AtCoder Beginner Contest 302——A-E题讲解

蒟蒻来讲题，还望大家喜。若哪有问题，大家尽可提！

Hello, 大家好哇！本初中生蒟蒻讲解一下AtCoder Beginner Contest 302这场比赛的A-Ex题！

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A - Attack

原题

Problem Statement

There is an enemy with stamina $A$. Every time you attack the enemy, its stamina reduces by $B$.
At least how many times do you need to attack the enemy to make its stamina $0$ or less?

Constraints

$1\le A,B\le 10^{18}$
$A$ and $B$ are integers.

Input

The input is given from Standard Input in the following format:

$A$ $B$

Output

Print the answer.

Sample Input 1

7 3

Sample Output 1

3

Attacking three times make the enemy’s stamina $-2$.
Attacking only twice makes the stamina $1$, so you need to attack it three times.

Sample Input 2

123456789123456789 987654321

Sample Output 2

124999999

Sample Input 3

999999999999999998 2

Sample Output 3

499999999999999999

题目大意

攻击一次，A减少B，问多少次可以让A减为0或者更小

---

思路

太简单，不写了，直接见代码

代码

#include 

using namespace std;

int main()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(0);
	
	long long a, b;
	
	cin >> a >> b;
	
	cout << a / b + (a % b != 0) << endl;
	
	return 0;
}

B - Find snuke

原题

Problem Statement

There is a grid with $H$ horizontal rows and $W$ vertical columns. Each cell has a lowercase English letter written on it.
We denote by $(i,j)$ the cell at the $i$-th row from the top and $j$-th column from the left.
The letters written on the grid are represented by $H$ strings $S_1,S_2,\dots ,S_H$, each of length $W$.
The $j$-th letter of $S_i$ represents the letter written on $(i,j)$.
There is a unique set of
contiguous cells (going vertically, horizontally, or diagonally) in the grid
with s, n, u, k, and e written on them in this order.

Find the positions of such cells and print them in the format specified in the Output section.
A tuple of five cells $(A_1,A_2,A_3,A_4,A_5)$ is said to form
a set of contiguous cells (going vertically, horizontally, or diagonally) with s, n, u, k, and e written on them in this order
if and only if all of the following conditions are satisfied.
$A_1,A_2,A_3,A_4$ and $A_5$ have letters s, n, u, k, and e written on them, respectively.
For all $1\le i\le 4$, cells $A_i$ and $A_{i+1}$ share a corner or a side.
The centers of $A_1,A_2,A_3,A_4$, and $A_5$ are on a common line at regular intervals.

Constraints

$5\le H\le 100$
$5\le W\le 100$
$H$ and $W$ are integers.
$S_i$ is a string of length $W$ consisting of lowercase English letters.
The given grid has a unique conforming set of cells.

Input

$H$ $W$
$S_1$
$S_2$
$⋮$
$S_H$

Output

Print five lines in the following format.
Let $(R_1,C_1),(R_2,C_2)\dots ,(R_5,C_5)$ be the cells in the sought set with s, n, u, k, and e written on them, respectively.
The $i$-th line should contain $R_i$ and $C_i$ in this order, separated by a space.
In other words, print them in the following format:
$R_1$ $C_1$
$R_2$ $C_2$
$⋮$
$R_5$ $C_5$

See also Sample Inputs and Outputs below.

Sample Input 1

6 6
vgxgpu
amkxks
zhkbpp
hykink
esnuke
zplvfj

Sample Output 1

5 2
5 3
5 4
5 5
5 6

Tuple $(A_1,A_2,A_3,A_4,A_5)=((5,2),(5,3),(5,4),(5,5),(5,6))$ satisfies the conditions.

Indeed, the letters written on them are s, n, u, k, and e;

for all $1\le i\le 4$, cells $A_i$ and $A_{i+1}$ share a side;

and the centers of the cells are on a common line.

Sample Input 2

5 5
ezzzz
zkzzz
ezuzs
zzznz
zzzzs

Sample Output 2

5 5
4 4
3 3
2 2
1 1

Tuple $(A_1,A_2,A_3,A_4,A_5)=((5,5),(4,4),(3,3),(2,2),(1,1))$ satisfies the conditions.

