Formula1 URAL1519
这题可以说是正式的插头dp，需要对插头标号，虽然研读了hh的模板和论文，但写起来还是花了很多时间，主要是细节方面的东西，比如第一列和最后一列需要特殊讨论，还有最后一个合法格子也需要特殊讨论
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <algorithm>
#include <vector>
#include <cstring>
#include <stack>
#include <cctype>
#include <utility>
#include <map>
#include <string>
#include <climits>
#include <set>
#include <string>
#include <sstream>
#include <utility>
#include <ctime>
using std::priority_queue;
using std::vector;
using std::swap;
using std::stack;
using std::sort;
using std::max;
using std::min;
using std::pair;
using std::map;
using std::string;
using std::cin;
using std::cout;
using std::set;
using std::queue;
using std::string;
using std::istringstream;
using std::make_pair;
using std::getline;
using std::greater;
using std::endl;
using std::multimap;
using std::deque;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PAIR;
typedef multimap<int, int> MMAP;
const int MAXN(1000010);
const int MAXM(10010);
const int MAXE(10010);
const int HSIZE(13131);
const int SIGMA_SIZE(26);
const int MAXH(19);
const int INFI(2000000000);
const int MOD(100000000);
const ULL BASE(31);
const LL LIM(10000000);
const int INV(-10000);
struct HASH_MAP
{
int first[HSIZE], next[MAXN];
LL state[MAXN];
LL value[MAXN];
int size;
void init()
{
memset(first, -1, sizeof(first));
size = 0;
}
void insert(LL ts, LL tv)
{
int h = ts%HSIZE;
for(int i = first[h]; ~i; i = next[i])
if(state[i] == ts)
{
value[i] += tv;
return;
}
state[size] = ts;
value[size] = tv;
next[size] = first[h];
first[h] = size++;
}
}hm[2];
HASH_MAP *cur, *last;
char mp[15][15];
int code[13];
int Num[13];
inline void decode(int m, LL ts)
{
for(int i = 0; i <= m; ++i)
{
code[i] = ts&7;
ts >>= 3;
}
}
inline LL encode(int m)
{
LL ret = 0;
int cnt = 0;
memset(Num, -1, sizeof(Num));
for(int i = m; i >= 0; --i)
if(code[i] == 0)
ret <<= 3;
else
{
if(Num[code[i]] < 0) Num[code[i]] = ++cnt;
ret = (ret << 3)|Num[code[i]];
}
return ret;
}
int li, lj;
inline bool lastgrid(int i, int j){ return i == li && j == lj;}
void updata(int i, int j, int m, LL tv)
{
int up = (i == 0)? 0: code[j+1];
int left = (j == 0)? 0: code[j];
if(mp[i][j] == '*')
{
if(up == 0 && left == 0)
{
code[j] = code[j+1] = 0;
cur->insert(encode(m), tv);
}
return;
}
if(up == 0 && left == 0)
{
if(j == m-1) //最后一列不允许有右插头
return;
code[j] = code[j+1] = 7;
}
else
if(up == 0 || left == 0)
{
code[j] = up+left;
code[j+1] = 0;
cur->insert(encode(m), tv);
if(j == m-1) //最后一列不允许有右插头
return;
code[j] = 0;
code[j+1] = up+left;
cur->insert(encode(m), tv);
return;
}
else if(up != left)
{
if(lastgrid(i, j))
return;
for(int i = 0; i <= m; ++i)
if(code[i] == up) code[i] = left;
code[j] = code[j+1] = 0;
}
else if(lastgrid(i, j)) //只有最后一个格子允许连接成一条回路
code[j] = code[j+1] = 0;
else
return;
cur->insert(encode(m), tv);
}
void solve(int n, int m)
{
cur = hm;
last = hm+1;
last->init();
last->insert(0, 1);
for(int i = 0; i < n; ++i)
for(int j = 0; j < m; ++j)
{
cur->init();
int sz = last->size;
for(int k = 0; k < sz; ++k)
{
decode(m, last->state[k]);
if(j == 0)
for(int k2 = m; k2 >= 1; --k2) //另起一行时需要把编码整体右移
code[k2] = code[k2-1];
updata(i, j, m, last->value[k]);
}
if(lastgrid(i, j))
{
LL ans = 0;
for(int i = 0; i < cur->size; ++i)
if(cur->state[i] == 0)
{
ans = cur->value[i];
break;
}
printf("%I64d\n", ans);
return;
}
swap(cur, last);
}
}
int main()
{
int n, m;
while(~scanf("%d%d", &n, &m))
{
for(int i = 0; i < n; ++i)
scanf("%s", mp[i]);
li = lj = -1;
for(int i = n-1; i >= 0; --i)
{
for(int j = m-1; j >= 0; --j)
if(mp[i][j] == '.')
