[bzoj1867][Noi1999][钉子和小球] (动态规划)

#include <stdio.h>
#define L long long
#define RG register

inline void Rin(RG int &x) {
  x=0;RG int c=getchar(),f=1;
  for(;c<48||c>57;c=getchar())
    if(!(c^45))f=-1;
  for(;c>47&&c<58;c=getchar())
    x=(x<<1)+(x<<3)+c-48;
  x*=f; }

inline void ploy(RG bool &x) {
  RG char c=getchar();
  while(c!=‘*‘&&c!=‘.‘)c=getchar();
  x=c==‘*‘?true:false; }

void Shiki(RG L x) {
  if(!x)return;
  Shiki(x/10);
  putchar(x%10+48); }

L gcd(RG L a,RG L b) {
  return b?gcd(b,a%b):a; }

bool _map[55][55];

int n,m;

struct fr{
  L n,d;

  fr(RG L _=0,RG L __=1) : n(_),d(__) {} }f[55][55];

inline void rec(fr &_this) {
  L t=gcd(_this.n,_this.d);
  _this.n/=t;
  _this.d/=t; }

fr operator + (const fr &a,const fr &b) {
  fr res;
  L t=gcd(a.d,b.d);
  res.n=b.d/t*a.n+a.d/t*b.n;
  res.d=a.d/t*b.d;
  return res; }

fr operator * (const fr &a,const fr &b) {
  fr res(a.n*b.n,a.d*b.d);
  rec(res);
  return res; }

void operator += (fr &a,const fr &b) {
  a=a+b; }

int main() {
  Rin(n),Rin(m);
  for(RG int i=1; i<=n; i++)
    for(RG int j=1; j<=i; j++)
      ploy(_map[i][j]);
  f[1][1]=fr(1,1);
  for(RG int i=1; i<=n; i++)
    for(RG int j=1; j<=i; j++)
      rec(f[i][j]),
      _map[i][j]?
    f[i+1][j]+=f[i][j]*fr(1,2),f[i+1][j+1]+=f[i][j]*fr(1,2):
    f[i+2][j+1]+=f[i][j];
  rec(f[n+1][m+1]);
  Shiki(f[n+1][m+1].n); putchar(‘/‘); Shiki(f[n+1][m+1].d);
  return 0;
}