However, for example, $(A_1,A_2,A_3,A_4,A_5)=((3,5),(4,4),(3,3),(2,2),(3,1))$ violates the third condition because the centers of the cells are not on a common line, although it satisfies the first and second conditions.

Sample Input 3

10 10
kseeusenuk
usesenesnn
kskekeeses
nesnusnkkn
snenuuenke
kukknkeuss
neunnennue
sknuessuku
nksneekknk
neeeuknenk

Sample Output 3

9 3
8 3
7 3
6 3
5 3

题目大意

上、下、左、右、左上、右下、左下、右上八个方向找snuke，找到后输出位置。

---

思路

找到’s’的位置后，八个方向遍历。

代码

#include 
#include 
 
using namespace std;
 
const int N = 1e2 + 10;
 
int n, m;
char a[N][N];
string s = " snuke";
 
int main()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(0);
	
	cin >> n >> m;
	
	for (int i = 1; i <= n; i ++)
		for (int j = 1; j <= m; j ++)
			cin >> a[i][j];
			
	for (int i = 1; i <= n; i ++)
		for (int j = 1; j <= m; j ++)
			if (a[i][j] == 's')
				for (int dx = -1; dx <= 1; dx ++)
					for (int dy = -1; dy <= 1; dy ++)
						if (dx != 0 || dy != 0)
						{
							int flg = 1;
							vector<pair<int, int>> res;
							res.push_back({i, j});
							for (int len = 2; len <= 5; len ++)
							{
								int xx = i + dx * (len - 1), yy = j + dy * (len - 1);
								if (a[xx][yy] != s[len])
								{
									flg = 0;
									break;
								}
								res.push_back({xx, yy});
							}
							if (flg)
							{
								for (auto c : res)
									cout << c.first << " " << c.second << endl;
								return 0;
							}
						}
	
	return 0;
}

C - Almost Equal

原题

Problem Statement

You are given $N$ strings $S_1,S_2,\dots ,S_N$, each of length $M$, consisting of lowercase English letter. Here, $S_i$ are pairwise distinct.
Determine if one can rearrange these strings to obtain a new sequence of strings $T_1,T_2,\dots ,T_N$ such that:
for all integers $i$ such that $1\le i\le N-1$, one can alter exactly one character of $T_i$ to another lowercase English letter to make it equal to $T_{i+1}$.

Constraints

$2\le N\le 8$
$1\le M\le 5$
$S_i$ is a string of length $M$ consisting of lowercase English letters. $(1\le i\le N)$
$S_i$ are pairwise distinct.

Input

The input is given from Standard Input in the following format:

$N$ $M$
$S_1$
$S_2$
$⋮$
$S_N$

Output

Print Yes if one can obtain a conforming sequence; print No otherwise.

Sample Input 1

4 4
bbed
abcd
abed
fbed

Sample Output 1

Yes

One can rearrange them in this order: abcd, abed, bbed, fbed. This sequence satisfies the condition.

Sample Input 2

2 5
abcde
abced

Sample Output 2

No

No matter how the strings are rearranged, the condition is never satisfied.

Sample Input 3

8 4
fast
face
cast
race
fact
rice
nice
case

Sample Output 3

Yes

题目大意

给定N个字符串，通过重新排序让相邻两个字符串只有一个字母不同。

---

思路

题目比较简单，但一定要注意全排序函数的使用，昨晚被这个题目折腾完了。
这道题可以对所有字符串的排列就行全排序，遍历哪一个排序能够符合题目的要求，即每两个相邻字符串只有一个字母不同。
这里要特别注意，在使用next_permutation()函数前，要先进行一次sort，不然结果就会有5个测试点WA，因为next_permutation()函数是接着上次的顺序向下排的。

