#4705. 递增

题目描述

题解

气死我了好不容易想出dp组合数写挂？

题解写的好清楚懒得写了...

代码

#include <bits/stdc++.h>
#define LL long long
using namespace std;
const int N=105,P=998244353,I=(P+1)>>1;
int n,f[N][N],g[N][N],jc[N],ny[N],B;
LL l[N],r[N],b[N],L[N],R[N];
int K(int x,int y){
    int z=1;
    for (;y;y>>=1,x=1ll*x*x%P)
        if (y&1) z=1ll*z*x%P;
    return z;
}
int inv(int x){
    return 1ll*ny[x]*jc[x-1]%P;
}
int C(LL x,int y){
    x=(x+y-1)%P;int v=1;
    for (int i=1;i<=y;i++)
        v=1ll*v*(x-i+1+P)%P*inv(i)%P;
    return v;
}
int W(){
    for (int i=1;i<=n;i++){
        if (L[i]>R[i]) return 0;
        b[++B]=L[i];b[++B]=R[i]+1;
    }
    sort(b+1,b+B+1);
    B=unique(b+1,b+B+1)-b-1;f[0][0]=1;
    for (int i=1;i<B;i++){
        LL x=b[i],y=b[i+1]-1;f[i][0]=1;
        for (int j=1;j<=n;j++){
            g[i][j]=g[i-1][j];
            f[i][j]=f[i-1][j];
            for (int k=j;k;k--){
                if (L[k]<=x && y<=R[k]){
                    (g[i][j]+=(1ll*g[i-1][k-1]*C(y-x+1,j-k+1)%P+1ll*f[i-1][k-1]*C(y-x+1,j-k+1)%P*((x+y)%P)%P*I%P*(j-k+1)%P)%P)%=P;
                    (f[i][j]+=1ll*f[i-1][k-1]*C(y-x+1,j-k+1)%P)%=P;
                }
                else break;
            }
        }
    }
    return g[B-1][n];
}
int main(){
    cin>>n;jc[0]=1;
    for (int i=1;i<=n;i++){
        jc[i]=1ll*i*jc[i-1]%P;
        scanf("%lld",&l[i]);
        if (i==1) L[i]=l[i];
        else L[i]=max(L[i-1],l[i]);
    }
    ny[n]=K(jc[n],P-2);
    for (int i=1;i<=n;i++)
        scanf("%lld",&r[i]);R[n]=r[n];
    for (int i=n-1;i;i--)
        R[i]=min(R[i+1],r[i]);
    for (int i=n;i;i--)
        ny[i-1]=1ll*i*ny[i]%P;
    cout<<W()<<endl;return 0;
}