AtCoder Grand Contest 021

A - Digit Sum 2

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Time limit : 2sec / Memory limit : 256MB

Score : 300 points

Problem Statement

Find the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.

Constraints

• 1≤N≤1016
• N is an integer.

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Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum possible sum of the digits (in base 10) of a positive integer not greater than N.

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Sample Input 1

Copy

100

Sample Output 1

Copy

18

For example, the sum of the digits in 99 is 18, which turns out to be the maximum value.

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Sample Input 2

Copy

9995

Sample Output 2

Copy

35

For example, the sum of the digits in 9989 is 35, which turns out to be the maximum value.

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Sample Input 3

Copy

3141592653589793

Sample Output 3

Copy

137

找小于等于一个数的位数和最大

很容易想到就是尽量多的填9，比如3位数我就可以填首位，其他的填9，所以就是首位-1+9*（位数-1）

但是99的时候我是可以99的啊，这种贪心就会忽略，所以正确的方式是先把这个数+1

公式为9*（位数-1）+（n+1）的首位-1

#include<bits/stdc++.h>
using namespace std;
long long n,s;
int main()
{
    cin>>n,n++;
    while(n>9)s+=9,n/=10;
    cout<<s+n-1;
    return 0;
}

B - Holes

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Time limit : 2sec / Memory limit : 256MB

Score : 600 points

Problem Statement

There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (xi,yi).

Let R=10101010. Ringo performs the following operation:

• Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.

For every i (1≤i≤N), find the probability that Snuke falls into the i-th hole.

Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:

• Pick two real numbers x and y independently according to uniform distribution on [−R,R].
• If x2+y2≤R2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Constraints

• 2≤N≤100
• |xi|,|yi|≤106(1≤i≤N)
• All given points are pairwise distinct.
• All input values are integers.

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Input

Input is given from Standard Input in the following format:

N
x1 y1
:
xN yN

Output

Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.

The output will be judged correct when, for all output values, the absolute or relative error is at most 10−5.

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Sample Input 1

Copy

2
0 0
1 1

Sample Output 1

Copy

0.5
0.5

If Ringo put Snuke in the region x+y≤1, Snuke will fall into the first hole. The probability of this happening is very close to 0.5. Otherwise, Snuke will fall into the second hole, the probability of which happening is also very close to 0.5.

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Sample Input 2

Copy

5
0 0
2 8
4 5
2 6
3 10

Sample Output 2

Copy

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

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这个题就是一个很简单的几何

#include<bits/stdc++.h>
using namespace std;
const double pi=acos(-1.);
const int N=105;
int n,x[N],y[N];
double p[N+N];
signed main()
{
    cin>>n;
    for(int i=0; i<n; i++)cin>>x[i]>>y[i];
    for(int i=0; i<n; i++)
    {
        int tot=0;
        for(int j=0; j<n; j++)
            if(i!=j)p[tot++]=atan2(y[j]-y[i],x[j]-x[i]);
        sort(p,p+tot);
        for(int j=0; j<tot; j++)p[j+tot]=p[j]+2*pi;
        double ans=0;
        for(int j=0; j<tot; j++)ans=max(ans,pi-p[j+tot-1]+p[j]);
        printf("%.8f
",ans/2/pi);
    }
    return 0;
}

C - Tiling

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Time limit : 2sec / Memory limit : 256MB

Score : 900 points

Problem Statement

Takahashi has an N×M grid, with N horizontal rows and M vertical columns. Determine if we can place A 1×2 tiles (1 vertical, 2horizontal) and B 2×1 tiles (2 vertical, 1 horizontal) satisfying the following conditions, and construct one arrangement of the tiles if it is possible:

• All the tiles must be placed on the grid.
• Tiles must not stick out of the grid, and no two different tiles may intersect.
• Neither the grid nor the tiles may be rotated.
• Every tile completely covers exactly two squares.

Constraints

• 1≤N,M≤1000
• 0≤A,B≤500000
• N, M, A and B are integers.

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Input

Input is given from Standard Input in the following format:

N M A B

Output

If it is impossible to place all the tiles, print NO. Otherwise, print the following:

YES
c11…c1M
:
cN1…cNM

Here, cij must be one of the following characters: ., <, >, ^ and v. Represent an arrangement by using each of these characters as follows:

• When cij is ., it indicates that the square at the i-th row and j-th column is empty;
• When cij is <, it indicates that the square at the i-th row and j-th column is covered by the left half of a 1×2 tile;
• When cij is >, it indicates that the square at the i-th row and j-th column is covered by the right half of a 1×2 tile;
• When cij is ^, it indicates that the square at the i-th row and j-th column is covered by the top half of a 2×1 tile;
• When cij is v, it indicates that the square at the i-th row and j-th column is covered by the bottom half of a 2×1 tile.

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Sample Input 1

Copy

3 4 4 2

Sample Output 1

Copy

YES
<><>
^<>^
v<>v

This is one example of a way to place four 1×2 tiles and three 2×1 tiles on a 3×4 grid.