代码

#include 
#include 
 
using namespace std;
 
int n, m;
string s[10];
 
int main()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(0);
	
	cin >> n >> m;
	
	if (m == 1)
	{
		cout << "Yes" << endl;
		return 0;
	}
	
	for (int i = 1; i <= n; i ++)
		cin >> s[i];
		
	sort(s + 1, s + n + 1));
		
	do
	{
		/*
		for(int i = 1; i <= n; i ++)
			cout << s[i] << endl;
		*/
		int flg = 1;
		for (int i = 1; i < n; i ++)
		{
			int cnt = 0;
			for (int j = 0; j < m; j ++)
				if (s[i][j] != s[i + 1][j])
					cnt ++;
					
			if (cnt != 1)
			{
				flg = 0;
				break;
			}
		}
		
		if (flg)
		{
			cout << "Yes" << endl;
			return 0;
		}
		
	}while(next_permutation(s + 1, s + n + 1));
	
	cout << "No" << endl;
	
	return 0;
}

D - Impartial Gift

原题

Problem Statement

Takahashi has decided to give one gift to Aoki and one gift to Snuke.

There are $N$ candidates of gifts for Aoki,
and their values are $A_1,A_2,\dots ,A_N$.

There are $M$ candidates of gifts for Snuke,
and their values are $B_1,B_2,\dots ,B_M$.
Takahashi wants to choose gifts so that the difference in values of the two gifts is at most $D$.
Determine if he can choose such a pair of gifts. If he can, print the maximum sum of values of the chosen gifts.

Constraints

$1\le N,M\le 2\times 10^5$
$1\le A_i,B_i\le 10^{18}$
$0\le D\le 10^{18}$
All values in the input are integers.

Input

The input is given from Standard Input in the following format:
$N$ $M$ $D$
$A_1$ $A_2$ $\dots$ $A_N$
$B_1$ $B_2$ $\dots$ $B_M$

Output

If he can choose gifts to satisfy the condition,
print the maximum sum of values of the chosen gifts.
If he cannot satisfy the condition, print $-1$.

Sample Input 1

2 3 2
3 10
2 5 15

Sample Output 1

8

The difference of values of the two gifts should be at most $2$.

If he gives a gift with value $3$ to Aoki and another with value $5$ to Snuke, the condition is satisfied, achieving the maximum possible sum of values.

Thus, $3+5=8$ should be printed.

Sample Input 2

3 3 0
1 3 3
6 2 7

Sample Output 2

-1

He cannot choose gifts to satisfy the condition.
Note that the candidates of gifts for a person may contain multiple gifts with the same value.

Sample Input 3

1 1 1000000000000000000
1000000000000000000
1000000000000000000

Sample Output 3

2000000000000000000

Note that the answer may not fit into a $32$-bit integer type.

Sample Input 4

8 6 1
2 5 6 5 2 1 7 9
7 2 5 5 2 4

Sample Output 4

14

---

思路

这道题我们可以用二分来做，在做之前首先我们要排序两个序列！

• 对于序列一，我们枚举每一个点，然后通过二分在序列B中找到最大的不超过当前枚举的点的权值，最后更新两个数的差。
• 对于序列二，我们枚举每一个点，然后通过二分在序列A中找到最大的不超过当前枚举的点的权值，最后给更新两个数的差。

注意：这里只用找到不超过枚举到的点（设为x）的权值是因为，如果有比当前点权值大的点（设为y），且他们两个的差更小，那么我们在枚举序列B的时候一定会枚举到y，此时x就在y的前面，自然会更新到这个更小的值

代码

#include 
#include 
#define int long long

using namespace std;

const int N = 2e5 + 10;

int n, m, d;
int a[N], b[N];

signed main()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(0);
	
	cin >> n >> m >> d;
	
	for (int i = 1; i <= n; i ++)
		cin >> a[i];
	for (int i = 1; i <= m; i ++)
		cin >> b[i];
		
	sort(a + 1, a + 1 + n);
	sort(b + 1, b + 1 + m);
	
	int res = -1;
	for (int i = 1; i <= n; i ++)
	{
		int l = 0, r = m;
		while (l < r)
		{
			int mid = l + r + 1 >> 1;
			if (b[mid] <= a[i]) l = mid;
			else r = mid - 1;
		}
		
