Atcoder Grand-014 Writeup

A - Cookie Exchanges

题面

Takahashi, Aoki and Snuke love cookies. They have A, B and C cookies, respectively. Now, they will exchange those cookies by repeating the action below:

Each person simultaneously divides his cookies in half and gives one half to each of the other two persons.

This action will be repeated until there is a person with odd number of cookies in hand.

How many times will they repeat this action? Note that the answer may not be finite.

题意

三个人，每次把自己的饼干分成两份给其他两个人。模拟，map判断是否循环。

代码

#include <bits/stdc++.h>
using namespace std;

map<pair<int,int> , int > m;
int a[5];
int b[5];
int ans;

int cmp(int q,int w)
{
	return q<w;
}

int main()
{
	cin>>a[0]>>a[1]>>a[2];
	while (1)
	{
		sort(a,a+3,cmp);
		if (a[0]%2 || a[1]%2 || a[2]%2)
		{
			cout<<ans<<endl;
			return 0;
		}
		if (m.count(make_pair(a[0],a[1])) && m[make_pair(a[0],a[1])]==a[2]) return 0*puts("-1");
		m[make_pair(a[0],a[1])]=a[2];
		b[0]=(a[1]+a[2])/2;
		b[1]=(a[0]+a[2])/2;
		b[2]=(a[1]+a[0])/2;
		for (int i=0;i<3;i++) a[i]=b[i];
		ans++;
	}
}

B - Unplanned Queries

题面

Takahashi is not good at problems about trees in programming contests, and Aoki is helping him practice.

First, Takahashi created a tree with N vertices numbered 1 through N, and wrote 0 at each edge.

Then, Aoki gave him M queries. The i-th of them is as follows:

Increment the number written at each edge along the path connecting vertices ai and bi, by one.

After Takahashi executed all of the queries, he told Aoki that, for every edge, the written number became an even number. However, Aoki forgot to confirm that the graph Takahashi created was actually a tree, and it is possible that Takahashi made a mistake in creating a tree or executing queries.

Determine whether there exists a tree that has the property mentioned by Takahashi.

题意

给出n个点和m条路（不一定直达），经过的路会+1，是否能构造一个图，使得m条路走完后，所有的路都是偶数。

代码

#include <bits/stdc++.h>
using namespace std;

int n;
int a[100010];
int m,x,y;

int main()
{
	cin>>n>>m;
	for (int i=1;i<=m;i++)
	{
		cin>>x>>y;
		++a[x],++a[y];
	}
	for (int i=1;i<=n;i++) if (a[i]%2) return 0*puts("NO");
	return 0*puts("YES");
}

C - Closed Rooms

题面

Takahashi is locked within a building.

This building consists of H×W rooms, arranged in H rows and W columns. We will denote the room at the i-th row and j-th column as (i,j). The state of this room is represented by a character Ai,j. If Ai,j= #, the room is locked and cannot be entered; if Ai,j= ., the room is not locked and can be freely entered. Takahashi is currently at the room where Ai,j= S, which can also be freely entered.

Each room in the 1-st row, 1-st column, H-th row or W-th column, has an exit. Each of the other rooms (i,j) is connected to four rooms: (i−1,j), (i+1,j), (i,j−1) and (i,j+1).

Takahashi will use his magic to get out of the building. In one cast, he can do the following:

Move to an adjacent room at most K times, possibly zero. Here, locked rooms cannot be entered.

Then, select and unlock at most K locked rooms, possibly zero. Those rooms will remain unlocked from then on.

His objective is to reach a room with an exit. Find the minimum necessary number of casts to do so.

It is guaranteed that Takahashi is initially at a room without an exit.

题意

给出一个迷宫，每次S能走k个白格子，然后走k个锁，问需要几个阶段S能逃走。

官方题解

先走到所有能走到的格子，不大于k也不解锁，ans=1+ceil(min(y-1,x-1,h-x,w-y)/k)

代码

#include <bits/stdc++.h>
using namespace std;

const int fx[] = { 0, 1, 0,-1};
const int fy[] = { 1, 0,-1, 0};

int n,m,k,sx,sy;
char s[1010];
bool b[1010][1010];
bool a[1010][1010];
bool flag;
queue<pair<int,int> > q;
queue<int> qs;
int main()
{
	cin>>n>>m>>k;
    for (int i=1;i<=n;i++)
	{
    	scanf("%s",s+1);
		for (int j=1;j<=m;j++) a[i][j] = s[j]!='#';
        for (int j=1;j<=m;j++) if (s[j]=='S') sx=i, sy=j;
    }

    if (sx == 1 || sx == n || sy == 1 || sy == m) return puts("0"), 0;

    b[sx][sy] = 1;
    q.push(make_pair(sx,sy));
	qs.push(0);
    while (!q.empty()) {
        int ux = q.front().first;
        int uy = q.front().second;
		q.pop();
        int us = qs.front(); qs.pop();
        if (us == k) continue;
        if (ux == 1 || ux == n || uy == 1 || uy == m) flag = 1;

