noip模拟赛 蒜头君救人

分析：之前的一道模拟赛题是dp+dfs,这道题是dp+bfs.

我们设f[stu][i][j]为当前状态为stu,走到(i,j)的答案，考虑怎么设计stu,每个人的状态有3种：要么在原地，要么被背着，要么已经到了终点，那么用一个3进制数保存就可以了.

下面考虑怎么转移，直接递推肯定是不对的，dfs也不行，只能bfs了.我们每次可以选择不走，或者如果当前点有人就背起来，或者到了终点就放下所有人或者放下所有使速度变慢的人，写好几次转移就过了.

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;
const int inf = 0x7ffffff;

int n, m, k, top, sx, sy, tx, ty, a[][], speed[], f[][][], dx[] = { , -, ,  }, dy[] = { , , , - },flag[];
char name[][],s[][];

struct node
{
    int x, y, zhuangtai;
};

int jisuan(int stu)
{
    int tot = ,sped = k;
    memset(flag, , sizeof(flag));
    while (stu)
    {
        tot++;
        flag[tot] = stu % ;
        stu /= ;
    }
    for (int i = ; i <= top; i++)
        if (flag[i] == )
            sped += speed[i];
    if (sped < )
        sped = ;
    return sped;
}

bool judge(int x, int y)
{
    if (x >=  && x <= n && y >=  && y <= m)
        return true;
    return false;
}

int bei(int stu, int x, int y)
{
    int cur, tot = ;
    for (int i = ; i <= top; i++)
        if (s[x][y] == name[i][])
        {
            cur = i;
            break;
        }
    memset(flag, , sizeof(flag));
    while (stu)
    {
        tot++;
        flag[tot] = stu % ;
        stu /= ;
    }
    if (flag[cur])
        return ;
    flag[cur] = ;
    for (int i = top; i >= ; i--)
        stu = stu *  + flag[i];
    return stu;
}

int fang1(int stu, int x, int y)
{
    memset(flag, , sizeof(flag));
    int tot = ;
    while (stu)
    {
        tot++;
        flag[tot] = stu % ;
        stu /= ;
    }
    for (int i = ; i <= top; i++)
        if (flag[i] == )
            flag[i] = ;
    for (int i = top; i >= ; i--)
        stu = stu *  + flag[i];
    return stu;
}

int fang2(int stu, int x, int y)
{
    int tot = ;
    memset(flag, , sizeof(flag));
    while (stu)
    {
        tot++;
        flag[tot] = stu % ;
        stu /= ;
    }
    for (int i = ; i <= top; i++)
        if (flag[i] ==  && speed[i] > )
            flag[i] = ;
    for (int i = top; i >= ; i--)
        stu = stu *  + flag[i];
    return stu;
}

int qpow(int a, int b)
{
    int res = ;
    while (b)
    {
        if (b & )
            res *= a;
        a *= a;
        b >>= ;
    }
    return res;
}

void bfs()
{
    queue <node> q;
    node temp;
    temp.x = sx;
    temp.y = sy;
    temp.zhuangtai = ;
    q.push(temp);
    while (!q.empty())
    {
        node u = q.front();
        q.pop();
        int sudu = jisuan(u.zhuangtai),x = u.x,y = u.y;
        //printf("%d %d %d\n", sudu, x, y);
        for (int i = ; i < ; i++)
        {
            int nx = x + dx[i], ny = y + dy[i];
            if (judge(nx, ny))
            {
                //只移动
                if (s[nx][ny] != '#' && f[u.zhuangtai][nx][ny] > f[u.zhuangtai][x][y] + sudu)
                {
                    f[u.zhuangtai][nx][ny] = f[u.zhuangtai][x][y] + sudu;
                    node temp;
                    temp.x = nx;
                    temp.y = ny;
                    temp.zhuangtai = u.zhuangtai;
                    q.push(temp);
                }
                //背人
                if (s[nx][ny] >= 'A' && s[nx][ny] <= 'Z')
                {
                    int stu = bei(u.zhuangtai, nx, ny);
                    if (f[stu][nx][ny] > f[u.zhuangtai][x][y] + sudu)
                    {
                        f[stu][nx][ny] = f[u.zhuangtai][x][y] + sudu;
                        node temp;
                        temp.zhuangtai = stu;
                        temp.x = nx;
                        temp.y = ny;
                        q.push(temp);
                    }
                }
                //放人
                if (s[nx][ny] == 't')
                {
                    int stu1 = fang1(u.zhuangtai, nx, ny);
                    int stu2 = fang2(u.zhuangtai, nx, ny);
                    if (f[stu1][nx][ny] > f[u.zhuangtai][x][y] + sudu)
                    {
                        f[stu1][nx][ny] = f[u.zhuangtai][x][y] + sudu;
                        node temp;
                        temp.zhuangtai = stu1;
                        temp.x = nx;
                        temp.y = ny;
                        q.push(temp);
                    }
                    if (f[stu2][nx][ny] > f[u.zhuangtai][x][y] + sudu)
                    {
                        f[stu2][nx][ny] = f[u.zhuangtai][x][y] + sudu;
                        node temp;
                        temp.zhuangtai = stu2;
                        temp.x = nx;
                        temp.y = ny;
                        q.push(temp);
                    }
                }
            }
        }
    }
}

int main()
{
    scanf("%d%d%d", &n, &m, &k);
    for (int i = ; i <= n; i++)
    {
        scanf("%s", s[i] + );
        for (int j = ; j <= m; j++)
        {
            if (s[i][j] == 's')
            {
                sx = i;
                sy = j;
            }
            else
            {
                if (s[i][j] == 't')
                {
                    tx = i;
                    ty = j;
                }
                else
                {
                    if (s[i][j] >= 'A' && s[i][j] <= 'Z')
                        top++;
                }
            }
        }
    }
    for (int i = ; i <= top; i++)
        scanf("%s%d", name[i], &speed[i]);
    for (int i = ; i <= ; i++)
        for (int j = ; j <= ; j++)
            for (int l = ; l <= ; l++)
                f[i][j][l] = inf;
    f[][sx][sy] = ;
    bfs();
    printf("%d\n", f[qpow(, top) - ][tx][ty]);

    return ;
}