Integer replacement algorithm

0

Given a positive integer n and you can do operations as follow:

  1. If n is even, replace n with n/2.
  2. If n is odd, you can replace n with either n + 1 or n – 1.

What is the minimum number of replacements needed for n to become 1?

Example 1:

Input:

8

Output:

3

Explanation:

8 -> 4 -> 2 -> 1

Example 2:

Input:

7

Output:

4

Explanation:

7 -> 8 -> 4 -> 2 -> 1

or

7 -> 6 -> 3 -> 2 -> 1

Answered question
0
Algol (anonymous) 0 Comments

Below is a simple self explanatory recursive algorithm using javascript

 

/**
 * @param {number} n
 * @return {number}
 */
var integerReplacement = function(n, count = 0) {
   if (n === 1)
       return count;
         if (n % 2 === 0)
        count = integerReplacement(Math.round(n/2), count+1);
    else
        count = Math.min(integerReplacement(n-1, count+1),
                         integerReplacement(n+1, count+1));
         return count;
};

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