Lucky Numbers | GeeksforGeeks

Lucky Numbers | GeeksforGeeks

Lucky numbers are subset of integers. Rather than going into much theory, let us see the process of arriving at lucky numbers,

Take the set of integers
1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,……

First, delete every second number, we get following reduced set.
1,3,5,7,9,11,13,15,17,19,…………

Now, delete every third number, we get
1, 3, 7, 9, 13, 15, 19,….….

Continue this process indefinitely……
Any number that does NOT get deleted due to above process is called “lucky”.

Therefore, set of lucky numbers is 1, 3, 7, 13,………

Now, given an integer ‘n’, write a function to say whether this number is lucky or not.

    bool isLucky(int n)

Before every iteration, if we calculate position of the given no, then in a given iteration, we can determine if the no will be deleted. Suppose calculated position for the given no. is P before some iteration, and each Ith no. is going to be removed in this iteration, if P < I then input no is lucky, if P is such that P%I == 0 (I is a divisor of P), then input no is not lucky.

bool isLucky(int n)

{

  static int counter = 2;

 

  /*variable next_position is just for readability of

     the program we can remove it and use n only */

  int next_position = n;

  if(counter > n)

    return 1;

  if(n%counter == 0)

    return 0;     

 

 /*calculate next position of input no*/

  next_position -= next_position/counter;

   

  counter++;

  return isLucky(next_position);

}

http://www.acmerblog.com/math-lucky-number-5407.html

主要是递推，考虑数字n的位置变化。第一n轮删除时，n的位置即为n，结束后的位置即为 n-n/2, 依此类推下去即可。
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