Submission #957119

#	Time	Username	Problem	Language	Result	Execution time	Memory
957119		GrindMachine	Cop and Robber (BOI14_coprobber)	C++17	100 / 100	354 ms	13848 KiB

coprobber

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a, b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a, b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

refs:
edi

key idea:
look at the game on a game state graph
n*n*2 nodes (cop,robber,turn)
dp[cop][robber][turn] = 1 if it's winning for the curr player, 0 if it's losing for the curr player, -1 if the game is never ending for the curr player

initially, all values = -1
we know that dp[i][i][0] = 1, dp[i][i][1] = 0

dp[i][j][k] is winning if it has an edge to at least 1 losing state
dp[i][j][k] is losing if all its outgoing edges are to winning states
also store par[i][j][k] = next node to choose in the winning strategy

run multiple iterations until no dp value changes and then stop

to optimize, run a bfs from the known values (dp[i][i][k])
and push neighboring states into the queue when their values are decided

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

#include "coprobber.h"

int n;
int dp[MAX_N][MAX_N][2];
bool a[MAX_N][MAX_N];
vector<int> adj[MAX_N];
int pos;
int par[MAX_N][MAX_N][2];

int start(int n_, bool a_[MAX_N][MAX_N])
{
    n = n_;
    rep(i,MAX_N){
        adj[i].clear();
    }

    rep(i,MAX_N){
        rep(j,MAX_N){
            a[i][j] = a_[i][j];
            if(a[i][j]){
                adj[i].pb(j);
            }
        }
    }

    memset(dp,-1,sizeof dp);
    memset(par,-1,sizeof par);
    queue<array<int,3>> q;

    rep(i,n){
        dp[i][i][0] = 1;
        dp[i][i][1] = 0;
        q.push({i,i,0});
        q.push({i,i,1});
    }

    int win_cnt[n][n][2], lose_cnt[n][n][2];
    memset(win_cnt,0,sizeof win_cnt);
    memset(lose_cnt,0,sizeof lose_cnt);

    rep(i,n){
        rep(j,n){
            if(i == j) conts;
            rep(k,2){
                if(k == 0){
                    win_cnt[i][j][k] = sz(adj[i])+1;
                }
                else{
                    lose_cnt[i][j][k] = sz(adj[j]);
                }
            }
        }
    }

    while(!q.empty()){
        auto [i,j,k] = q.front();
        q.pop();

        if(k == 0){
            // police wins, sub 1 from lose_cnt[i][v][k^1]
            if(dp[i][j][k]){
                trav(v,adj[j]){
                    if(dp[i][v][k^1] == -1){
                        lose_cnt[i][v][k^1]--;
                        if(!lose_cnt[i][v][k^1]){
                            q.push({i,v,k^1});
                            dp[i][v][k^1] = 0;
                        }   
                    }
                }
            }
            // police loses, add unvis adj robber states
            else{
                trav(v,adj[j]){
                    if(dp[i][v][k^1] == -1){
                        q.push({i,v,k^1});
                        dp[i][v][k^1] = 1;
                        par[i][v][k^1] = j;
                    }
                }
            }
        }
        else{
            // robber loses, add unvis adj police states
            if(!dp[i][j][k]){
                trav(v,adj[i]){
                    if(dp[v][j][k^1] == -1){
                        q.push({v,j,k^1});
                        dp[v][j][k^1] = 1;
                        par[v][j][k^1] = i;
                    }
                }

                {
                    int v = i;
                    if(dp[v][j][k^1] == -1){
                        q.push({v,j,k^1});
                        dp[v][j][k^1] = 1;
                        par[v][j][k^1] = i;
                    }
                }
            }
            // robber wins, sub 1 from win_cnt[v][j][k^1]
            else{
                trav(v,adj[i]){
                    if(dp[v][j][k^1] == -1){
                        win_cnt[v][j][k^1]--;
                        if(!win_cnt[v][j][k^1]){
                            q.push({v,j,k^1});
                            dp[v][j][k^1] = 0;
                        }   
                    }
                }

                {
                    int v = i;
                    if(dp[v][j][k^1] == -1){
                        win_cnt[v][j][k^1]--;
                        if(!win_cnt[v][j][k^1]){
                            q.push({v,j,k^1});
                            dp[v][j][k^1] = 0;
                        }   
                    }
                }
            }
        }
    }

    // rep(i,n){
    //     rep(j,n){
    //         cout << dp[i][j][0] << " " << dp[i][j][1] << endl;
    //     }
    //     cout << endl;
    // }

    pos = -1;

    rep(u,n){
        bool ok = true;
        rep(v,n){
            if(dp[u][v][0] != 1){
                ok = false;
            }
        }

        if(ok){
            pos = u;
        }
    }

    return pos;
}

int nextMove(int v)
{
    pos = par[pos][v][0];
    return pos;
}

• Subtask 1: 16 / 16
• Subtask 2: 14 / 14
• Subtask 3: 30 / 30
• Subtask 4: 40 / 40