2017.10.20 模拟赛

题目链接

T1

考虑遇到一个首位为奇数的233或者或者223

会发生两者之间的相互转变

那么只需要考虑剩余的操作数的奇偶性即可

#include<cstring>
#include<cstdio>
#define N 1000010
int n,k;
char ch[N];

int main()
{
    freopen("trans.in","r",stdin);
    freopen("trans.out","w",stdout);
    while(scanf("%d%d",&n,&k)!=EOF)
    {
        scanf("%s",1+ch);
        int a=1;
        while(k--)
        {
            while((ch[a]!='2'||ch[a+1]!='3')&&a<=n) a++;
            if(a>n) break;
            if(a%2==1)
            {
                if(ch[a+2]=='3') k%=2;
                ch[a+1]='2';
            }
            else
            {
                ch[a]='3';
                a--;
            }
        }
        printf("%s\n",1+ch);
    }
    fclose(stdin); fclose(stdout);
    return 0;
}

 

T2

把豆豆和砖块丢在一起dp
f[i][j][k]:到第i行,蛇的长度还剩下j,从k位置出第i行的最大得分
g[j][l][r]:蛇的长度剩下j,从当前行l到r区间内仍为死亡的最大得分
初始化:对于每个i，g[j][k][k]=f[i-1][j-a[i][k]][k]+max(-a[i][k],0) 为初始状态
方程g[j][l][r] = max(g[j-a[i][l]][l+1][r] + max(-a[i][j],0),g[j-a[i][r]][l][r-1]+max(-a[i][k],0));
最后f[i][j][k] = max{g[j][l][r](1≤l≤k ≤r ≤5)}

#include <cstdlib>
#include <cstdio>
#include <cmath>
#define N 205

bool fw[N][6],vis[N][15][2];
int n,m,ans,fx[5]={0,0,1,-1},fy[5]={1,-1,0,0},a[N][6];
inline int max(int a,int b) {return a>b?a:b;}
void Dfs(int x,int y,int life,int point)
{
    if(x==n+1)
    {
        ans=max(ans,point);
        return ;
    } 
    if(life+a[x][y]<0)
    {
        ans=max(ans,point);
        return;
    }
    fw[x][y]=1;
    for(int i=0;i<4;i++)
    {
        if(fx[i]==1&&vis[x][y][1]==1) continue;
        if(fy[i]==-1&&vis[x][y][0]==1) continue;
        int tx=x+fx[i],ty=y+fy[i];
        if(tx<=n+1&&tx>0&&ty<=5&&ty>0&&fw[tx][ty]==0)
        {
            if(a[x][y]>0) Dfs(tx,ty,life+a[x][y],point);
            else Dfs(tx,ty,life+a[x][y],point-a[x][y]);
        } 
    }
    fw[x][y]=0;
}
int main(int argc,char *argv[])
{
    freopen("snakevsblock.in","r",stdin);
    freopen("snakevsblock.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;++i)
     for(int j=1;j<=5;++j)
      scanf("%d",&a[i][j]);
    scanf("%d",&m);
    for(int x,y,i=1;i<=m;++i)
     scanf("%d%d",&x,&y),vis[x][y][1]=1,vis[x][y+1][0]=1;
    Dfs(1,3,4,0);
    printf("%d\n",ans);
    fclose(stdin); fclose(stdout);
    return 0;
}

#include<iostream>
#include<cstdio>
#include<cstring>

#define N 207
#define M 10005

using namespace std;
int a[N][5],f[N][M][5],g[M][5][5];
bool flag[N][4];
int n,m,maxi,ans,val;

inline int read()
{
    int x=0,f=1;char c=getchar();
    while(c>'9'||c<'0'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int main()
{
    freopen("snakevsblock.in","r",stdin);
    freopen("snakevsblock.out","w",stdout);
    n=read();int x,y;
    for(int i=1;i<=n;i++) for(int j=0;j<5;j++)
      a[i][j]=read();
    m=read();
    for(int i=1;i<=m;i++)
    {
        x=read();y=read();
        flag[x][y-1]=1;
    }
    memset(f,-0x7f7f7f,sizeof f);
    f[0][4][2]=0;maxi=n*50;
    
