LuoGuP4294:[WC2008]游览计划

Posted 2022-07-20 chitongz

Pre

作为斯坦纳树的第一道题

Solution

以每一个格子建立点，然后直接跑斯坦纳树就可以了。

code

#include <cstdio>
#include <bitset>
#include <iostream>
#include <queue>
#include <limits.h>
#include <cstring>
#define ll long long
#define xx first
#define yy second
#define testname kkksc03
using namespace std;
const int N = 100 + 5, M = 10 + 5, mx = 2139062143, NN = 2800;
struct _in 
    const _in operator , (int &a) const 
        a = 0;
        char k = getchar ();
        int f = 1;
        while (k > '9' || k < '0') 
            if (k == '-') f = -1;
            k = getchar ();
        
        while (k >= '0' && k <= '9') 
            a = a * 10 + k - '0';
            k = getchar ();
        
        a *= f;
        return*this;
    
;
inline int add (int u, int v) 
    if (u == mx || v == mx) return mx;
    else return u + v;

inline int mns (int u, int v) 
    return u == mx ? mx : u - v;

inline int min (int u, int v) 
    return u > v ? v : u;

inline int max (int u, int v) 
    return u > v ? u : v;

int dp[N][NN], n, m, mp[M][M];
inline int get (int x, int y) 
    return (x - 1) * m + y;

inline int GetLne (int x) 
    return (x - 1) / m + 1;

inline int GetCol (int x) 
    return (x - 1) % m + 1;

int anspos;
queue<int> q;
bool inq[N];
pair<int, int> s[N][NN];
inline void update (int u, int v, int w) 
    if (dp[v][w] > add (dp[u][w], mp[GetLne (v)][GetCol (v)])) 
        dp[v][w] = add (dp[u][w], mp[GetLne (v)][GetCol (v)]);
        s[v][w] = make_pair (u, w);
        if (!inq[v]) 
            inq[v] = 1;
            q.push (v);
        
    

inline void SPFA (int st) 
    while (!q.empty ()) 
        int tmp = q.front ();
        q.pop ();
        inq[tmp] = 0;
        int x = GetLne (tmp), y = GetCol (tmp);
        if (x != 1) update (tmp, tmp - m, st);
        if (x != n) update (tmp, tmp + m, st);
        if (y != 1) update (tmp, tmp - 1, st);
        if (y != m) update (tmp, tmp + 1, st);
    

int k;
int op[M][M];
inline void dfs (int u, int v) 
//  printf ("%d ", u);
//  cout << bitset <8> (v) << " ";
//  printf ("%d ",s[u][v].xx);
//  cout << bitset <8> (s[u][v].yy) << endl;
    if (s[u][v].xx == -1) 
        int x = GetLne (u), y = GetCol (u);
        if (!mp[x][y]) op[x][y] = 'x';
        else op[x][y] = 'o';
        return ;
    
    int x = GetLne (u), y = GetCol (u);
    op[x][y] = mp[x][y] ? 'o' : 'x';
    x = s[u][v].xx, y = s[u][v].yy;
    dfs (x, y);
    if (x == u) dfs (u, y ^ v);

int main () 
//  #ifdef chitongz
//  freopen ("x.in", "r", stdin);
//  freopen ("x.out", "w", stdout);
//  #endif
    memset (dp, 127, sizeof dp);
    memset (s, -1, sizeof s);
    scanf ("%d%d", &n, &m);
    for (int i = 1; i <= n; ++i) 
        for (int j = 1; j <= m; ++j) 
            op[i][j] = '_';
            scanf ("%d", &mp[i][j]);
            if (!mp[i][j]) 
                anspos = get (i, j);
                ++k;
                dp[get (i, j)][1 << (k - 1)] = 0;
            
        
    
    int ans = INT_MAX;
    for (int j = 1; j <= (1 << k) - 1; ++j) 
        for (int i = 1; i <= n * m; ++i) 
            for (int tmp = j; tmp; tmp = (tmp - 1) & j) 
                if (dp[i][j] > mns (add (dp[i][tmp], dp[i][tmp ^ j]), mp[GetLne (i)][GetCol (i)])) 
                    dp[i][j] = mns (add (dp[i][tmp], dp[i][tmp ^ j]), mp[GetLne (i)][GetCol (i)]);
                    s[i][j] = make_pair (i, tmp);
                
                if (dp[i][j] != dp[0][0]) 
                    q.push (i);
                    inq[i] = 1;
                
            
        
        SPFA (j);
    
    for (int i = 1; i <= n * m; ++i) 
        if (dp[i][(1 << k) - 1] < ans) 
            ans = dp[i][(1 << k) - 1];
            anspos = i;
        
    
    printf ("%d\n", ans);
    dfs (anspos, (1 << k) - 1);
    for (int i = 1; i <= n; ++i) 
        for (int j = 1; j <= m; ++j) 
            printf ("%c", op[i][j]);
        
        puts ("");
    
    return 0;

Conclusion

空间开小查错查了半天没有查出来，交上去发现 \(M\) 一般应该是 \(10 + 5\) ，我写的 \(M=10\)