A 跑步训练
小明要做一个跑步训练。
初始时，小明充满体力，体力值计为10000。如果小明跑步，每分钟损耗600 的体力。
如果小明休息，每分钟增加 300 的体力。体力的损耗和增加都是均匀变化的。
小明打算跑一分钟、休息一分钟、再跑一分钟、再休息一分钟……如此循环。
如果某个时刻小明的体力到达0，他就停止锻炼。
请问小明在多久后停止锻炼。为了使答案为整数，请以秒为单位输出答案。
答案中只填写数，不填写单位。
答案
直接口算就可以了，需要注意的是，答案以秒输出，而且不一定是整分钟，并且是到0就停止，所以可能加上300是满600的，但是却没有办法跑整1分钟。
$10000÷300=32......400$
$400÷10=40$
$40+32×2×60=3880$
⭐⭐一定要细心！！
B 纪念日
2020 年 7 月 1 日是中国某党成立 99 周年纪念日。中国某党成立于 1921 年 7 月 23 日。
请问从 1921 年 7 月 23 日中午 12 时到 2020 年 7 月 1 日中午 12 时一含多少分钟？
答案
52038720
日期模拟
#include<iostream>
using namespace std;
int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
int main(){
int y=1921,m=7,d=23,res=0;
while(1){
if(y==2020&&m==7&&d==1) break;
d++;
if((y%4==0&&y%100!=0)||(y%400==0)) day[2]=29;
else day[2]=28;
if(d>day[m]){
m++;
d=1;
if(m>12){
y++;
m=1;
}
}
res++;
}
cout<<res*24*60;
}
一定要注意闰年的判断时是：
可以被4整除但不能被100整除，或者可以被400整除的是闰年！
C 合并检测
新冠疫情由新冠病毒引起，最近在 A 国蔓延，为了尽快控制疫情，A 国准备给大量民众进病毒核酸检测。
然而，用于检测的试剂盒紧缺。为了解决这一困难，科学家想了一个办法：合并检测。
即将从多个人（k个）采集的标本放到同一个试剂盒中进行检测。
如果结果为阴性，则说明这 k个人都是阴性，用一个试剂盒完成了 k 个人的检测。
如果结果为阳性，则说明至少有一个人为阳性，需要将这 k 个人的样本全部重新独立检测
（从理论上看，如果检测前 k - 1 个人都是阴性可以推断出第k个人是阳性，但是在实际操作中不会利用此推断，而是将k 个人独立检测），加上最开始的合并检测，一共使用了 k + 1 个试剂盒完成了 k 个人的检测。
A 国估计被测的民众的感染率大概是 1%，呈均匀分布。请问 k 取多少能最节省试剂盒？
答案
10
如果k>100，那么每组都会出现患者，合并检测没有意义，故而k<100
以100人讨论
k人一组，则总组数为100/k
其中100人中有1人患病，即对应有一组需要k+1个试剂盒
故而总试剂盒数为 100/k+k
k取10时取得最小值
D REPEAT 程序
附件 prog.txt 中是一个用某种语言写的程序。
其中 REPEAT k 表示一个次数为 k 的循环。循环控制的范围由缩进表达，
从次行开始连续的缩进比该行多的（前面的空白更长的）为循环包含的内容。
请问该程序执行完毕之后，A 的值是多少？
(计算数据在文末)
样例
输入
REPEAT 2:
A = A + 4
REPEAT 5:
REPEAT 6:
A = A + 5
A = A + 7
A = A + 8
A = A + 9
A = A + 4 所在的行到 A = A + 8 所在的行都在第一行的循环两次中。
REPEAT 6: 所在的行到 A = A + 7 所在的行都在 REPEAT 5: 循环中。
A = A + 5 实际总共的循环次数是 2 × 5 × 6 = 60 次。
答案
241830
思路
数空格，计算每一层对应的权值（乘上上一层权值），之后对应进行计算即可
C++ 代码
#include<iostream>
#include<string>
#include<cstring>
using namespace std;
string s[1010];
int q[20];
int res=0;
int main(){
for(int i=0;i<1000;i++){
getline(cin,s[i]);
}
//初始化权值为1（用memset会得出错误答案，暂不知为什么）
for(int i=0;i<20;i++){
q[i]=1;
}
for(int i=0;i<1000;i++){
int j=0;
for(;s[i][j]==' ';j++);
if(s[i][j]=='R'){
q[j/4+1]=(s[i][j+7]-'0')*q[j/4];
}
if(s[i][j]=='A'){
res+=(s[i][j+8]-'0')*q[j/4];
}
}
cout<<res;
return 0;