    for(int i=1;i<=n;i++)
    {
        memset(g,-0x7f7f7f,sizeof g);
        for(int j=0;j<=maxi;j++)
          for(int k=0;k<5;k++)
            if(j-a[i][k]>=0 && j-a[i][k]<=maxi)
              f[i][j][k]=g[j][k][k]=f[i-1][j-a[i][k]][k]+max(-a[i][k],0);

        for(int l=1;l<=4;l++)
          for(int j=0,k=j+l;k<5;j++,k++)
            for(int v=0;v<=maxi;v++)
            {
                if(!flag[i][j]  && (val=v-a[i][j])>=0 && val<=maxi) g[v][j][k] = g[val][j + 1][k] + max(-a[i][j], 0);//g[v][j][k]=max(g[v][j][k],g[val][j+1][k]+max(-a[i][j],0));
                if(!flag[i][k-1]&& (val=v-a[i][k])>=0 && val<=maxi) g[v][j][k]=max(g[v][j][k],g[val][j][k-1]+max(-a[i][k],0));
                for(int to=j;to<=k;to++) f[i][v][to]=max(f[i][v][to],g[v][j][k]);
            }
    }
    
    for(int i=0;i<=n;i++)
      for(int j=0;j<=maxi;j++)
        for(int k=0;k<5;k++)
          ans=max(f[i][j][k],ans);
          
    printf("%d\n",ans);
    return 0;
}

 

T3

任意将一个站点设置为树的根，首先求出DFS序，倒序处理，对于每个站点，如果有以以其LCA的且未被切断的路径，则将这个站点标记为损坏，用树链剖分维护即可

#include <cstdlib>
#include <cstdio>
#include <set>
#define N 100005
using namespace std;

set<int>se;
struct node
{
    int x,y;
}e[N],v[N*3];
bool vis[N];
int n,m,k,limit,which[N],fa[N];
int find_(int x) {return x==fa[x]?x:fa[x]=find_(fa[x]);}
bool judge()
{
    for(int i=1;i<=n;++i) fa[i]=i;
    for(int i=1;i<=m;++i)
    {
        int x=e[i].x,y=e[i].y;
        if(se.find(x)==se.end()||se.find(y)==se.end()) continue; 
        int fx=find_(x),fy=find_(y);
        if(fx!=fy) fa[fy]=fx;
    }
    int sum=0;
    for(int i=1;i<=k;++i)
    {
        int x=v[i].x,y=v[i].y;
        if(x==y) continue; 
        int fx=find_(x),fy=find_(y);
        if(fx!=fy)  sum++;
    }
    if(sum) return true;
}
void Dfs(int goal,int pos)
{
    if(se.size()==goal)
    {
        if(judge())
        {
            printf("%d\n",goal);
            for(set<int> :: iterator it=se.begin();it!=se.end();++it)
            printf("%d ",*it);
            exit(0);
        }
        return ;
    }
    for(int i=pos+1;i<=limit;++i)
    {
        se.insert(which[i]);
        Dfs(goal,i);
        se.erase(which[i]);  
    }
}
int main(int argc,char *argv[])
{
//    freopen("ping.in","r",stdin);
//    freopen("ping.out","w",stdout);
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;++i)
    {
        scanf("%d%d",&e[i].x,&e[i].y);
        int p=e[i].x>e[i].y?e[i].x:e[i].y;
    }
    scanf("%d",&k);
    for(int i=1;i<=k;++i)
    {
        scanf("%d%d",&v[i].x,&v[i].y);
        if(!vis[v[i].x]) vis[v[i].x]=true,which[++limit]=v[i].x;
        if(!vis[v[i].y]) vis[v[i].y]=true,which[++limit]=v[i].y;
    }
    for(int i=1;i<=limit;++i) Dfs(i,0);
    fclose(stdin);
    fclose(stdout);
    return 0;
}

