国庆 day 7 上午

思路：模拟，set记录一下。

#include<set>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
set<int>se;
int n,k,x,ans;
int main(){
    freopen("del.in","r",stdin);
    freopen("del.out","w",stdout);
    scanf("%d%d",&n,&k);
    for(int i=;i<=n;i++){
        scanf("%d",&x);
        if(se.find(x)!=se.end())    k--;
        else{
            se.insert(x);
            ans++;
        }
    }
    if(k<=)    cout<<ans<<endl;
    else cout<<ans-k<<endl;
}

思路：搜索

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
#include <cstdlib>
using namespace std;

int board[][], isKing[][];
int dir[][] = {{, }, {, -}, {-, }, {-, -}};
int best_deep;
vector<int> w;
vector<int> ways;

void dfs(int step, int x, int y, int isKing)
{
    w.push_back(x *  + y);
    if (step > best_deep)
    {
        best_deep = step;
        ways.clear();
        ways.push_back(w[]);
    }
    else if (step >  && step == best_deep)
    {
        ways.push_back(w[]);
    }

    int dis_limit = isKing ?  : ;

    for (int d = ; d < ; d++)
    {
        bool pass = false;
        int passx = , passy = ;
        for (int dis = ; dis <= dis_limit; dis++)
        {
            int nxtX = x + dis * dir[d][];
            int nxtY = y + dis * dir[d][];
            if (!( <= nxtX && nxtX <  &&  <= nxtY && nxtY < ))
                break;
            if (board[nxtX][nxtY] ==  || board[nxtX][nxtY] == )
                break;
            if (pass && board[nxtX][nxtY] == )
                break;
            if (board[nxtX][nxtY] == )
            {
                pass = true;
                passx = nxtX;
                passy = nxtY;
            }
            else
            {
                if (!pass)
                    continue;
                board[passx][passy] = ;
                dfs(step + , nxtX, nxtY, isKing);
                board[passx][passy] = ;
            }
        }
    }
    w.pop_back();
}

bool getAvailable()
{
    ways.clear();
    w.clear();
    best_deep = ;
    for (int curX = ; curX < ; curX++)
        for (int curY = ; curY < ; curY++)
            if (board[curX][curY] == )
                dfs(, curX, curY, isKing[curX][curY]);
    if (best_deep == )
    {
        for (int curX = ; curX < ; curX++)
            for (int curY = ; curY < ; curY++)
                if (board[curX][curY] == )
                {
                    if (isKing[curX][curY])
                    {
                        for (int x = curX + , y = curY + ;  <= x && x <  &&  <= y && y < ; x++, y++)
                            if (!board[x][y])
                                ways.push_back(curX *  + curY);
                            else
                                break;
                        for (int x = curX + , y = curY - ;  <= x && x <  &&  <= y && y < ; x++, y--)
                            if (!board[x][y])
                                ways.push_back(curX *  + curY);
                            else
                                break;
                        for (int x = curX - , y = curY + ;  <= x && x <  &&  <= y && y < ; x--, y++)
                            if (!board[x][y])
                                ways.push_back(curX *  + curY);
                            else
                                break;
                        for (int x = curX - , y = curY - ;  <= x && x <  &&  <= y && y < ; x--, y--)
                            if (!board[x][y])
                                ways.push_back(curX *  + curY);
                            else
                                break;
                    }
                    else
                    {
                        if (curX -  >=  && curY -  >=  && !board[curX - ][curY - ])
                            ways.push_back(curX *  + curY);
                        if (curX -  >=  && curY +  <  && !board[curX - ][curY + ])
                            ways.push_back(curX *  + curY);
                    }
                }
    }
    if (!ways.size())
        return false;
    return true;
}

int main(){
    freopen("chess.in", "r", stdin);
    freopen("chess.out", "w", stdout);
    memset(board, , sizeof(board));
    memset(isKing, , sizeof(isKing));
    for (int i = ; i < ; i++)
        for (int j = ; j < ; j++)
        {
            char c;
            scanf(" %c", &c);
            board[i][j] = c - '';
        }
    for (int i = ; i < ; i++)
        for (int j = ; j < ; j++)
        {
            char c;
            scanf(" %c", &c);
            isKing[i][j] = c - '';
        }
    getAvailable();
    if (!ways.size())
        printf("0\n");
    else {
        sort(ways.begin(), ways.end());
        printf("%d\n", (int)ways.size());
        for (int i = ; i < (int)ways.size(); i++)
            printf("(%d,%d)\n", ways[i] /  + , ways[i] %  + );
    }
}

思路：状压DP.

对后续决策有影响的是什么？

现在已经吃了哪些馅饼

令F[i][s]表示考虑前i次馅饼掉落事件，吃了s这个二进制状态表示的馅饼，期望的美味值

对于每一次掉馅饼，枚举掉下来的馅饼是谁

若s&a[j]==a[j]（a[j]为前提馅饼集合） F[i][s] -> F[i+1][s|(1<<(j-1))] 注意要 /n

递推的顺序？

一个起始状态，多个目标状态，正推会导致无效状态

反着推

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int n,k,x,y;
int w[],f[];
double dp[][];
int main(){
    freopen("bonus.in","r",stdin);
    freopen("bonus.out","w",stdout);
    scanf("%d%d",&n,&k);
    for(int i=;i<n;i++){
        scanf("%d",&w[i]);
        while(scanf("%d",&x)&&x) f[i]|=<<x-;
    }
    for(int s=;s<(<<n);s++) dp[k][s]=;
    for(int i=k-;i>=;i--)
        for(int s=;s<(<<n);s++)
            for(int j=;j<n;j++)
                if((s&f[j])==f[j]) dp[i][s]+=1.0/n*max(dp[i+][s],dp[i+][s|(<<j)]+w[j]);
                else dp[i][s]+=1.0/n*dp[i+][s];
    printf("%.6f\n",dp[][]);
}