Submission #1035406

#	Time	Username	Problem	Language	Result	Execution time	Memory
1035406		CSQ31	Board Game (JOI24_boardgame)	C++17	100 / 100	1743 ms	85900 KiB

Main

#pragma GCC optimize("Ofast") 
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
const int MAXN = 5e4+50;
vector<int>adj[MAXN];
ll ans[MAXN];
ll dp[200][MAXN];
int main()
{
    int n,m,k;
    cin>>n>>m>>k;
    for(int i=0;i<n;i++)ans[i] = 1e18;
    for(int i=0;i<m;i++){
        int u,v;
        cin>>u>>v;
        u--;
        v--;
        adj[u].pb(v);
        adj[v].pb(u);
    }

    string s;
    cin>>s;
    vector<int>T(k);
    for(int i=0;i<k;i++){cin>>T[i];T[i]--;}
    vector<ll>rdist(n,1e9),bdist(n,1e9),ndist(n,1e9),ones;
    deque<int>q;
    if(true){
        queue<int>q;
        q.push(T[0]);
        vector<ll>d(n,n);
        d[T[0]] = 0;
        while(!q.empty()){
            int v = q.front();
            q.pop();
            ndist[v] = ans[v] = d[v];
            if(v != T[0] && s[v] == '1'){
                ones.pb(v);
                continue;
            }
            for(int x:adj[v]){
                if(d[x] > d[v]+1){
                    d[x] = d[v]+1;
                    q.push(x);
                }
            }
        }
    } 
    for(int i=0;i<n;i++){
        if(s[i] == '0')continue;
        int cnt = 0;
        for(int x:adj[i])cnt += s[x]=='1';
        if(cnt){
            rdist[i] = 0;
            q.pb(i);
        }
    }
    while(!q.empty()){
        int v = q.front();
        q.pop_front();
        for(int x:adj[v]){
            if(rdist[x] == 1e9){
                if(s[x] == '1'){
                    rdist[x] = rdist[v];
                    q.push_front(x);
                }else{
                    rdist[x] = rdist[v]+1;
                    q.push_back(x);
                }
            }
        }
    } //min dist to a red node
    for(int i=0;i<n;i++){if(s[i] == '1')rdist[i]++;}
    for(int i=0;i<n;i++){
        if(s[i] == '1'){
            for(int x:adj[i]){
                if(bdist[x] > 1){
                    bdist[x] = 1;
                    q.pb(x);
                }
            }
        }
    }
    while(!q.empty()){
        int v = q.front();
        q.pop_front();
        for(int x:adj[v]){
            if(bdist[x] == 1e9){
                bdist[x] = bdist[v]+1;
                q.push_back(x);
            }
        }
    } //min dist to a black node

   // for(int i=0;i<n;i++)cout<<bdist[i]<<" "<<rdist[i]<<'\n';
    if(k-1 <= 300){ //half of the sqrt sol
        ll sum = 0;
        vector<ll>f;
        for(int i=1;i<k;i++){
            sum += bdist[T[i]];
            f.pb(rdist[T[i]] - bdist[T[i]]);
        }
        sort(all(f));
        for(int i=0;i<k;i++){
            ll c = 2*(k-1) - i;
            vector<ll>dist(n,1e18);
            priority_queue<PII,vector<PII>,greater<PII>>pq;
            for(int v:ones){ 
                for(int x:adj[v]){
                    ll cost = ndist[v] + sum + 1;
                    if(s[x] == '1')cost += c;
                    if(dist[x] > cost){
                        dist[x] = cost;
                        pq.push({dist[x],x});
                    }
                }
            }
    