}
⭐⭐
使用getline(cin,s[i]);可以保存空格
使用s[i][j+7]-'0'可以char->int，同理还可以用-‘a’来确定做下标等
E 矩阵
把 1 ∼ 2020 放在 2 × 1010 的矩阵里。
要求同一行中右边的比左边大，列中下边的比上边的大。一共有多少种方案？
答案很大，你只需要给出方案数除以 2020 的余数即可。
答案
1340
思路
线性DP，类似于AcWing中898线性三角形的题目。
正推反推，分类讨论，确定状态数组及转移方程。
正推枚举几种情况：（其实反推会更利于写状态转移方程）
数字1一定放在(1,1)的位置
分类讨论：
当第一行数量>第二行时，可以放在第一行或者第二行
当第二行数量=第一行时，只可以放在第一行
状态数组：
$f[i][j]$：数字0~i，第一行放j个数，有多少种方法
状态转移方程：
if(j<i-j) continue;
f[i][j]+= f[i-1][j-1]; //一定可以放在第一行
if(j>=i-j) f[i][j]+=f[i-1][j]; //可以放在第二行的情况(需要反推一下)
C++ 代码
#include<iostream>
using namespace std;
int mp[2025][1015];
int main(){
mp[1][1]=1;
int res=0;
for(int i=2;i<=2020;i++){
for(int j=1;j<=i;j++){
if(j<i-j) continue;
mp[i][j]+= mp[i-1][j-1]; //一定可以放在第一行
if(j>=i-j) mp[i][j]+=mp[i-1][j]; //可以放在第二行的情况
mp[i][j]%=2020;
}
}
cout<<mp[2020][1010];
return 0;
}
附件
题D计算数据
A = 0
REPEAT 2:
A = A + 4
REPEAT 5:
REPEAT 6:
A = A + 5
A = A + 7
REPEAT 6:
A = A + 7
REPEAT 4:
A = A + 2
A = A + 7
A = A + 2
REPEAT 7:
REPEAT 4:
A = A + 8
A = A + 7
A = A + 4
A = A + 5
A = A + 8
REPEAT 8:
A = A + 5
REPEAT 1:
A = A + 2
REPEAT 7:
A = A + 5
A = A + 5
REPEAT 2:
REPEAT 3:
A = A + 1
A = A + 1
REPEAT 5:
A = A + 1
REPEAT 9:
REPEAT 6:
A = A + 5
A = A + 1
REPEAT 6:
A = A + 2
A = A + 8
A = A + 3
REPEAT 2:
A = A + 5
REPEAT 3:
A = A + 9
REPEAT 1:
A = A + 4
REPEAT 2:
A = A + 9
REPEAT 1:
A = A + 6
A = A + 6
A = A + 4
REPEAT 3:
A = A + 7
A = A + 1
REPEAT 2:
A = A + 3
REPEAT 5:
A = A + 2
A = A + 5
A = A + 2
A = A + 4
A = A + 3
REPEAT 4:
A = A + 4
A = A + 3
A = A + 7
REPEAT 5:
REPEAT 4:
A = A + 5
A = A + 7
REPEAT 5:
A = A + 3
REPEAT 3:
A = A + 3
A = A + 1
A = A + 8
A = A + 2
REPEAT 9:
A = A + 5
REPEAT 1:
A = A + 5
A = A + 2
A = A + 8
A = A + 6
REPEAT 3:
REPEAT 4:
A = A + 9
REPEAT 5:
A = A + 2
A = A + 1
REPEAT 9:
A = A + 9
A = A + 2
REPEAT 1:
A = A + 6
A = A + 8
REPEAT 2:
A = A + 9
A = A + 4
A = A + 7
REPEAT 2:
REPEAT 7:
A = A + 3
A = A + 5
REPEAT 3:
A = A + 5
A = A + 3
A = A + 6
A = A + 4
REPEAT 9:
A = A + 2
A = A + 8
A = A + 2
A = A + 3
REPEAT 2:
REPEAT 8:
A = A + 5
A = A + 1
A = A + 6
A = A + 1
A = A + 2
REPEAT 6:
REPEAT 1:
A = A + 3
REPEAT 1:
A = A + 2
REPEAT 4:
A = A + 7
A = A + 1
A = A + 8
REPEAT 6:
A = A + 5
REPEAT 6:
A = A + 3
