Hamiltonian Wall

合集 - 刷题集(97)

1.妖梦拼木棒2023-05-232.[USACO1.2]回文平方数 Palindromic Squares2023-05-243.[COCI2012-2013#1] LJUBOMORA2023-05-254.火柴棒等式2023-05-255.Kieszonkowe2023-05-256.[COCI2014-2015#5] TRAKTOR2023-05-267.硬币翻转2023-05-268.[蓝桥杯 2020 省 AB1] 走方格2023-05-269.P2097 资料分发2023-05-2610.[AHOI2005]约数研究2023-05-2611.[NOIP2004 普及组] 火星人2023-05-2612.我焯,原神(这真是个题)2023-05-2613.滑雪 OJ36512023-05-2414.CV的人有福啦!YTU贪心训练2(部分注释)2023-05-2715.砝码称重2023-05-2716.警钟长鸣-----找零钱2023-05-2817.[USACO09OCT]Barn Echoes G2023-05-2818.【CSGRound2】光骓者的荣耀2023-05-2919.初见蓝桥杯2023-05-3020.[蓝桥杯 2022 省 B] 扫雷2023-05-3121.开餐馆2023-05-3122.P9241 [蓝桥杯 2023 省 B] 飞机降落2023-06-0123.P7083 [NWRRC2013] Energy Tycoon2023-06-0324.高精度2023-06-0425.P7954 [COCI2014-2015#6] PAPRIKA2023-06-0426.(输出路径搜索)[USACO06OCT] Cows on Skates G2023-06-0427.畜栏保留问题2023-06-0428.(贪心+搜索+剪枝)P8801 [蓝桥杯 2022 国 B] 最大数字2023-06-0529.蓝桥杯 入门----普及-2023-06-0630.[NOIP2016 提高组] 玩具谜题2023-06-0631.[NOIP2002 提高组] 字串变换(无向图查重)2023-06-0632.[NOIP2000 提高组] 单词接龙2023-06-0733.POJ 硬币2023-06-0734.动态规划学习 1(最长上升子序列问题)2023-06-0735.动态规划学习 2(背包问题及其变形)2023-06-0836. 切割回文2023-06-1037.[NOIP2001 提高组] 数的划分(剪枝)2023-06-1038.字符串转换数字,sscanf和sprintf大法2023-06-1039.[CTSC1997] 选课(树状DP)2023-06-1040. k 倍区间(同余定理,组合数)2023-06-1141.[蓝桥杯 2018 省 AB] 全球变暖2023-06-1142.马的遍历(对bfs的更深一层探讨)2023-06-1143.找零钱2023-06-1144.Pasha Maximizes2023-06-1245.Newspaper Headline2023-06-1246.Balanced Ternary String2023-06-1347.(数论)素数,质数2023-06-1348.(数论) 约数2023-06-1349.Helping the Nature2023-06-1450.(博弈论)Even Number Addicts2023-06-1451.Present2023-06-1552.Mr. Kitayuta's Colorful Graph(二维并查集,弱化版)2023-06-1653.Edgy Trees(dfs,并查集,快速幂,树形结构,红黑树)2023-06-1654.并查集2023-05-2455.再谈 前缀和,差分,离散化2023-06-1656.Best Cow Fences(前缀和+特殊二分)2023-06-1757.二分2023-06-1758.同类型,类背包动态规划,选地dp2023-06-1759.Primes on Interval(欧拉筛+二分+滑动窗口)2023-06-1860.字符串(KMP , Trie树 , STL)2023-06-1861.Codeforces1 #879 div.22023-06-1962.Add Modulo 10(数论,思维,数学,规律)2023-06-2063.期末考试YTU4035: Shmily(数学,等差数列)2023-06-2064.[POI2006] OKR-Periods of Words2023-06-2165.Getting Zero(Bfs)2023-06-2166.快速幂2023-06-2167.Dreaming of Freedom(数论,贪心)2023-06-2368.Scoring Subsequences2023-06-2469.Dolce Vita2023-06-2970.Cake Assembly Line2023-06-2971.Constructive Problem2023-06-3072.Forever Winter2023-06-3073.Maximum Sum(前缀和)2023-07-1074.Contrast Value(数学规律)2023-07-1075.Lamps(STL+双端队列)2023-07-1076.Long Long2023-07-1177.Sum in Binary Tree2023-07-1178.Apple Tree(树状搜索,树形DP)2023-07-1179.Strong Password(贪心思想)2023-07-1280.Come Together2023-07-1281.Notepad2023-07-13