#include <bits/stdc++.h>
using namespace std;
int n, m, P, u, v, to[200005], nxt[200005], p[100005], deep[100005], q[500005][2];
int son[100005], fa[100005], size[100005], top[100005], dfsx[100005], cnt, ans;
int lca[500005], Q[500005], lr[100005][2];
int sta[100005];
bool flag[400005];
void dfs(int x)
{
    size[x] = 1;
    for (int i = p[x]; i != -1; i = nxt[i])
        if (to[i] != fa[x])
        {
            fa[to[i]] = x;
            deep[to[i]] = deep[x] + 1;
            dfs(to[i]);
            if (son[x] == -1 || size[to[i]] > size[son[x]]) son[x] = to[i];
            size[x] += size[to[i]];
        }
}
void dfs1(int x)
{
    dfsx[x] = ++cnt;
    if (son[x] != -1) top[son[x]] = top[x], dfs1(son[x]);
    for (int i = p[x]; i != -1; i = nxt[i])
        if (to[i] != fa[x] && to[i] != son[x])
            top[to[i]] = to[i], dfs1(to[i]);
}
int findlca(int x, int y)
{
    while (1)
    {
        if (top[x] == top[y]) return deep[x] > deep[y]? y : x;
        if (deep[top[x]] > deep[top[y]]) x = fa[top[x]];
        else y = fa[top[y]];
    }
}
bool query(int x, int l, int r, int ll, int rr)
{
    if (l == ll && r == rr) return flag[x];
    int mid = (l + r) >> 1, L = x << 1, R = L | 1;
    if (rr <= mid) return query(L, l, mid, ll, rr);
    else if (ll > mid) return query(R, mid + 1, r, ll, rr);
    else return query(L, l, mid, ll, mid) | query(R, mid + 1, r, mid + 1, rr);
}
void modify(int x, int l, int r, int to)
{
    flag[x] = true;
    if (l == r) return;
    int mid = (l + r) >> 1, L = x << 1, R = L | 1;
    if (to <= mid) modify(L, l, mid, to);
    else modify(R, mid + 1, r, to);
}
bool Query(int x, int y)
{
    while (1)
    {
        if (top[x] == top[y])
        {
            if (deep[x] < deep[y]) return query(1, 1, cnt, dfsx[x], dfsx[y]);
            else return query(1, 1, cnt, dfsx[y], dfsx[x]);
        }
        if (deep[top[x]] > deep[top[y]])
            if (query(1, 1, cnt, dfsx[top[x]], dfsx[x])) return true;
            else x = fa[top[x]];
        else
        {
            if (query(1, 1, cnt, dfsx[top[y]], dfsx[y])) return true;
            else y = fa[top[y]];
        }
    }
}
void work(int x)
{
    for (int i = p[x]; i != -1; i = nxt[i])
        if (to[i] != fa[x])
            work(to[i]);
    for (int i = lr[x][0]; i <= lr[x][1]; i++)
        if (!Query(q[Q[i]][0], q[Q[i]][1]))
        {
            modify(1, 1, cnt, dfsx[x]);
            sta[++ans] = x;
            return;
        }
}
bool cmp(int x, int y) {return lca[x] < lca[y];}
int main()
{
    freopen("ping.in","r",stdin);
    freopen("ping.out","w",stdout);
    scanf("%d%d", &n, &m);
    for (int i = 0; i <= n; i++) p[i] = son[i] = -1, top[i] = size[i] = fa[i] = deep[i] = 0;
    for (int i = 1; i <= n * 4; i++) flag[i] = false;
    for (int i = 1; i <= m; i++)
    {
        scanf("%d%d", &u, &v);
        u--, v--;
        to[i * 2 - 1] = v;
        nxt[i * 2 - 1] = p[u];
        p[u] = i * 2 - 1;
        to[i * 2] = u;
        nxt[i * 2] = p[v];
        p[v] = i * 2;
    }
    deep[0] = 1;
    dfs(0);
    cnt = 0;
    dfs1(0);
    scanf("%d", &P);
    for (int i = 1; i <= P; i++)
    {
        scanf("%d%d", &u, &v);
        u--, v--;
        q[i][0] = u, q[i][1] = v;
        lca[i] = findlca(u, v);
        Q[i] = i;
    }
    sort(Q + 1, Q + P + 1, cmp);
    for (int i = 0; i <= n; i++) lr[i][0] = P + 1, lr[i][1] = 0;
    for (int i = 1; i <= P; i++)
    {
        lr[lca[Q[i]]][0] = min(lr[lca[Q[i]]][0], i);
        lr[lca[Q[i]]][1] = max(lr[lca[Q[i]]][1], i);
    }
    ans = 0;
    work(0);
    printf("%d\n", ans);
    for (int i = 1; i <= ans; i++) printf("%d ", sta[i] + 1);
    return 0;
}