Coding - Minimum Operations to Reduce an Integer to 0

Problem Statement

You are given a positive integer n. In one operation, you may either add or subtract any power of two. Return the minimum number of operations required to make n equal to 0. To preserve the original n < 2^60 bound exactly in this practice environment, n is provided to your function as a base-10 string.

Examples

Example 1: Input: n = "16" Output: 5 Explanation: We can do: n - 1 = 15 n - 1 = 14 n - 1 = 13 n + 1 = 14 n - 1 = 0 The total number of operations is 5.

Example 2: Input: n = "821" Output: 11 Explanation: We can do: n - 1 = 820 n - 10 = 810 n - 100 = 710 n - 1000 = 10 n + 1 = 11 n + 1 = 10 n + 100 = 110 n + 100 = 210 n + 1000 = 1210 n - 1000 = 210 n + 1 = 211 n - 1 = 210 n - 10 = 200 The total number of operations is 11.

Constraints

• 1 <= n.length <= 5 * 10^4
• n consists of only digits.
• 1 <= n < 2^60

Hints

1. The problem can be solved using a greedy approach.
2. Consider the binary representation of the number to understand the operations needed.