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Joseph Ring implemented in Python -- who is the actress

編輯：Python

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What is Joseph's ring

Joseph ring （ Joseph's question ） It's an application of mathematics ： It is known that n personal （ To number 1,2,3…n respectively ） Sit around a round table . From the number k People began to count , Count to m The man of the circle ; His next man from 1 Start counting , Count to m The man of the circle ; Repeat this rule , Until the last winner remains .

give an example : Which actress can become the heroine

for example ： Yes 10 All the actresses with good acting skills came to run for the heroine of the play , So how to choose , They can play a game , Sit at a round table and play the game , Everyone is numbered 1-10 . If the specified number reaches 3 People out of circles . The game process is as follows .

Pictured

The process of the game

Start counting , First count to 3 Of people 3 Number ,3 No. 1 out of circle .
1, 2,【 $3 \color{red}{3}$ 3】, 4, 5, 6, 7, 8, 9, 10.
from 4 No 1 Start counting , Then count to 3 Of people 6 Number ,6 No. 1 out of circle .
1, 2,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 7, 8, 9, 10.
from 7 No 1 Start counting , Then count to 3 Of people 9 Number ,9 No. 1 out of circle .
1, 2,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 7, 8, 【 $9 \color{red}{9}$ 9】, 10.
from 10 No 1 Start counting , because 10 I call it ring structure , Then count to 3 Of people 2 Number ,2 No. 1 out of circle .
1, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 7, 8, 【 $9 \color{red}{9}$ 9】, 10.
from 4 No 1 Start counting , Then count to 3 Of people 7 Number ,7 No. 1 out of circle .
1, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 【 $7 \color{red}{7}$ 7】, 8, 【 $9 \color{red}{9}$ 9】, 10.
from 8 No 1 Start counting , Then count to 3 Of people 1 Number ,1 No. 1 out of circle .
【 $1 \color{red}{1}$ 1】, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 【 $7 \color{red}{7}$ 7】, 8, 【 $9 \color{red}{9}$ 9】, 10.
from 4 No 1 Start counting , Then count to 3 Of people 8 Number ,8 No. 1 out of circle .
【 $1 \color{red}{1}$ 1】, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 5, 【 $6 \color{red}{6}$ 6】, 【 $7 \color{red}{7}$ 7】, 【 $8 \color{red}{8}$ 8】, 【 $9 \color{red}{9}$ 9】, 10.
from 10 No 1 Start counting , Then count to 3 Of people 5 Number ,5 No. 1 out of circle .
【 $1 \color{red}{1}$ 1】, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 【 $5 \color{red}{5}$ 5】, 【 $6 \color{red}{6}$ 6】, 【 $7 \color{red}{7}$ 7】, 【 $8 \color{red}{8}$ 8】, 【 $9 \color{red}{9}$ 9】, 10.
from 10 No 1 Start counting , Then count to 3 Of people 10 Number ,10 No. 1 out of circle .
【 $1 \color{red}{1}$ 1】, 【 $2 \color{red}{2}$ 2】,【 $3 \color{red}{3}$ 3】, 4, 【 $5 \color{red}{5}$ 5】, 【 $6 \color{red}{6}$ 6】, 【 $7 \color{red}{7}$ 7】, 【 $8 \color{red}{8}$ 8】, 【 $9 \color{red}{9}$ 9】, 【 $10 \color{red}{10}$ 10】.
Final surplus 4 Number ,4 Actress No. 1 was elected as the leading lady .

Algorithm implementation

Ideas

use python List solution ：

First use a list to identify this n Personal status , By default, it's all 1 , That is, they are all in the circle , On the count of m After people out of the circle , The logo is set to 0（ Just out of the circle ）, Clear the alarm at the same time 0, The next person is from 1 Start . Before each count, judge whether he is in the circle （ That is, whether his logo is 1 ）, If you are in the circle, you will continue to count off . Define a variable to record the number of people in the circle , The number of people out of the circle is equal to n-1 when , Then the game is over .

Detailed code and running results

def select_actor(n, m):
    count = 0   # Record the number of people who have left the circle 
    num = 0     # Counter 
    status_list = []  # The status of the players , It all started with 1
    for i in range(n):
        status_list.append(1)
   # Start the game , Number off , Count 
    while count < n - 1:
        for i in range(n):
            if status_list[i] == 1:
                num +=1
                if num==m: # This person counts to m Then the circle , The buzzer is cleared 
                    count += 1
                    print("%d Withdraw from the election on the th " % (i+1))
                    status_list[i] = 0
                    num = 0
                if count == n - 1:
                    break
    for idx, val in enumerate(status_list):
        if val==1:
            print("%d No. 1 qualified to be a leading lady " % (idx+1))
select_actor(10, 3)

Running results