CF 559C - Gerald and Giant Chess （组合计数）

\(C_{x+y}^y\)的公式，DP容斥删多余贡献。
#include <cstdio>

#include <iostream>

#include <cstring>

#include <algorithm>

#include <cmath>

#define R(a,b,c) for(register int a = (b); (a) <= (c); ++(a))

#define nR(a,b,c) for(register int a = (b); (a) >= (c); --(a))

#define Fill(a,b) memset(a, b, sizeof(a))

#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))

#define ll long long

#define u32 unsigned int

#define u64 unsigned long long

//#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("\n----------\n")

#define D_e(x) cout << (#x) << " : " << x << endl

#define Pause() system("pause")

#define FileOpen() freopen("in.txt", "r", stdin)

#define FileSave() freopen("out.txt", "w", stdout)

#include <ctime>

#define TIME() fprintf(stderr, "\ntime: %.3fms\n", clock() * 1000.0 / CLOCKS_PER_SEC)

#else

#define D_e_Line ;

#define D_e(x) ;

#define Pause() ;

#define FileOpen() ;

#define FileSave() ;

#define TIME() ;

//char buf[1 << 21], *p1 = buf, *p2 = buf;

//#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)

#endif

using namespace std;

struct ios{

    template<typename ATP>inline ios& operator >> (ATP &x){

        x = 0; int f = 1; char ch;

        for(ch = getchar(); ch < '0' || ch > '9'; ch = getchar()) if(ch == '-') f = -1;

        while(ch >= '0' && ch <= '9') x = x * 10 + (ch ^ '0'), ch = getchar();

        x *= f;

        return *this;

    }

}io;

template<typename ATP>inline ATP Max(ATP a, ATP b){

    return a > b ? a : b;

}

template<typename ATP>inline ATP Min(ATP a, ATP b){

    return a < b ? a : b;

}

template<typename ATP>inline ATP Abs(ATP a){

    return a < 0 ? -a : a;

}

const int N = 200007;

const int mod = 1000000007;

#define int long long

struct nod{

	int x, y;

	bool operator < (const nod &com) const{

		if(x != com.x) return x < com.x;

		return y < com.y;

	}

}a[N];

int fac[N], inv[N], n, m, K;

inline int Pow(int a, int b){

	int s = 1;

	while(b){

		if(b & 1) s = s * a % mod;

		a = a * a % mod, b >>= 1;

	}

	return s;

}

inline void Init(){

	fac[0] = fac[1] = inv[0] = 1;

	R(i,2,n + m) fac[i] = fac[i - 1] * i % mod;

	R(i,1,n + m) inv[i] = Pow(fac[i], mod - 2);

}

inline int Calc(int x, int y){

	if(x < 0 || y < 0) return 0;

	return fac[x + y] * inv[x] % mod * inv[y] % mod;

}

int f[N];

#undef int

int main(){

#define int long long

//FileOpen();

//FileSave();

	io >> n >> m >> K;

	Init();

	R(i,1,K){

		io >> a[i].x >> a[i].y;

	}

	sort(a + 1, a + K + 1);

	a[K + 1] = (nod){ n, m};

	R(i,1,K + 1){

		int x = a[i].x - 1, y  = a[i].y - 1;

		f[i] = Calc(x, y);

		R(j,1, i - 1){

			int dx = a[i].x - a[j].x, dy = a[i].y - a[j].y;

			int del = Calc(dx, dy) * f[j] % mod;

			f[i] = (f[i] - del + mod) % mod;

		}

	}

	printf("%lld", f[K + 1]);

	return 0;

}
巴特西

CF 559C - Gerald and Giant Chess （组合计数）

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