{
li = i;
lj = j;
break;
}
if(~li)
break;
}
if(li == -1)
printf("0\n");
else
solve(n, m);
}
return 0;
}
括号表示法(对于回路问题效率要比最小表示法高)
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <algorithm>
#include <vector>
#include <cstring>
#include <stack>
#include <cctype>
#include <utility>
#include <map>
#include <string>
#include <climits>
#include <set>
#include <string>
#include <sstream>
#include <utility>
#include <ctime>
using std::priority_queue;
using std::vector;
using std::swap;
using std::stack;
using std::sort;
using std::max;
using std::min;
using std::pair;
using std::map;
using std::string;
using std::cin;
using std::cout;
using std::set;
using std::queue;
using std::string;
using std::istringstream;
using std::make_pair;
using std::getline;
using std::greater;
using std::endl;
using std::multimap;
using std::deque;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PAIR;
typedef multimap<int, int> MMAP;
const int MAXN(20010);
const int MAXM(5010);
const int MAXE(10010);
const int HSIZE(13131);
const int SIGMA_SIZE(26);
const int MAXH(19);
const int INFI((INT_MAX-1) >> 1);
const int MOD(123456791);
const ULL BASE(31);
const LL LIM(10000000);
const int INV(-10000);
int N, M;
char mp[15][15];
struct HASH_MAP
{
int first[HSIZE];
int next[MAXN], state[MAXN];
LL value[MAXN];
int size;
void init()
{
memset(first, -1, sizeof(first));
size = 0;
}
void insert(int ts, LL tv)
{
int h = ts%HSIZE;
for(int i = first[h]; ~i; i = next[i])
if(state[i] == ts)
{
value[i] += tv;
return;
}
value[size] = tv;
state[size] = ts;
next[size] = first[h];
first[h] = size++;
}
} hm[2];
HASH_MAP *cur, *last;
int acc[4] = {0, -1, 1, 0}; //无插头，左括号，右括号
inline int getB(int ts, int i){ return (ts >> (i << 1))&3;} //获得指定位
inline int getLB(int ts, int i) //通过右括号找到左括号
{
int ret = i, cnt = 1;
while(cnt)
{
--ret;
cnt += acc[getB(ts, ret)];
}
return ret;
}
inline int getRB(int ts, int i) //通过左括号找到右括号
{
int ret = i, cnt = -1;
while(cnt)
{
++ret;
cnt += acc[getB(ts, ret)];
}
return ret;
}
inline void setB(int &ts, int i, int tv){ts = (ts&~(3 << (i << 1)))|(tv << (i << 1));} //设置指定位
int lx, ly;
inline bool lastgrid(int x, int y){return x == lx && y == ly;}
void updata(int x, int y, int ts, LL tv)
{
int left = (y == 0)? 0: getB(ts, y);
int up = (x == 0)? 0: getB(ts, y+1);
int tts;
if(mp[x][y] == '*')
{
if(left == 0 && up == 0)
{
tts = ts;
setB(tts, y, 0);
setB(tts, y+1, 0);
cur->insert(tts, tv);
}
return;
}
if(left == 0 && up == 0)
{
if(x == N-1 || y == M-1) return;
tts = ts;
setB(tts, y, 1);
setB(tts, y+1, 2);
cur->insert(tts, tv);
}
else
if(left == 0 || up == 0)
{
if(x < N-1)
{
tts = ts;
setB(tts, y, up+left);
setB(tts, y+1, 0);
cur->insert(tts, tv);
}
if(y < M-1)
{
tts = ts;
setB(tts, y, 0);
setB(tts, y+1, up+left);
cur->insert(tts, tv);
}
}
else
{
tts = ts;
setB(tts, y, 0);
setB(tts, y+1, 0);
if(left == 1 && up == 1)
{
setB(tts, getRB(ts, y+1), 1);
cur->insert(tts, tv);
}
else if(left == 1 && up == 2)
{
if(!lastgrid(x, y)) return;
cur->insert(tts, tv);
}
else if(left == 2 && up == 1)
{
cur->insert(tts, tv);
}
else if(left == 2 && up == 2)
{
setB(tts, getLB(ts, y), 2);
cur->insert(tts, tv);
}
}
}
void solve()
{
cur = hm;
last = hm+1;
last->init();
last->insert(0, 1);
for(int i = 0; i < N; ++i)
{
int sz = last->size;
for(int k = 0; k < sz; ++k)
last->state[k] <<= 2;
for(int j = 0; j < M; ++j)
{
cur->init();
sz = last->size;
for(int k = 0; k < sz; ++k)
updata(i, j, last->state[k], last->value[k]);
swap(cur, last);
}
}
LL ans = 0;
for(int i = 0; i < last->size; ++i)
if(last->state[i] == 0)
{
ans = last->value[i];
break;
}
printf("%I64d\n", ans);
}
int main()
{
while(~scanf("%d%d", &N, &M))
{
for(int i = 0; i < N; ++i)
scanf("%s", mp[i]);
lx = -1;
ly = -1;
for(int i = N-1; i >= 0 && lx == -1; --i)
for(int j = M-1; j >= 0; --j)
if(mp[i][j] == '.')
{
lx = i;
ly = j;
break;
}
solve();
}
return 0;
}