JXCPC 试题册
JXCPC 试题册
Input file: standard input
Output file: standard output
Time limit: 1s
Memory limit: 256 megabytes
Problem A. Cotree
Avin has two trees which are not connected. He asks you to add an edge between them to make them connected while minimizing the function \(\sum_{i=1}^{n} \sum_{j=i+1}^{n} dis(i,j)\)
,where dis(i,j) represents the number of edges of the path from i to j . He is happy with only the function value.
Input
The first line contains a number n(\(2 \leq n \leq 100,000\)). In each of the following n-2 lines , there are two numbers u and v , meaning that there is an edge between u and v .The input is guaranteed to contain exactly two trees.
Output
Just print the minimum function value
中文简述题意
给出两棵树T1,T2，连接一条边使得这两颗树合成一棵树，你所连的边要使\(\sum_{i=1}^{n} \sum_{j=i+1}^{n} dis(i,j)\)最小，dis(i,j)指链接i,j的简单路径所含边的数目
Example
-
Input
3 1 2 -
Output
4
Problem B.Math
Avin sells robots to clients. At second 0,Avin is at the location (0,0) on a number axis with a robot. He wants to go to (L,0) with the robot. He walks a unit distance per second , and he can only stop at integer coordinates. Now he decides to follow these walking rules repeatedly until he arrives (L,0) with the robot :
-
- If Avin has the robot with himself,the robot may be dropped down with probability p
-
- If Avin had dropped the robot , he will figure it out with probability q. Specially, if Avin arrives at (L,0) without robot , he will trun around immediately
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- If Avin does not see that the robot had been dropped, he walks one step right; otherwise, he walks left until he is at the same location as the robot.
What is the expectation of walking time he needs to arrive (L,0) with the robot.
中文简述题意
Avin要带着机器人从0走到L，走路速度为每秒一格并且只会在整数格停下，他走路按照以下规则：
- 如果Avin没有弄丢机器人，则有p的概率弄丢机器人
- 如果Avin已经弄丢了机器人，则有q的概率发现，特别的，当他到达终点却没有机器人时，会立刻发现
- 如果Avin发现他弄丢了机器人，则会一直往左走直到遇见机器人，否则他会向右走一格
Input
One line with three numbers L,p and q, where L(\(1\leq L \leq100,000\)) is an integer,p and q are real numbers with three digits and within(0,1)
Output
Print the expected walking time . Your answer is considered correct if the absolute or relative error doesn't exceed \(10^{-6}\).Formally, let you answer be a , and the jury's answer be b. Your answer is considered correct if \(\frac{|a-b|}{max(1,|b|)} \leq 10^{-6}\)
Problem C.Trap
GuGuGu
Problem D.Wave
Avin is studying series. A series is called "wave" if the following conditions are satiffied:
-
It contains at least two elements
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All elements at odd positions are the same
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All elements at even positions are the same
-
Elements at odd positions are NOT the same as the elements at even positions
You are given a series with length n. Avin asks you to find the longest "wave" subseries. A subseries is a subsequence of a series.
Input
The first line contains two numbers n,c(\(1 \leq n \leq 100,000, 1 \leq c \leq 100\)). The second line contains n integers whose range is [1,c] , which represents the series. It is guaranteed that there is always a "wave" subseries.
Output
Print the length of the longest "wave" subseries.
插几句嘴qwq
本题考试时\(O(nc^2)\)可以通过,实际上\(O(nc^2) \leq O(10^5 \times (10^2)^2) = O(10^9)\),不能通过
所以很迷...我写的是\(O(nc)\)
Example
-
Input
5 3 1 2 1 3 2 -
Output
4
Problem E.Packing
GuGuGu
Problem F.String
Avin has a string. He would like to uniform-randomly select four characters (selecting the same character is allowed) from it. You are asked to calculate to probability of four characters being "avin" in order.
Input
The first line contains n(\(1 \leq n \leq 100\)), the length of the string. The second line contains the string. To simplify the problem , the characters of the string are from 'a' , 'v' , 'i' , 'n'.
Output
Print the reduced fraction (the greatest common divisor of the numerator and denominator is 1),representing the probability. If the answer is 0 , you should output "0/1"
Example
-
Input1
4 avin -
Output1
1/256 -
Input2
4 aaaa -
Output2
0/1
Problem G.Traffic
GuGuGu
Problem H.RNG(RNG 牛逼)
Avin is studying how to synthesize data . Given a integer n, he constructs ans interval using the following method: He first generates a integer r between 1 and n (both inclusize) uniform-randomly, and generates a integer l between 1 and r (both inclusize) uniform-randomly. The interval [l,r] is the constructed. Avin has constructed two intervals using the method above. He asks you what the probalility that two intervals intersect(相交) is. You should print \(q \times q^{-1}(MOD 1,000,000,007)\), while \(\frac{p}{q}\) denoting the probalility.
Input
Just one line contains the number n (\(1 \leq n \leq 1,000,000\))
Output
Print the answer
Example
-
Input1
1 -
Output1
1 -
Input2
2 -
Output2
750000006
Problem I.Budget
Avin's company has many ongoing projects with difference budgets. His company records the budgets using numbers rounded to 3 digits after the decimal place.However, the company is updating the system and all budgets will be rounded up to 2 digits after the decimal place. For example, 1.004 will be rounded down to 1.00 while 1.995 will be rounded up to 2.00. Avin wants to konw the difference of the total budget caused by update.
Input
The first line contains an integer n(\(1 \leq n \leq 1,000\)). The second line contains n decimals, and the i-th decimal \(a_i\)(\(0 \leq n \leq 10^{18}\)) repersents the budget of the i-th project. All decimals are rounded to 3 digits.
Output
Print the difference rounded to 3 digits.
Example
-
Input1
1 1.001 -
Output1
-0.001 -
Input2
1 0.999 -
Output2
0.001 -
Input3
2 1.001 0.999 -
Output3
0.000
Problem J.Worker
Avin meets a rich customer today. He will earn 1 million dollars if he can solve a hard problem. There are n warehouses and m workers. Any worker in the i-th warehouse can handle \(a_i\) orders per day. The customer wonders whether there exists one worker assignment method satiisfying that every warehouse handles the ssame number of orders every day. Note that each worker should be assigned to exactly warehouse and no worker is lazy when working.
Input
The first line contains two integers n(\(1 \leq n \leq 1,000\)) ,m(\(1 \leq m \leq 10^{18}\)). The second lie contains n integers. The i-th integer \(a_i\) (\(1 \leq a_i \leq 10\)) represensts one worker in the i-th warehouse can handle \(a_i\) orders per day.
Output
If there is feasible assignment method, orint "Yes" in the first line. Then , i th second line, print n integers with i-th integer representing the number of workers assigned too the i-th warehouse. Otherwise , print "No" in one line. If there are multiple solutions, any is accepted.
Example
-
Input1
2 6 1 2 -
Output1
Yes 4 2 -
Input2
2 5 1 2 -
Output2
No
Problem K.Class
Avin has two integers a,b(\(1 \leq a,b \leq 1,000\)).
Given x=a+b and y=a-b, can you calculate a*b?
Input
The first line contains two integers x,y.
Output
Print the result of a*b.
Example
-
Input1
4 2 -
Output1
3