82.Hamiltonian Wall2023-07-13

83.7.17作业2023-07-1684.逛画展(双指针)2023-07-1985.#8852023-07-2086.树状数组2023-07-2087.Subsequence Addition2023-07-2288.7.22作业2023-07-2289.Diverse Substrings2023-07-2490.Tracking Segments(二分,区间前缀)2023-07-2791.最大食物链计数2023-07-2792.线段树12023-07-2293.[TJOI2007] 线段(状态机)2023-07-2994.#8782023-07-3095.测试12023-07-3096.李白打酒2023-07-3097.砍竹子2023-07-30

收起

# Hamiltonian Wall

## 题面翻译

给你一个 $2\times m$ 的矩阵，矩阵中只可能包含字符 `B` 和 `W`。每一列都有字符 `B`。问能否找出一条路径，满足：

- 路径中相邻两格有公共边（只有公共点的不算）。
- 每个 `B` 格恰好被覆盖一次。
- 每个 `W` 格都没有被覆盖到。

如果存在这样的路径，输出 `YES`，否则输出 `NO`。

## 题目描述

Sir Monocarp Hamilton is planning to paint his wall. The wall can be represented as a grid, consisting of $2$ rows and $m$ columns. Initially, the wall is completely white.

Monocarp wants to paint a black picture on the wall. In particular, he wants cell $(i,j)$ (the $j$ -th cell in the $i$ -th row) to be colored black, if $c_{i,j}=$ 'B', and to be left white, if $c_{i,j}=$ 'W'. Additionally, he wants each column to have at least one black cell, so, for each $j$ , the following constraint is satisfied: $c_{1,j}$ , $c_{2,j}$ or both of them will be equal to 'B'.

In order for the picture to turn out smooth, Monocarp wants to place down a paint brush in some cell $(x_1,y_1)$ and move it along the path $(x_1,y_1),(x_2,y_2),\dots ,(x_k,y_k)$ so that:

- for each $i$ , $(x_i,y_i)$ and $(x_{i+1},y_{i+1})$ share a common side;
- all black cells appear in the path exactly once;
- white cells don't appear in the path.

Determine if Monocarp can paint the wall.

## 输入格式

The first line contains a single integer $t$ ( $1\le t\le {10}^4$ ) — the number of testcases.

The first line of each testcase contains a single integer $m$ ( $1\le m\le 2\cdot {10}^5$ ) — the number of columns in the wall.

The $i$ -th of the next two lines contains a string $c_i$ , consisting of $m$ characters, where each character is either 'B' or 'W'. $c_{i,j}$ is 'B', if the cell $(i,j)$ should be colored black, and 'W', if the cell $(i,j)$ should be left white.

Additionally, for each $j$ , the following constraint is satisfied: $c_{1,j}$ , $c_{2,j}$ or both of them are equal to 'B'.

The sum of $m$ over all testcases doesn't exceed $2\cdot {10}^5$ .

## 输出格式

For each testcase, print "YES" if Monocarp can paint a wall. Otherwise, print "NO".

## 样例 #1

### 样例输入 #1

```
6
3
WBB
BBW
1
B
B
5
BWBWB
BBBBB
2
BW
WB
5
BBBBW
BWBBB
6
BWBBWB
BBBBBB
```

### 样例输出 #1

```
YES
YES
NO
NO
NO
YES
```

## 提示

In the first testcase, Monocarp can follow a path $(2,1)$ , $(2,2)$ , $(1,2)$ , $(1,3)$ with his brush. All black cells appear in the path exactly once, no white cells appear in the path.

In the second testcase, Monocarp can follow a path $(1,1)$ , $(2,1)$ .