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Sample Input 2

Copy

4 5 5 3

Sample Output 2

Copy

YES
<>..^
^.<>v
v<>.^
<><>v

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Sample Input 3

Copy

7 9 20 20

Sample Output 3

Copy

NO

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C这是要大力模拟？没有想到好做法

抄了一个思路

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int m,n,a,b;
char c[1005][1005];
int main()
{
    scanf("%d%d%d%d",&m,&n,&a,&b);
    for(int i=1; i<=m; i++)
        for(int j=1; j<=n; j++)c[i][j]='.';
    if(n&1)
    {
        for(int i=1; i<m&&b; i+=2)
            c[i][n]='^',c[i+1][n]='v',b--;
    }
    if((b&1)&&(m&1)&&n>2&&m>1)
        c[m-1][n-2]='^',c[m][n-2]='v',b--;
    for(int i=1; i<m; i++)
        for (int j=1; j<=n-(n&1)&&b; j++)
            if(c[i][j]=='.'&&c[i+1][j]=='.')
                c[i][j]='^',c[i+1][j]='v',b--;
    for(int i=1; i<=m; i++)
        for(int j=1; j<n&&a; j++)
            if(c[i][j]=='.'&&c[i][j+1]=='.')
                c[i][j]='<',c[i][j+1]='>',a--;
    if(a||b)
        puts("NO");
    else
    {
        puts("YES");
        for(int i=1; i<=m; i++)printf("%s
",c[i]+1);
    }
    return 0;
}

D - Reversed LCS

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Time limit : 2sec / Memory limit : 256MB

Score : 900 points

Problem Statement

Takahashi has decided to give a string to his mother.

The value of a string T is the length of the longest common subsequence of T and T', where T' is the string obtained by reversing T. That is, the value is the longest length of the following two strings that are equal: a subsequence of T (possibly non-contiguous), and a subsequence of T' (possibly non-contiguous).

Takahashi has a string S. He wants to give her mother a string of the highest possible value, so he would like to change at most Kcharacters in S to any other characters in order to obtain a string of the highest possible value. Find the highest possible value achievable.

Constraints

• 1≤|S|≤300
• 0≤K≤|S|
• S consists of lowercase English letters.
• K is an integer.

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Input

Input is given from Standard Input in the following format:

S
K

Output

Print the highest possible value achievable.

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Sample Input 1

Copy

abcabcabc
1

Sample Output 1

Copy

7

Changing the first character to c results in cbcabcabc. Let this tring be T, then one longest common subsequence of T and T' is cbabcbc, whose length is 7.

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Sample Input 2

Copy

atcodergrandcontest
3

Sample Output 2

Copy

15

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一个字符串S，你可以改变其中k个字母，使其变为T，T和T的反转串T' 最长公共子串长度

相当于再求回文串，我改变or不改变然后向内向左扩展就可以了，记忆化搜索避免超时

#include<bits/stdc++.h>
using namespace std;
const int N=305;
string s;
int dp[305][305][305],K;
int dfs(int l,int r,int x)
{
    if(r<l)return 0;
    if(l==r)return 1;
    if(dp[l][r][x]!=-1)return dp[l][r][x];//记忆化思想，减少搜索次数
    int t=max(dfs(l+1,r,x),dfs(l,r-1,x));//向左或右扩展一个
    if(s[l]==s[r])t=max(t,dfs(l+1,r-1,x)+2);//相等，进行扩展
    else if(x)t=max(t,dfs(l+1,r-1,x-1)+2);//改变一个字符，向内扩展
    return dp[l][r][x]=t;
}
int main()
{
    cin>>s>>K;
    memset(dp,-1,sizeof(dp));
    cout<<dfs(0,s.size()-1,K)<<endl;
    return 0;
}

E - Ball Eat Chameleons

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Time limit : 2sec / Memory limit : 256MB

Score : 1200 points

Problem Statement

In Republic of AtCoder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets. Ringo keeps NSnuke Chameleons in a cage.

A Snuke Chameleon that has not eaten anything is blue. It changes its color according to the following rules:

• A Snuke Chameleon that is blue will change its color to red when the number of red balls it has eaten becomes strictly larger than the number of blue balls it has eaten.
• A Snuke Chameleon that is red will change its color to blue when the number of blue balls it has eaten becomes strictly larger than the number of red balls it has eaten.

Initially, every Snuke Chameleon had not eaten anything. Ringo fed them by repeating the following process K times:

• Grab either a red ball or a blue ball.
• Throw that ball into the cage. Then, one of the chameleons eats it.

After Ringo threw in K balls, all the chameleons were red. We are interested in the possible ways Ringo could have thrown in Kballs. How many such ways are there? Find the count modulo 998244353. Here, two ways to throw in balls are considered different when there exists i such that the color of the ball that are thrown in the i-th throw is different.

Constraints

• 1≤N,K≤5×105
• N and K are integers.

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Input

Input is given from Standard Input in the following format:

N K

Output

Print the possible ways Ringo could have thrown in K balls, modulo 998244353.

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Sample Input 1

Copy

2 4

Sample Output 1

Copy

7

We will use R to represent a red ball, and B to represent a blue ball. There are seven ways to throw in balls that satisfy the condition: BRRR, RBRB, RBRR, RRBB, RRBR, RRRB and RRRR.

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Sample Input 2

Copy

3 7

Sample Output 2

Copy

57

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Sample Input 3

Copy

8 3

Sample Output 3

Copy

0

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Sample Input 4

Copy

8 10

Sample Output 4

Copy

46

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Sample Input 5

Copy

123456 234567

Sample Output 5

Copy

857617983

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给你n，k