REPEAT 2:
A = A + 2
A = A + 9
A = A + 7
REPEAT 9:
A = A + 8
REPEAT 9:
A = A + 8
A = A + 9
A = A + 3
A = A + 2
REPEAT 6:
A = A + 3
REPEAT 9:
A = A + 1
A = A + 9
A = A + 5
REPEAT 2:
A = A + 4
A = A + 9
A = A + 8
REPEAT 5:
A = A + 6
A = A + 9
A = A + 1
REPEAT 1:
A = A + 4
A = A + 2
REPEAT 9:
REPEAT 3:
A = A + 4
REPEAT 7:
A = A + 8
A = A + 3
REPEAT 5:
A = A + 9
REPEAT 8:
A = A + 9
A = A + 8
REPEAT 4:
A = A + 7
A = A + 7
A = A + 3
A = A + 5
REPEAT 6:
A = A + 7
REPEAT 7:
A = A + 2
A = A + 2
A = A + 1
REPEAT 8:
REPEAT 1:
REPEAT 4:
A = A + 6
A = A + 6
A = A + 2
REPEAT 5:
A = A + 4
A = A + 8
A = A + 4
REPEAT 1:
A = A + 5
REPEAT 7:
A = A + 8
REPEAT 6:
A = A + 4
A = A + 4
A = A + 8
REPEAT 4:
A = A + 2
REPEAT 2:
A = A + 4
REPEAT 2:
A = A + 3
REPEAT 1:
A = A + 2
A = A + 8
REPEAT 2:
A = A + 7
REPEAT 8:
A = A + 6
A = A + 1
A = A + 7
REPEAT 8:
A = A + 2
REPEAT 8:
REPEAT 6:
A = A + 1
A = A + 6
REPEAT 2:
A = A + 4
A = A + 1
A = A + 7
A = A + 4
REPEAT 4:
REPEAT 9:
A = A + 2
REPEAT 1:
A = A + 2
A = A + 5
REPEAT 8:
REPEAT 6:
A = A + 3
REPEAT 4:
A = A + 1
A = A + 6
A = A + 1
REPEAT 7:
A = A + 7
REPEAT 7:
A = A + 3
A = A + 9
A = A + 1
A = A + 9
REPEAT 3:
A = A + 5
A = A + 5
A = A + 6
A = A + 2
REPEAT 1:
A = A + 4
REPEAT 2:
A = A + 7
REPEAT 1:
A = A + 7
REPEAT 4:
A = A + 7
A = A + 2
REPEAT 5:
A = A + 9
A = A + 1
A = A + 9
A = A + 5
A = A + 9
REPEAT 5:
A = A + 5
REPEAT 1:
A = A + 6
REPEAT 2:
A = A + 3
A = A + 2
A = A + 6
A = A + 8
A = A + 8
A = A + 7
A = A + 5
A = A + 5
REPEAT 2:
A = A + 1
A = A + 7
A = A + 3
REPEAT 2:
A = A + 7
A = A + 1
A = A + 4
REPEAT 1:
REPEAT 7:
REPEAT 2:
A = A + 3
A = A + 5
A = A + 2
A = A + 6
A = A + 1
A = A + 2
A = A + 4
A = A + 9
REPEAT 1:
A = A + 8
REPEAT 8:
REPEAT 4:
REPEAT 8:
A = A + 4
REPEAT 3:
A = A + 1
A = A + 8
REPEAT 7:
A = A + 8
REPEAT 7:
A = A + 7
A = A + 7
REPEAT 7:
A = A + 6
REPEAT 5:
A = A + 9
A = A + 3
REPEAT 4:
A = A + 5
A = A + 5
A = A + 4
REPEAT 9:
REPEAT 3:
A = A + 4
A = A + 3
A = A + 6
REPEAT 1:
A = A + 3
A = A + 3
A = A + 6
REPEAT 6:
A = A + 7
A = A + 7
A = A + 5
A = A + 5
A = A + 1
A = A + 2
A = A + 6
A = A + 6
REPEAT 9:
A = A + 6
REPEAT 1:
REPEAT 2:
A = A + 4
A = A + 7
REPEAT 3:
A = A + 6
REPEAT 5:
