
  krt_table table;
  krt_ways ways;
  if (!verity_map(map))
    return false;
  table = create_table(map);
  int min_num = pow(2, (*map)[0].size());
  dfs(map, &table, 0, &min_num, &ways, krt_circle());
  *equ = resolv_ways(&ways);
  return true;
}

krt_map KarnaughMap::get_circle(krt_elem src, krt_elem dst) {
  krt_map ret;
  int len = src.size(), mid = len / 2;
  krt_elem lsrc = src.substr(0, mid), rsrc = src.substr(mid, len - mid);
  krt_elem ldst = dst.substr(0, mid), rdst = dst.substr(mid, len - mid);

  krt_elem tmp_elem = rsrc;
  while (lsrc != ldst) {
    while (tmp_elem != rdst) {
      ret.push_back(lsrc + tmp_elem);
      Gray tmp(stoi(tmp_elem, nullptr, 2), len - mid);
      tmp.add(1);
      tmp_elem = tmp.to_bin();
    }
    ret.push_back(lsrc + tmp_elem);
    tmp_elem = rsrc;
    Gray tmp(stoi(lsrc, nullptr, 2), mid);
    tmp.add(1);
    lsrc = tmp.to_bin();
  }

  while (tmp_elem != rdst) {
    ret.push_back(lsrc + tmp_elem);
    Gray tmp(stoi(tmp_elem, nullptr, 2), len - mid);
    tmp.add(1);
    tmp_elem = tmp.to_bin();
  }
  ret.push_back(lsrc + tmp_elem);

  sort(ret.begin(), ret.end());
  return ret;
}

bool KarnaughMap::circle_is_valid(krt_map *map, krt_map *circle) {
  int map_len = map[0].size(), circle_len = circle->size();
  bool flag = false;

  for (int tmp = 0; tmp <= map_len; tmp++) {
    if (pow(2, tmp) == circle_len) {
      flag = true;
      break;
    }
  }

  if (!flag)
    return false;

  for (krt_elem item : *circle) {
    if (std::find(map->begin(), map->end(), item) == map->end())
      return false;
  }
  return true;
}

krt_circle KarnaughMap::get_max_circle(krt_map *map, krt_elem elem) {
  krt_circle ret;
  krt_map tmp_circle;
  uint32_t max_size = 0;

  for (krt_elem item : *map) {
    tmp_circle = get_circle(elem, item);
    if (circle_is_valid(map, &tmp_circle)) {
      if (tmp_circle.size() > max_size) {
        ret.clear();
        max_size = tmp_circle.size();
      }
      if (tmp_circle.size() == max_size)
        ret.insert(tmp_circle);
    }

    tmp_circle = get_circle(item, elem);
    if (circle_is_valid(map, &tmp_circle)) {
      if (tmp_circle.size() > max_size) {
        ret.clear();
        max_size = tmp_circle.size();
      }
      if (tmp_circle.size() == max_size)
        ret.insert(tmp_circle);
    }
  }

  return ret;
}

krt_table KarnaughMap::create_table(krt_map *map) {
  krt_table ret;

  for (krt_elem item : *map) {
    krt_circle max_circle = get_max_circle(map, item);
    ret[item] = max_circle;
  }

  return ret;
}

void KarnaughMap::delete_circle(krt_map *map, krt_map *circle) {
  for (krt_elem item : *circle) {
    auto it = std::find(map->begin(), map->end(), item);
    if (it != map->end())
      map->erase(it);
  }
}

void KarnaughMap::dfs(krt_map *map, krt_table *table, int num, int *min_num,
                      krt_ways *ways, krt_circle record_way) {

  if (num > *min_num) {
    return;
  }

  if (map->size() == 0) {
    if (num < *min_num) {
      *min_num = num;
      ways->clear();
    }
    if (num == *min_num) {
      krt_circle tmp = record_way;
      // sort(tmp.begin(), tmp.end());
      auto it = std::find(ways->begin(), ways->end(), tmp);
      if (it == ways->end())
        ways->push_back(tmp);
    }
    return;
  }

  for (krt_elem it0 : *map) {
    for (krt_map it1 : (*table)[it0]) {
      krt_map tmp_krt_map = *map;
      delete_circle(map, &it1);
      record_way.insert(it1);
      dfs(map, table, num + 1, min_num, ways, record_way);
      record_way.erase(it1);
      *map = tmp_krt_map;
    }
  }
}