codeforces 559C|51nod1486 Gerald and Giant Chess(组合数学+逆元)

codeforces 559C|51nod1486

题目

思路

代码

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std ;
#define LL __int64
const LL MOD = 1e9+7 ;
struct node{
LL x , y ;
}p[3100];
LL h , w , n ;
LL fac[310000] , inv[310000] ;
LL sum[3100] ;
int cmp(node a,node b) {
return a.x < b.x || (a.x == b.x && a.y < b.y) ;
}
LL pow(LL x,LL k) {
LL ans = 1 ;
while( k ) {
if( k&1 ) ans = ans*x%MOD ;
k = k>>1 ;
x = (x*x)%MOD ;
}
return ans ;
}
void init() {
LL i , j , c ;
fac[0] = inv[0] = 1 ;
for(i = 1 ; i <= h+w ; i++)
fac[i] = (fac[i-1]*i)%MOD ;
c = max(h,w) ;
inv[c] = pow(fac[c],MOD-2) ;
for(i = c-1 ; i > 0 ; i--) {
inv[i] = inv[i+1]*(i+1)%MOD ;
}
}
int main() {
LL i , j ;
LL ans ;
while( scanf("%I64d %I64d %I64d", &h, &w, &n) != EOF ) {
init() ;
for(i = 0 ; i < n ; i++)
scanf("%I64d %I64d", &p[i].x, &p[i].y) ;
p
.x = h ; p[n++].y = w ;
sort(p,p+n,cmp) ;
int x1 , y1 , x2 , y2 ;
for(i = 0 ; i < n ; i++) {
x1 = p[i].x-1 ; y1 = p[i].y-1 ;
sum[i] = fac[x1+y1]*inv[x1]%MOD*inv[y1]%MOD ;
for(j = 0 ; j < i ; j++) {
if( p[j].x <= p[i].x && p[j].y <= p[i].y ) {
x2 = x1 - p[j].x+1 ; y2 = y1 - p[j].y+1 ;
sum[i] = (sum[i]-fac[x2+y2]*inv[x2]%MOD*inv[y2]%MOD*sum[j]%MOD)%MOD ;
if( sum[i] <= 0 ) sum[i] = (sum[i]+MOD)%MOD;
}
}
}
printf("%I64d\n", sum[n-1]) ;
}
return 0 ;
}