		if (b[l] == 0) continue;
		else
			if (a[i] - b[l] <= d)
				res = max(res, a[i] + b[l]);
	}
	
	for (int i = 1; i <= m; i ++)
	{
		int l = 0, r = n;
		while (l < r)
		{
			int mid = l + r + 1 >> 1;
			if (a[mid] <= b[i]) l = mid;
			else r = mid - 1;
		}
		
		if (a[l] == 0) continue;
		else
			if (b[i] - a[l] <= d)
				res = max(res, b[i] + a[l]);
	}
	
	cout << res << endl;
	
	return 0;
}

E - Isolation

原题

Problem Statement

There is an undirected graph with $N$ vertices numbered $1$ through $N$, and initially with $0$ edges.

Given $Q$ queries, process them in order. After processing each query,
print the number of vertices that are not connected to any other vertices by an edge.
The $i$-th query, ${\mathrm{query}}_i$, is of one of the following two kinds.
1 u v: connect vertex $u$ and vertex $v$ with an edge. It is guaranteed that, when this query is given, vertex $u$ and vertex $v$ are not connected by an edge.
2 v: remove all edges that connect vertex $v$ and the other vertices. (Vertex $v$ itself is not removed.)

Constraints

$2\le N\le 3\times 10^5$
$1\le Q\le 3\times 10^5$
For each query of the first kind, $1\le u,v\le N$ and $u\ne v$.
For each query of the second kind, $1\le v\le N$.
Right before a query of the first kind is given, there is no edge between vertices $u$ and $v$.
All values in the input are integers.

Input

The input is given from Standard Input in the following format:
$N$ $Q$
${\mathrm{query}}_1$
${\mathrm{query}}_2$
$⋮$
${\mathrm{query}}_Q$

Output

Print $Q$ lines.

The $i$-th line $(1\le i\le Q)$ should contain the number of vertices that are not connected to any other vertices by an edge.

Sample Input 1

3 7
1 1 2
1 1 3
1 2 3
2 1
1 1 2
2 2
1 1 2

Sample Output 1

1
0
0
1
0
3
1

After the first query, vertex $1$ and vertex $2$ are connected to each other by an edge, but vertex $3$ is not connected to any other vertices.

Thus, $1$ should be printed in the first line.
After the third query, all pairs of different vertices are connected by an edge.

However, the fourth query asks to remove all edges that connect vertex $1$ and the other vertices, specifically to remove the edge between vertex $1$ and vertex $2$, and another between vertex $1$ and vertex $3$.
As a result, vertex $2$ and vertex $3$ are connected to each other, while vertex $1$ is not connected to any other vertices by an edge.

Thus, $0$ and $1$ should be printed in the third and fourth lines, respectively.

Sample Input 2

2 1
2 1

Sample Output 2

2

When the query of the second kind is given, there may be no edge that connects that vertex and the other vertices.

---

思路

• 对于操作一，我们就直接减无向边，同时如果加之前一个点或两个点都没有连边，那么就从总答案的点数减去没有连边的点数。
• 对于操作二，我们把哪个点的所有点删掉，因为建的是无向边，我们还要把他删掉的边所对应的另一个的点与这个点相连的边也删掉，如果删掉后没有其余边了，再加1

代码

#include 
#include 

using namespace std;

const int N = 3e5 + 10;

int n, q;
int op, a, b;
set<int> g[N];

int main()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(0);
	
	cin >> n >> q;
	
	int res = n;
	while (q --)
	{
		cin >> op >> a;
		
		if (op == 1)
		{
			cin >> b;
			if (g[a].size() == 0) res --;
			if (g[b].size() == 0) res --;
			g[a].insert(b);
			g[b].insert(a);
		}
		else
		{
			for (auto c : g[a])
			{
				g[c].erase(a);
				if (g[c].size() == 0) res ++;
			}
			if (g[a].size() > 0) res ++;
			g[a].clear();
		}
		cout << res << endl;
	}
	
	return 0;
}

今天就到这里了！

大家有什么问题尽管提，我都会尽力回答的！

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