Integer Replacement

Desicription

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:

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Input:
8

Output:
3

Explanation:
8 -> 4 -> 2 -> 1

Example 2:

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Input:
7

Output:
4

Explanation:
7 -> 8 -> 4 -> 2 -> 1
or
7 -> 6 -> 3 -> 2 -> 1

Solution

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class Solution {
private:
std::unordered_map<long long , long long> map = std::unordered_map<long long, long long>{};
public:
int integerReplacement(long long n) {
if(n == 1) {
return 0;
}

if(map[n] == 0) {
if(n & 1 == 1) {
map[n] = 2 + std::min(integerReplacement((n + 1) / 2), integerReplacement((n - 1) / 2));
} else {
map[n] = 1 + integerReplacement(n / 2);
}
}

return map[n];
}
};