AtCoder Beginner Contest 086 (ABCD)

A - Product

题目链接:https://abc086.contest.atcoder.jp/tasks/abc086_a

Time limit : 2sec / Memory limit : 256MB

Score : 100 points

Problem Statement

AtCoDeer the deer found two positive integers, a and b. Determine whether the product of a and b is even or odd.

Constraints

  • 1  a,b  10000
  • a and b are integers.

Input

Input is given from Standard Input in the following format:

a b

Output

If the product is odd, print Odd; if it is even, print Even.


Sample Input 1

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3 4

Sample Output 1

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Even

As 3×4=12 is even, print Even.


Sample Input 2

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1 21

Sample Output 2

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Odd

As 1×21=21 is odd, print Odd.

 #include<bits/stdc++.h>
using namespace std; int main()
{
int a,b;
while(cin>>a>>b){
if((a*b)%==) cout<<"Even"<<endl;
else cout<<"Odd"<<endl;
}
return ;
}

B - 1 21

题目链接:https://abc086.contest.atcoder.jp/tasks/abc086_b

Time limit : 2sec / Memory limit : 256MB

Score : 200 points

Problem Statement

AtCoDeer the deer has found two positive integers, a and b. Determine whether the concatenation of a and b in this order is a square number.

Constraints

  • 1  a,b  100
  • a and b are integers.

Input

Input is given from Standard Input in the following format:

a b

Output

If the concatenation of a and b in this order is a square number, print Yes; otherwise, print No.


Sample Input 1

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1 21

Sample Output 1

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Yes

As 121 = 11 × 11, it is a square number.


Sample Input 2

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100 100

Sample Output 2

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No

100100 is not a square number.


Sample Input 3

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12 10

Sample Output 3

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No

题解:直接判断是否能开方

 #include<bits/stdc++.h>
using namespace std;
bool prime(int x)
{
int y=sqrt(x);
return y*y==x;
}
int main()
{
int a,b;
while(cin>>a>>b){
if(a<b) swap(a,b);
int flag=;
if(a<&&b<){
if(prime(a+*b)||prime(a*+b)) flag=;
}
else if(a>=&&a<&&b<){
if(prime(a+*b)||prime(a*+b)) flag=;
}
else if(a>=&&a<&&b>=&&b<){
if(prime(a+*b)||prime(a+*b)) flag=;
}
else if(a==&&b>=&&b<){
if(prime(a+*b)||prime(a*+b)) flag=;
}
if(flag) cout<<"Yes"<<endl;
else cout<<"No"<<endl;
}
return ;
}

C - Traveling

题目链接:https://abc086.contest.atcoder.jp/tasks/arc089_a

C - Traveling


Time limit : 2sec / Memory limit : 256MB

Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane. In his plan, he will depart from point (0,0) at time 0, then for each i between 1 and N (inclusive), he will visit point (xi,yi) at time ti.

If AtCoDeer is at point (x,y) at time t, he can be at one of the following points at time t+1(x+1,y)(x−1,y)(x,y+1) and (x,y−1). Note that he cannot stay at his place. Determine whether he can carry out his plan.

Constraints

  • 1  N  105
  • 0  xi  105
  • 0  yi  105
  • 1  ti  105
  • ti < ti+1 (1  i  N−1)
  • All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t1 x1 y1
t2 x2 y2
:
tN xN yN

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.


Sample Input 1

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2
3 1 2
6 1 1

Sample Output 1

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Yes

For example, he can travel as follows: (0,0)(0,1)(1,1)(1,2)(1,1)(1,0), then (1,1).


Sample Input 2

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1
2 100 100

Sample Output 2

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No

It is impossible to be at (100,100) two seconds after being at (0,0).


Sample Input 3

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2
5 1 1
100 1 1

Sample Output 3

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No

题解:判断纵坐标和横坐标之后是否大于t 如果大于再减去t判断是否能够被我整除
 #include<bits/stdc++.h>
using namespace std;
bool test(int t,int x,int y)
{
int z=x+y;
if(t<z) return ;
else{
if((t-z)%==) return ;
else return ;
}
}
int main()
{
int n;
while(cin>>n){
int t,x,y;
int flag=;
while(n--){
cin>>t>>x>>y;
if(!test(t,x,y)) flag=;
}
if(flag) cout<<"Yes"<<endl;
else cout<<"No"<<endl;
}
return ;
}

D - Checker (前缀和)

题目链接:https://abc086.contest.atcoder.jp/tasks/arc089_b

Time limit : 2sec / Memory limit : 256MB

Score : 500 points

Problem Statement

AtCoDeer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K. Here, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K × K square. Below is an example of a checked pattern of side 3:

AtCoder Beginner Contest 086 (ABCD)

AtCoDeer has N desires. The i-th desire is represented by xiyi and ci. If ci is B, it means that he wants to paint the square (xi,yi) black; if ci is W, he wants to paint the square (xi,yi) white. At most how many desires can he satisfy at the same time?