In the third testcase:

- the path $(1,1)$ , $(2,1)$ , $(2,2)$ , $(2,3)$ , $(1,3)$ , $(2,4)$ , $(2,5)$ , $(1,5)$ doesn't suffice because a pair of cells $(1,3)$ and $(2,4)$ doesn't share a common side;
- the path $(1,1)$ , $(2,1)$ , $(2,2)$ , $(2,3)$ , $(1,3)$ , $(2,3)$ , $(2,4)$ , $(2,5)$ , $(1,5)$ doesn't suffice because cell $(2,3)$ is visited twice;
- the path $(1,1)$ , $(2,1)$ , $(2,2)$ , $(2,3)$ , $(2,4)$ , $(2,5)$ , $(1,5)$ doesn't suffice because a black cell $(1,3)$ doesn't appear in the path;
- the path $(1,1)$ , $(2,1)$ , $(2,2)$ , $(2,3)$ , $(2,4)$ , $(2,5)$ , $(1,5)$ , $(1,4)$ , $(1,3)$ doesn't suffice because a white cell $(1,4)$ appears in the path.

//Hamiltonian Wall
//一开始想的dfs,从最左边开始,然后一直遍历,如果全部能遍历一次的话,就可以
//但是一直超时,后来高人点明由于就两行,可以用模拟暴力来求
//如果同列可以走,先走同列,然后再走同行,如果不能走同行就直接返回
#include <bits/stdc++.h>
//#define int long long
using namespace std;
const int N=2e5+3,mod=1e9+7;
string s[2];
int n,t,res,num,ans,m;
int dx[]={1,-1,0},dy[]={0,0,1};
bool vis[2][N];
bool dfs(int u,int v,int cnt)
{
    if(cnt==num) return true;
    for(int i=0;i<3;i++){
        int x=u+dx[i],y=v+dy[i];
        if(x>=0&&x<=1&&y>=0&&y<n&&!vis[x][y]&&s[x][y]=='B'){
            vis[x][y]=true;
            if(dfs(x,y,cnt+1)) return true;
            vis[x][y]=false;
        }
    }
    return false;
}
int main()
{
    std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
    cin>>t;
    while(t--){
        cin>>n;
        num=0;
        bool f=false,f1=false,f2=false;
        cin>>s[0]>>s[1];
        for(int i=0;i<n;++i){
            if(s[0][i]=='B') num++;
            if(s[1][i]=='B') num++;
        }
            if(f) break;
            if(s[0][0]=='B'){
                vis[0][0]=true;
                if(dfs(0,0,1)) cout<<"YES"<<endl,f1=true;
                for(int i=0;i<n;i++) vis[0][i]=false,vis[1][i]=false;
                f=true;
            }
            if(s[1][0]=='B'&&!f1){
                vis[1][0]=true;
                if(dfs(1,0,1)) cout<<"YES"<<endl,f2=true;
                f=true;
            } 
        if(!f1&&!f2) cout<<"NO"<<endl;
        for(int i=0;i<n;i++) vis[0][i]=false,vis[1][i]=false;
    }
    return 0;
}

#include <bits/stdc++.h>
#define int long long
using namespace std;
const int N=1e6+10,mod=1e9+7;
string s[2];
int n,t,a[N],f[N],res,num,ans,m;
bool vis[N];
bool chk(int u)
{
    bool now=u;
    if(s[u][0]=='B') now=!now;
    for(int i=1;i<n;i++){
        if(s[now][i]=='W') return false;
        if(s[!now][i]=='B') now=!now;
    } 
    return true;
}
bool solve()
{
    cin >> n >> s[0] >> s[1];
    if (s[0][0] == 'B') {if (chk(1)) return true;}
    if (s[1][0] == 'B') {if (chk(0)) return true;}
    return false;
}
signed main()
{
    std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
    cin>>t;
    while(t--){
        if(solve()) cout<<"YES"<<endl;
        else cout<<"NO"<<endl;
    }
    return 0;
}

 

__EOF__

本文作者：Sakurajimamai
本文链接：https://www.cnblogs.com/o-Sakurajimamai-o/p/17551863.html
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