            while(!pq.empty()){
                int v = pq.top().se;
                ll d = pq.top().fi;
                pq.pop();
                if(d != dist[v])continue;
                //cout<<v<<" "<<d<<'\n';
                for(int x:adj[v]){
                    if(s[x] == '0'&& dist[x] > d+1){
                        dist[x] = d+1;
                        pq.push({dist[x],x});
                    }
                    if(s[x] == '1' && dist[x] > d+c+1){
                        dist[x] = d+c+1;
                        pq.push({dist[x],x});
                    }
                }
            }
            for(int j=0;j<n;j++){
                //cout<<dist[j]<<" ";
                if(s[j] == '1')ans[j] = min(ans[j],dist[j]-c);
                else ans[j] = min(ans[j],dist[j]);
            }
            if(i!=k-1)sum+=f[i];
        }
        for(int i=0;i<n;i++)cout<<ans[i]<<'\n';
        return 0;
    }
    vector<int>stops(n,1e9);
    stops[T[0]] = 0;
    q.pb(T[0]);
    while(!q.empty()){
        int v = q.front();
        q.pop_front();
        for(int x:adj[v]){
            if(s[x] == '0' && stops[x] > stops[v]){
                stops[x] = stops[v];
                q.push_front(x);
            }
            if(s[x] == '1' && stops[x] > stops[v]+1){
                stops[x] = stops[v]+1;
                q.pb(x);
            }
        }
    }
    for(int i=0;i<200;i++){
        for(int j=0;j<n;j++)dp[i][j] = 1e18;
    }
    dp[0][T[0]] = 0;
    queue<array<int,3>>qq;
    qq.push({0,0,T[0]});
    while(!qq.empty()){
        int v = qq.front()[2];
        int len = qq.front()[1];
        int num = qq.front()[0];
        qq.pop();
        //cout<<v<<" "<<len<<" "<<num-stops[v]<<" "<<dp[num-stops[v]][v]<<'\n';
        for(int x:adj[v]){
            if(s[x] == '0'){
                int d = num - stops[x];
                if(d < 200 && dp[d][x] > len + 1){
                    dp[d][x] = len + 1;
                    qq.push({num,len+1,x});
                }
            }else{
                int d = num+1 - stops[x];
                if(d < 200 && dp[d][x] > len + 1){
                    dp[d][x] = len + 1;
                    qq.push({num+1,len+1,x});
                }
            }
        }
    }
    vector<ll>cost(n+2,0),inc(n+2,0);
    for(int i=1;i<k;i++){
        int v = T[i];
        ll a = bdist[v];
        ll b = rdist[v];
        cost[1] += min(a,b);
        //a + 2*(x-1) > b + (x-1)
        //x >= b-a+1
        //x = b-a+1
        ll diff = b-a+1;
        //cout<<v<<" "<<a<<" "<<b<<" "<<diff<<'\n';
        if(diff >= 2){
            inc[2] += 2;
            if(diff <= n){
                inc[diff] -= 2;
                cost[diff] -= 2*(diff-2);
                cost[diff] -= min(a,b);

                cost[diff] += b + (diff-1);
                inc[diff+1] ++;
                
            }
        }else inc[2]++;
    }

    for(int i=1;i<=n;i++)inc[i] += inc[i-1];
    for(int i=1;i<=n;i++)cost[i] += cost[i-1] + inc[i];

    //for(int i=0;i<=n;i++)cout<<cost[i]<<" ";
   // cout<<'\n';
    for(int i=0;i<n;i++){
        if(i==T[0])continue;
        ans[i] = 1e18;
        for(int j=0;j<200;j++){
            int len = j + stops[i];
            if(s[i] == '1')len--;
            if(len > n)continue;
            //cout<<i<<" "<<len<<" "<<dp[j][i]<<" "<<cost[len]<<'\n';
            ans[i] = min(ans[i],dp[j][i] + cost[len]);
        }
    }

    for(int i=0;i<n;i++)cout<<ans[i]<<'\n';
}

• Subtask 1: 3 / 3
• Subtask 2: 7 / 7
• Subtask 3: 7 / 7
• Subtask 4: 19 / 19
• Subtask 5: 23 / 23
• Subtask 6: 9 / 9
• Subtask 7: 23 / 23
• Subtask 8: 9 / 9