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8.2.cpp
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8.2.cpp
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#include <iostream>
#include <cstdio>
#include <stack>
using namespace std;
typedef long long ll;
typedef struct point{
int x, y;
}point;
stack<point> sp;
const int MAXN = 20;
int g[MAXN][MAXN];
point vp[MAXN+MAXN];
ll path(ll m, ll n){
if(m == 1 || n == 1) return 1;
else return path(m-1, n) + path(m, n-1);
}
ll fact(ll n){
if(n == 0) return 1;
else return n*fact(n-1);
}
ll path1(ll m, ll n){
return fact(m-1+n-1)/(fact(m-1)*fact(n-1));
}
bool get_path(int m, int n){
point p; p.x=n; p.y=m;
sp.push(p);
if(n==1 && m==1) return true;
bool suc = false;
if(m>1 && g[m-1][n])
suc = get_path(m-1, n);
if(!suc && n>1 && g[m][n-1])
suc = get_path(m, n-1);
if(!suc) sp.pop();
return suc;
}
void print_paths(int m, int n, int M, int N, int len){
if(g[m][n] == 0) return;
point p; p.x=n; p.y=m;
vp[len++] = p;
if(m == M && n == N){
for(int i=0; i<len; ++i)
cout<<"("<<vp[i].y<<", "<<vp[i].x<<")"<<" ";
cout<<endl;
}
else{
print_paths(m, n+1, M, N, len);
print_paths(m+1, n, M, N, len);
}
}
int main(){
freopen("8.2.in", "r", stdin);
for(int i=1; i<10; ++i)
cout<<path(i, i)<<endl;
cout<<endl;
for(int i=1; i<10; ++i)
cout<<path1(i, i)<<endl;
cout<<endl;
int M, N;
cin>>M>>N;
for(int i=1; i<=M; ++i)
for(int j=1; j<=N; ++j)
cin>>g[i][j];
cout<<"one of the paths:"<<endl;
get_path(M, N);
while(!sp.empty()){
point p = sp.top();
cout<<"("<<p.y<<", "<<p.x<<")"<<" ";
sp.pop();
}
cout<<endl<<"all paths:"<<endl;
print_paths(1, 1, M, N, 0);
fclose(stdin);
return 0;
}