Codeforces 433E

数位DP与自动机实战

自动机+数位dp

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#include<cstdio>
#include<iostream>
#include<queue>
#include<cstring>
using namespace std;
typedef __int64 LL;
const int N=220;
const int inf=1<<25;
const int MN=220*220+100;
const int SZ=30;
const int mod=1e9+7;
int ch[MN][SZ];int val[MN];
int sz,tot;
void init(){tot=1;sz=26;memset(ch[0],0,sizeof(ch[0]));val[0]=0;}
void Ins(int ss[],int n,int v){
    int u=0;
    for(int i=0;i<n;i++){
        int c=ss[i];
        if(!ch[u][c]){
            memset(ch[tot],0,sizeof(ch[tot]));val[tot]=0;
            ch[u][c]=tot++;
        }
        u=ch[u][c];
        //printf("%d ",u);
    }//printf("\n");
    val[u]+=v;
}
int f[MN],last[MN];
int getFail(){
    queue<int> qq;
    f[0]=0;last[0]=0;
    for(int c=0;c<sz;c++){
        int u=ch[0][c];
        if(u){f[u]=0;last[u]=0;qq.push(u);}
    }
    while(!qq.empty()){
        int r=qq.front();qq.pop();
        for(int c=0;c<sz;c++){
            int u=ch[r][c];
            if(!u){
                ch[r][c]=ch[f[r]][c];continue;
            }
            qq.push(u);
            f[u]=ch[f[r]][c];
            last[u]=val[f[u]]?f[u]:last[f[u]];
            val[u]+=val[f[u]];
        }
    }
}

int l,ll[N],r,rr[N];int n,m,k;
LL dp[210][420][520];
int a,aa[N],v;
LL dfs(int h,int s,int now,bool flag, bool zero){
    now -= val[s];
    if(now < 0) return 0;
    if(h==r) {
        //cout << sum << " " << now << endl;
        return 1;
    }
    if(!flag && !zero && dp[h][s][now] != -1) return dp[h][s][now];

    LL res = 0;
    if(zero){
        res += dfs(h+1,s,now,flag && rr[h]==0,true);
        res %= mod;
    }else{
        res += dfs(h+1,ch[s][0],now,flag && rr[h]==0,false);
        res %= mod;
    }

    int up = flag?rr[h]:m-1;
    for(int i=1;i<=up;i++){
        res += dfs(h+1,ch[s][i],now,flag && i==up,false);
        res %= mod;
    }

    if(!flag && !zero) dp[h][s][now] = res;
    return res;
}
int main(){
    #ifdef DouBi
    freopen("in.cpp","r",stdin);
    #endif // DouBi
    while(scanf("%d%d%d",&n,&m,&k)!=EOF){
        scanf("%d",&l);for(int i=0;i<l;i++)scanf("%d",&ll[i]);
        scanf("%d",&r);for(int i=0;i<r;i++)scanf("%d",&rr[i]);
        for(int i=1;i<=l;i++){
            ll[r-i]=ll[l-i];
        }
        for(int i=0;i<r-l;i++)ll[i]=0;
        for(int i=r-1;i>=0;i--){
            if(ll[i]){
                ll[i]--;
                for(int j=i+1;j<r;j++){
                    ll[j]=m-1;
                }
                break;
            }
        }
        init();
        for(int i=0;i<n;i++){
            scanf("%d",&a);
            for(int j=0;j<a;j++){
                scanf("%d",&aa[j]);
            }
            scanf("%d",&v);
            Ins(aa,a,v);
        }
        getFail();
        LL ans=0;
        memset(dp,-1,sizeof(dp));
        ans=dfs(0,0,k,1,1);
        //printf("%I64d ",ans);
        for(int i=0;i<r;i++){
            rr[i]=ll[i];
        }
        memset(dp,-1,sizeof(dp));
        ans-=dfs(0,0,k,1,1);
        printf("%I64d\n",(ans%mod+mod)%mod);
    }
    return 0;
}
### Codeforces 887E Problem Solution and Discussion The problem **887E - The Great Game** on Codeforces involves a strategic game between two players who take turns to perform operations under specific rules. To tackle this challenge effectively, understanding both dynamic programming (DP) techniques and bitwise manipulation is crucial. #### Dynamic Programming Approach One effective method to approach this problem utilizes DP with memoization. By defining `dp[i][j]` as the optimal result when starting from state `(i,j)` where `i` represents current position and `j` indicates some status flag related to previous moves: ```cpp #include <bits/stdc++.h> using namespace std; const int MAXN = ...; // Define based on constraints int dp[MAXN][2]; // Function to calculate minimum steps using top-down DP int minSteps(int pos, bool prevMoveType) { if (pos >= N) return 0; if (dp[pos][prevMoveType] != -1) return dp[pos][prevMoveType]; int res = INT_MAX; // Try all possible next positions and update 'res' for (...) { /* Logic here */ } dp[pos][prevMoveType] = res; return res; } ``` This code snippet outlines how one might structure a solution involving recursive calls combined with caching results through an array named `dp`. #### Bitwise Operations Insight Another critical aspect lies within efficiently handling large integers via bitwise operators instead of arithmetic ones whenever applicable. This optimization can significantly reduce computation time especially given tight limits often found in competitive coding challenges like those hosted by platforms such as Codeforces[^1]. For detailed discussions about similar problems or more insights into solving strategies specifically tailored towards contest preparation, visiting forums dedicated to algorithmic contests would be beneficial. Websites associated directly with Codeforces offer rich resources including editorials written after each round which provide comprehensive explanations alongside alternative approaches taken by successful contestants during live events. --related questions-- 1. What are common pitfalls encountered while implementing dynamic programming solutions? 2. How does bit manipulation improve performance in algorithms dealing with integer values? 3. Can you recommend any online communities focused on discussing competitive programming tactics? 4. Are there particular patterns that frequently appear across different levels of difficulty within Codeforces contests?
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