A = A + 3
A = A + 6
REPEAT 9:
A = A + 3
A = A + 6
REPEAT 5:
A = A + 8
A = A + 8
REPEAT 3:
A = A + 7
A = A + 9
A = A + 8
A = A + 3
A = A + 3
A = A + 9
REPEAT 6:
A = A + 9
A = A + 1
REPEAT 4:
REPEAT 1:
A = A + 7
REPEAT 9:
A = A + 2
A = A + 9
A = A + 1
A = A + 2
A = A + 8
A = A + 7
A = A + 9
A = A + 6
REPEAT 4:
REPEAT 2:
A = A + 3
REPEAT 3:
A = A + 4
A = A + 4
REPEAT 6:
A = A + 6
A = A + 1
A = A + 5
A = A + 8
REPEAT 2:
A = A + 6
REPEAT 1:
REPEAT 2:
A = A + 2
REPEAT 3:
A = A + 1
REPEAT 1:
A = A + 8
A = A + 7
A = A + 4
A = A + 2
A = A + 8
A = A + 4
REPEAT 5:
REPEAT 6:
A = A + 8
REPEAT 9:
A = A + 5
A = A + 5
REPEAT 5:
A = A + 5
REPEAT 3:
REPEAT 5:
A = A + 4
REPEAT 4:
A = A + 6
A = A + 3
REPEAT 7:
A = A + 3
A = A + 3
A = A + 1
A = A + 7
A = A + 7
A = A + 6
A = A + 5
A = A + 5
A = A + 6
REPEAT 1:
A = A + 9
A = A + 3
REPEAT 1:
REPEAT 1:
A = A + 1
REPEAT 8:
A = A + 5
REPEAT 8:
A = A + 6
REPEAT 4:
A = A + 9
A = A + 4
REPEAT 2:
A = A + 3
A = A + 7
REPEAT 5:
A = A + 7
A = A + 5
A = A + 8
A = A + 7
A = A + 8
A = A + 5
REPEAT 2:
A = A + 5
A = A + 7
A = A + 8
A = A + 5
A = A + 9
REPEAT 2:
REPEAT 6:
A = A + 9
A = A + 1
A = A + 8
A = A + 7
A = A + 1
A = A + 5
REPEAT 3:
A = A + 3
A = A + 9
A = A + 7
REPEAT 3:
A = A + 9
A = A + 1
REPEAT 6:
A = A + 1
REPEAT 9:
REPEAT 7:
A = A + 3
REPEAT 5:
A = A + 5
A = A + 8
A = A + 8
A = A + 1
A = A + 2
REPEAT 4:
A = A + 6
REPEAT 3:
A = A + 3
A = A + 7
REPEAT 8:
REPEAT 1:
A = A + 7
A = A + 8
A = A + 3
A = A + 1
A = A + 2
A = A + 4
A = A + 7
REPEAT 1:
REPEAT 1:
REPEAT 1:
A = A + 4
A = A + 6
REPEAT 1:
A = A + 3
A = A + 9
A = A + 6
REPEAT 9:
A = A + 1
A = A + 6
REPEAT 5:
A = A + 3
A = A + 9
A = A + 5
A = A + 5
A = A + 7
A = A + 2
REPEAT 2:
A = A + 7
A = A + 7
REPEAT 7:
REPEAT 4:
A = A + 6
A = A + 8
REPEAT 6:
A = A + 6
REPEAT 2:
A = A + 1
A = A + 7
A = A + 6
A = A + 7
REPEAT 4:
REPEAT 7:
A = A + 1
REPEAT 2:
A = A + 2
A = A + 5
A = A + 8
A = A + 2
A = A + 1
A = A + 4
REPEAT 8:
A = A + 5
A = A + 6
REPEAT 7:
REPEAT 6:
REPEAT 9:
A = A + 7
A = A + 8
REPEAT 4:
A = A + 6
A = A + 4
A = A + 3
A = A + 6
REPEAT 9:
A = A + 3
REPEAT 9:
A = A + 2
A = A + 7
A = A + 5
A = A + 2
REPEAT 7:
REPEAT 8:
REPEAT 6:
A = A + 4
A = A + 9
A = A + 5
