【HDOJ6656】Kejin Player（期望DP）

题意：玩一个共有n级的游戏，i级出发每次可以花a[i]的代价，有p[i]的几率变成i+1级，有1-p[i]的几率变成x[i]级，x[i]<=i

多次询问，每次询问从l级升到r级的期望总代价

n,q<=5e5，0<=a[i]<=1e9

思路：

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef pair<ll,ll> Pll;
 typedef vector<int> VI;
 typedef vector<PII> VII;
 #define N  1100000
 #define M  4100000
 #define fi first
 #define se second
 #define MP make_pair
 #define pi acos(-1)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
 #define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
 #define lowbit(x) x&(-x)
 #define Rand (rand()*(1<<16)+rand())
 #define id(x) ((x)<=B?(x):m-n/(x)+1)
 #define ls p<<1
 #define rs p<<1|1

 const ll MOD=1e9+,inv2=(MOD+)/;
       double eps=1e-;
       int INF=1e9;

 ll s[N];

 ll read()
 {
    ll v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 ll pw(ll x,ll y)
 {
     ll t=;
     while(y)
     {
         if(y&) t=t*x%MOD;
         x=x*x%MOD;
         y>>=;
     }
     return t;
 }

 int main()
 {
     //freopen("1.in","r",stdin);
     int cas;
     scanf("%d",&cas);
     while(cas--)
     {
         int n,q;
         scanf("%d%d",&n,&q);
         rep(i,,n) s[i]=;
         rep(i,,n)
         {
             ll ri=read(),si=read(),xi=read(),ai=read();
             ll fi=(si*ai%MOD+(si-ri+MOD)*(s[i-]-s[xi-]+MOD)%MOD)%MOD*pw(ri,MOD-)%MOD;
             //printf("i=%d fi=%I64d\n",i,fi);
             s[i]=(s[i-]+fi)%MOD;
         }
         rep(i,,q)
         {
             int l,r;
             scanf("%d%d",&l,&r);
             //printf("l=%d r=%d\n",l,r);
             printf("%I64d\n",(s[r-]-s[l-]+MOD)%MOD);
         }
     }

     return ;
 }