m0_54132659 2021-03-10 11:20 采纳率: 83.3%

# c# 编程题，请会的大佬直接留下代码，输入输出得一致

Here is a wheel with 10 numbers:

Suppose that the wheel begins in the position above. We are given an integer N in the range 0 ≤ N ≤ 100. We will spin the wheel three times. On each of the three spins, the wheel will rotate counterclockwise by a number of positions randomly chosen (uniformly) from the integers 0 .. N. For example, if N = 3, then on each spin there is

• a 1/4 chance that it will not rotate
• a 1/4 chance that it will rotate by 1 position
• a 1/4 chance that it will rotate by 2 positions
• a 1/4 chance that it will rotate by 3 positions

What is the exact probability that after the 3 spins the wheel will end up in the same position in which it started, i.e. pointing to number 1?

Write a program that can answer this question. The program should read the integer N on a single line of standard input, and write the answer as a fraction in reduced form.

Sample input:

``````3
``````

Output:

``````1/64
``````

Explanation: When N = 3, the wheel cannot possibly make a complete rotation in 3 spins. So it will end up at the starting position only if it never moves. On each spin, the probability that it won't move is 1/4, so the probability that it never moves is

(1/4)(1/4)(1/4) = 1/64

Sample input #2:

``````9
``````

Output:

``````1/10
``````

Explanation:

When N = 9, the wheel will be in a (uniformly) random position after every spin. Therefore after 3 spins (or any number of spins, for that matter), the probability that it will be pointing to the number 1 is 1/10.

Sample input #3:

``````7
``````

Output:

``````13/128
``````

Hint:

Consider every possible sequence of 3 spins, and count how many of them end at the starting position. The probability of ending at the starting position is this count divided by the number of possible sequences.

• 写回答

#### 1条回答默认 最新

• ProfSnail 2021-03-10 12:55
关注

因为题目的n比较小，是一百以内的，O(n^3)也只有10^6，所以暴力解就行了，一般不会超时。

``````using System;
namespace HelloWorldApplication
{
class HelloWorld
{
static int gcd(int a, int b){
if(b == 0)return a;
return gcd(b, a%b);
}
static int Main(string[] args)
{

//int n = 3;
if(n == 0){
Console.WriteLine("1");
return 0;
}
int trueNum=0, allNum=0;
for(int i = 0; i <= n; i++){
for(int j = 0; j <= n; j++){
for(int k = 0; k <= n; k++){
int sum = i + j + k;
if(sum % 10 == 0){
trueNum++;
}
allNum++;
}
}
}
int ggcd = gcd(trueNum, allNum);
trueNum /= ggcd;
allNum /= ggcd;
Console.WriteLine(trueNum+"/"+allNum);
return 0;
}
}
}
``````
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