A = A + 3
A = A + 9
REPEAT 4:
REPEAT 1:
A = A + 6
A = A + 8
REPEAT 1:
A = A + 6
A = A + 4
A = A + 6
REPEAT 3:
A = A + 7
REPEAT 3:
A = A + 4
A = A + 4
A = A + 2
A = A + 3
A = A + 7
REPEAT 5:
A = A + 6
A = A + 5
REPEAT 1:
REPEAT 8:
A = A + 5
REPEAT 3:
A = A + 6
REPEAT 9:
A = A + 4
A = A + 3
REPEAT 6:
REPEAT 2:
A = A + 1
A = A + 5
A = A + 2
A = A + 2
A = A + 7
REPEAT 4:
A = A + 7
A = A + 9
A = A + 2
REPEAT 8:
A = A + 9
REPEAT 9:
REPEAT 2:
A = A + 3
A = A + 2
A = A + 1
A = A + 5
REPEAT 9:
A = A + 1
A = A + 3
A = A + 9
REPEAT 7:
A = A + 2
REPEAT 5:
A = A + 9
A = A + 3
REPEAT 2:
A = A + 4
REPEAT 8:
A = A + 9
REPEAT 5:
A = A + 5
A = A + 4
A = A + 2
A = A + 4
REPEAT 6:
A = A + 2
REPEAT 5:
A = A + 7
A = A + 7
A = A + 8
A = A + 3
REPEAT 8:
A = A + 2
A = A + 5
REPEAT 1:
A = A + 8
A = A + 5
A = A + 1
A = A + 1
A = A + 5
REPEAT 2:
A = A + 6
REPEAT 6:
A = A + 9
A = A + 2
A = A + 5
REPEAT 4:
A = A + 7
A = A + 1
REPEAT 6:
A = A + 8
A = A + 4
REPEAT 3:
REPEAT 2:
A = A + 1
A = A + 5
REPEAT 2:
A = A + 7
REPEAT 9:
A = A + 6
A = A + 8
A = A + 9
A = A + 5
REPEAT 9:
REPEAT 3:
A = A + 7
A = A + 7
A = A + 9
A = A + 7
REPEAT 5:
A = A + 7
A = A + 2
A = A + 1
A = A + 8
A = A + 3
A = A + 5
A = A + 1
REPEAT 8:
A = A + 4
A = A + 2
A = A + 2
A = A + 8
REPEAT 4:
REPEAT 4:
A = A + 8
REPEAT 7:
A = A + 5
A = A + 2
REPEAT 2:
A = A + 6
REPEAT 4:
A = A + 8
A = A + 6
A = A + 1
A = A + 3
A = A + 2
A = A + 7
A = A + 4
REPEAT 8:
A = A + 2
A = A + 4
REPEAT 5:
REPEAT 3:
REPEAT 6:
A = A + 8
A = A + 1
A = A + 6
A = A + 5
A = A + 9
REPEAT 8:
A = A + 7
REPEAT 6:
A = A + 4
A = A + 5
REPEAT 3:
A = A + 1
REPEAT 1:
REPEAT 5:
A = A + 6
A = A + 2
REPEAT 9:
REPEAT 5:
A = A + 9
A = A + 3
REPEAT 9:
A = A + 9
A = A + 8
REPEAT 8:
REPEAT 5:
A = A + 9
A = A + 4
REPEAT 9:
A = A + 3
A = A + 4
A = A + 5
REPEAT 9:
REPEAT 7:
A = A + 5
REPEAT 3:
A = A + 7
REPEAT 9:
REPEAT 6:
A = A + 4
A = A + 6
REPEAT 5:
REPEAT 6:
A = A + 5
A = A + 3
A = A + 3
A = A + 3
A = A + 5
REPEAT 7:
A = A + 5
REPEAT 2:
A = A + 5
A = A + 6
REPEAT 2:
A = A + 2
A = A + 5
A = A + 3
A = A + 5
A = A + 5
REPEAT 4:
A = A + 2
A = A + 1
REPEAT 9:
A = A + 9
A = A + 5
A = A + 6
A = A + 2
A = A + 2
A = A + 5
REPEAT 9:
A = A + 5