        for (int i=0;i<4;i++)
		{
            int vx = ux + fx[i], vy = uy + fy[i];
            if (vx<1 || vx>n || vy<1 || vy>m) continue;
            if (!b[vx][vy] && a[vx][vy])
			{
                b[vx][vy] = 1;
                q.push(make_pair(vx,vy));
				qs.push(us+1);
            }
        }
    }

    if (flag) return puts("1"), 0;

    int ans = 2147483647;
    for (int i=1;i<=n;i++)
        for (int j=1;j<=m;j++)
			if (b[i][j])
			{
            	int t = min( min(i-1,j-1) , min(n-i,m-j) );
            	int cur = (t+k-1) / k;
            	ans = min(ans, cur+1);
        	}
    cout << ans << endl;
    return 0;
}

D - Black and White Tree

题面

There is a tree with N vertices numbered 1 through N. The i-th of the N−1 edges connects vertices ai and bi.

Initially, each vertex is uncolored.

Takahashi and Aoki is playing a game by painting the vertices. In this game, they alternately perform the following operation, starting from Takahashi:

Select a vertex that is not painted yet.

If it is Takahashi who is performing this operation, paint the vertex white; paint it black if it is Aoki.

Then, after all the vertices are colored, the following procedure takes place:

Repaint every white vertex that is adjacent to a black vertex, in black.

Note that all such white vertices are repainted simultaneously, not one at a time.

If there are still one or more white vertices remaining, Takahashi wins; if all the vertices are now black, Aoki wins. Determine the winner of the game, assuming that both persons play optimally.

题意

先手执白，后手执黑，全染色后黑色将相邻染黑，全黑后手胜，问存不存在后手必胜的情况。

树的完备匹配。

代码

#include <bits/stdc++.h>
using namespace std;
vector<int> e[1000500];
int p[1000500];
int n;
void link(int a,int b)
{
	e[a].push_back(b);
	e[b].push_back(a);
}

void dfs(int u,int fa)
{
    for (int i=0;i<e[u].size();i++)
	{
        int v=e[u][i];
		if (v==fa) continue;
        dfs(v,u);
    }
    if (!p[u] && !p[fa]) p[u] = p[fa] = 1;
}

int main() {
    cin>>n;
    for (int i=1;i<n;i++)
    {
    	int x,y;
    	cin>>x>>y;
    	link(x,y);
    }
    p[0] = 1;
    dfs(1,0);
    int ans = 1;
    for (int i=1;i<=n;i++) if (!p[i]) ans = 0;
    puts(!ans?"First":"Second");
    return 0;
}

E - Blue and Red Tree

题意

不清

F - Strange Sorting

题面

Takahashi loves sorting.

He has a permutation (p1,p2,…,pN) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,…,N):

First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.

Then, let a1,a2,…,ak be the values of the high elements, and b1,b2,…,bN−k be the values of the low elements in the current permutation, in the order they appear in it.

Lastly, rearrange the permutation into (b1,b2,…,bN−k,a1,a2,…,ak).

How many operations are necessary until the permutation is sorted?

题意

把每次第一个开头的递增子序列取出，放在最后面，问几次能排好序列。

官方题解

思考过程：如果拿掉1，发现序列变化过程，基本相似。但是还是要参考1，如果最后例如2，3，……，1，……，n-1，n。则T=T+1;

那我们很容易想到去递推。

如果一个序列，i,i+1,i+2这种连一起的，我们可以看作一个整体。

对于（a,b,c），a<b<c。我们认为（a,b,c）=(b,c,a)=(c,a,b) 因为他们做整体变换，不消耗次数。

如果出现其他状况，如c,b,a。那么就需要移动了。移动后，bc就作为一个整体，变成，（b，a）需要处理

代码

#include <bits/stdc++.h>
using namespace std;

int a[200010];
int q[200010];
int T[200010];
int f[200010];
int n;
int cnt;

int main()
{
	cin>>n;
	for (int i=1;i<=n;i++) cin>>a[i];
	for (int i=1;i<=n;i++) q[a[i]]=i;

	for (int i=n-1;i;i--)
    {
        if( !T[ i + 1 ] )
        {
            if( q[i] > q[i+1] ) T[i]=1, f[i]=i+1;
            else T[i] = 0;
        }
        else
        {
            int cnt = 0;
            cnt += q[f[i+1]] < q[i];
            cnt += q[i] < q[i+1];
            cnt += q[i+1] < q[f[i+1]];
            if (cnt==2) T[i]=T[i+1],f[i]=f[i+1];
            else T[i]=T[i+1]+1,f[i]=i+1;
        }
    }
    cout<<T[1];
}

赛后总结

自己还是太菜了qwq

只会两题，第三题没想进去，第四题发现了一种结论，但是打不来。

要抓紧订正题目，搞了半天还有一堆题目坑没填。

比赛链接

http://agc014.contest.atcoder.jp