题解

k_helen_now_go · 2023-01-08 13:22:56 · 题解

没什么好讲的，直接上代码：

#include <bits/stdc++.h>

using pii = std::pair<int,int>;
const int inf = 1e7;

int dx[] = {0,1,0,-1};
int dy[] = {1,0,-1,0};

int n,m,dis[12][12],ban[12][12];

std::map< std::vector<int> , int >dp[12][12];   

std::vector<int> process(std::vector<int>S) {
    int cnt = 1;
    int vis[30] = {0};
    for (int i = 1; i <= n + 1; ++ i) {
        if (S[i] == 0 || S[i] == 1) continue;
        if (!vis[S[i]]) { vis[S[i]] = ++cnt; S[i] = cnt; }
        else S[i] = vis[S[i]];
    } return S;
}
std::vector<int> shift(std::vector<int>S){ for (int i = 1; i <= n; ++ i) S[i] = S[i+1]; S[n+1] = 0; return S; }
std::vector<int> trans(std::vector<int>S,int i) { std::swap(S[i],S[i+1]); return S; }
std::vector<int> create(std::vector<int>S,int i) { S[i] = S[i+1] = 20; return process(S); }
std::vector<int> merge(std::vector<int>S,int i) {
    int p = S[i], q = S[i+1], flag = 20;
    if (p == 1 || q == 1) flag = 1;
    for (int i = 1; i <= n + 1; ++ i) if (S[i] == p || S[i] == q) S[i] = flag;
    S[i] = S[i+1] = 0;
    return process(S);
}

int main() {

    scanf("%d%d",&n,&m);
    for (int i = 1; i <= m; ++ i) {
        int x,y;
        scanf("%d%d",&x,&y);
        ban[x][y] = 1;
        assert( not ( (x == 1 && y == n)  or (x == n && y == 1) ) );
    }

    auto bfs = [&]() {
        std::memset(dis,-1,sizeof(dis));
        std::queue< pii >q;
        q.push( { 1,n } );
        dis[1][n] = 0;
        while (q.size()) {
            auto u = q.front(); q.pop();
            int x = u.first, y = u.second;
            for (int i = 0; i < 4; ++ i) {
                int x1 = x + dx[i], y1 = y + dy[i];
                if (x1 < 1 || x1 > n || y1 < 1 || y1 > n || dis[x1][y1] != -1 || ban[x1][y1]) continue;
                dis[x1][y1] = dis[x][y] + 1;
                q.push( { x1,y1 } );
            }
        } 
    };  bfs();

    std::vector<int>v(n+2);
    v[n+1] = 1; dp[1][n-1][v] = 1;
    v[n+1] = 0; v[n] = 1; dp[1][n-1][v] = 1;

    for (int i = 1; i <= n; ++ i) {
        for (int j = n - (i == 1); j >= 1; j --) {
            for (auto P:dp[i][j]) {
                auto S = P.first; int v = P.second;
                int p = S[j], q = S[j+1];
                if (p == 0 && q == 0) dp[i][j-1][S] = std::max(dp[i][j-1][S],v);
                if (ban[i][j]) continue;
                if (p == 0 && q == 0) {
                    auto T = create(S,j);
                    dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
                }
                if ((p != 0) + (q != 0) == 1) {
                    dp[i][j-1][S] = std::max(dp[i][j-1][S],v + 1);
                    auto T = trans(S,j);
                    dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
                }
                if (p && q && p != q) {
                    auto T = merge(S,j);
                    dp[i][j-1][T] = std::max(dp[i][j-1][T],v + 1);
                }
            }
        } for (auto P:dp[i][0]) {
            auto S = P.first; int v = P.second;
            if (S[1] == 0) dp[i+1][n][shift(S)] = dp[i][0][S];
        }
    }
    std::vector<int>S1(n+2),S2(n+2);
    S1[1] = 1; S2[2] = 1;
    printf("%d",std::max(dp[n][1][S1],dp[n][1][S2]) - dis[n][1]);
    return 0;
}