A = A + 4
REPEAT 4:
REPEAT 4:
A = A + 1
A = A + 2
REPEAT 6:
A = A + 9
A = A + 3
REPEAT 2:
A = A + 5
A = A + 1
A = A + 1
A = A + 3
A = A + 8
REPEAT 7:
A = A + 4
REPEAT 6:
A = A + 9
REPEAT 5:
A = A + 9
A = A + 8
A = A + 3
A = A + 9
A = A + 4
A = A + 6
REPEAT 7:
A = A + 9
REPEAT 9:
A = A + 4
A = A + 9
A = A + 1
A = A + 3
REPEAT 5:
REPEAT 1:
A = A + 4
A = A + 4
REPEAT 8:
A = A + 9
A = A + 6
A = A + 2
REPEAT 3:
A = A + 4
A = A + 4
REPEAT 3:
A = A + 5
A = A + 2
A = A + 8
A = A + 3
A = A + 6
A = A + 4
A = A + 9
A = A + 1
A = A + 9
A = A + 5
A = A + 3
REPEAT 3:
A = A + 2
A = A + 5
A = A + 8
A = A + 2
A = A + 5
REPEAT 8:
REPEAT 2:
A = A + 6
A = A + 7
A = A + 6
A = A + 9
A = A + 2
REPEAT 2:
A = A + 3
REPEAT 8:
A = A + 7
A = A + 2
A = A + 1
A = A + 4
A = A + 1
A = A + 5
A = A + 2
A = A + 1
REPEAT 1:
A = A + 1
REPEAT 6:
A = A + 4
A = A + 3
A = A + 3
REPEAT 5:
A = A + 3
REPEAT 6:
REPEAT 1:
A = A + 5
A = A + 7
A = A + 7
A = A + 7
REPEAT 5:
A = A + 9
A = A + 7
REPEAT 5:
A = A + 9
A = A + 1
A = A + 9
A = A + 8
REPEAT 1:
A = A + 2
REPEAT 5:
A = A + 8
REPEAT 3:
A = A + 2
A = A + 9
A = A + 6
A = A + 3
REPEAT 5:
REPEAT 6:
A = A + 5
A = A + 5
REPEAT 4:
A = A + 5
A = A + 4
REPEAT 8:
A = A + 9
A = A + 1
REPEAT 8:
A = A + 8
A = A + 1
A = A + 4
REPEAT 6:
A = A + 6
REPEAT 2:
A = A + 3
A = A + 9
A = A + 6
A = A + 9
REPEAT 1:
A = A + 4
REPEAT 3:
A = A + 3
A = A + 4
A = A + 2
A = A + 8
REPEAT 2:
A = A + 4
A = A + 1
REPEAT 9:
A = A + 2
A = A + 9
A = A + 7
REPEAT 7:
REPEAT 7:
REPEAT 5:
A = A + 7
REPEAT 5:
A = A + 1
A = A + 1
REPEAT 5:
A = A + 6
REPEAT 1:
A = A + 4
REPEAT 9:
A = A + 4
A = A + 1
REPEAT 6:
A = A + 8
A = A + 5
REPEAT 1:
A = A + 4
REPEAT 5:
A = A + 8
A = A + 7
A = A + 2
REPEAT 3:
A = A + 3
REPEAT 8:
REPEAT 8:
A = A + 4
A = A + 7
REPEAT 5:
A = A + 1
REPEAT 8:
A = A + 7
A = A + 8
A = A + 4
A = A + 7
A = A + 6
A = A + 9
A = A + 5
REPEAT 3:
A = A + 5
REPEAT 9:
A = A + 1
A = A + 7
REPEAT 1:
A = A + 8
A = A + 4
REPEAT 8:
REPEAT 7:
A = A + 2
REPEAT 4:
A = A + 6
A = A + 6
REPEAT 1:
A = A + 7
A = A + 1
REPEAT 9:
REPEAT 5:
A = A + 6
A = A + 5
REPEAT 7:
A = A + 3
A = A + 6
A = A + 8
REPEAT 2:
A = A + 7
A = A + 1
A = A + 9
REPEAT 3:
REPEAT 3:
A = A + 5