Constraints

  • 1  N  105
  • 1  K  1000
  • 0  xi  109
  • 0  yi  109
  • If i  j, then (xi,yi)  (xj,yj).
  • ci is B or W.
  • NKxi and yi are integers.

Input

Input is given from Standard Input in the following format:

N K
x1 y1 c1
x2 y2 c2
:
xN yN cN

Output

Print the maximum number of desires that can be satisfied at the same time.


Sample Input 1

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4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

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4

He can satisfy all his desires by painting as shown in the example above.


Sample Input 2

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2 1000
0 0 B
0 1 W

Sample Output 2

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2

Sample Input 3

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6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

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4

题解:思路是对的 但是暴力过不了 看看大佬的解法 转自:https://www.cnblogs.com/8023spz/p/8409399.html

这道题数据挺大的,首先是移动到2k*2k的框框里,不影响坐标(也就是横纵坐标都移动2k的整数倍,如果只移动k的整数倍不能保证颜色不变)。
最初先默认数黑色或者白色都可以,这里先默认数黑色,白色的通过变色移动(横或纵坐标+k)映射到黑色的位置,然后整个图里只剩下黑色的。
最后求出结果,只需要取sum 和 n - sum中大的那个就行了,因为默认是黑色,黑白可以互换。
然后是移动k宫格在不同位置,一共有k*k种情况,直接在2k*2k的框框里操作,需要计算二维前缀和,之前是一个一个点去判断超时了,想想也不能一味的暴力啊,肯定得用点妙招,然后移动x轴,计算一维前缀和时间勉强没超。
k宫格是从左下角开始移动就是从(0,0)开始,需要记录的是k宫格里黑色的个数,以及斜对角的矩形里黑色的个数,因为斜对角的颜色相同,横竖相邻的区域颜色相异。
计算二维前缀和需要用离散学的容斥定理,最后求单独区域需要前缀和相减,也要用到容斥定理。
 #include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iomanip> using namespace std; int v[][];
int n,k;
int num(int x1,int y1,int x2,int y2){
return v[x2][y2] - v[x2][y1] - v[x1][y2] + v[x1][y1];///前缀和 减去左边 下边和左下边的k宫格前缀和 容斥定理:左边和下边都包含了左下边 需要加上一个左下边
}
int main()
{
int x,y,ans = ,sum;
char ch;
scanf("%d%d",&n,&k);
for(int i = ;i <= n;i ++){
scanf("%d%d %c",&x,&y,&ch);
x %= * k;///把所有点都移动到 2k * 2k 的区域
y %= * k;
x += k * (ch == 'W');///x可以变成y W 也可以变成 B 这里白色都变成黑色的 如果转换后的黑色是满足的那么原来的白色也一定是满足的
v[x % ( * k) + ][y % ( * k) + ] ++;///求前缀和要求从(1,1)开始
}
for(int i = ;i <= * k;i ++)///求前缀和
for(int j = ;j <= * k;j ++)
v[i][j] += v[i - ][j] + v[i][j - ] - v[i - ][j - ];///加上左边下边和左下角的和 容斥定理:左边和下边的都包含了左下边的 要减去一个左下边的for(int i = 1;i <= k;i++)///k * k个格子依次做为起点构成新的k宫格 也就是移动k宫格 看看有几个黑色点包含在内 (默认黑色 可互换)
for(int j = 1;j <= k;j++)
{
///斜对角的k宫格是相同颜色 2k * 2k区域最多有五个这样的区域
sum = num(,,i,j) + num(i,j,k + i,k + j) + num(k + i,k + j, * k, * k) + num(k + i,, * k,j) + num(,k + j,i, * k);
ans = max(ans,max(sum,n - sum));///黑白色可以互换
}
printf("%d\n",ans);
}
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