Number of Decrements to Reach Zero - Google Top Interview Questions

Problem Statement :

You are given an integer n. In one operation you can either

Decrement n by one

If n is even, decrement by n / 2

If n is divisible by 3, decrement by 2 * (n / 3)

Return the minimum number of operations required to decrement n to zero.


n ≤ 10 ** 9

Example 1


n = 15




Since n = 15 is divisible by 3 we decrement by 10 = 2 * (15 / 3) to get 5. Then we decrement by one to 
get 4. Then we decrement by 2 since n is even. Then we decrement n by one twice to get 0

Solution :


                        Solution in C++ :

unordered_map<int, int> dp;
int solve(int n) {
    if (n == 0) return 0;

    if (n == 1) return 1;

    if (n < 0) assert(false);

    if (dp.count(n)) return dp[n];

    int md3 = n % 3;
    int md2 = n % 2;

    dp[n] = min(md2 + 1 + solve((n - md2) / 2), md3 + 1 + solve((n - md3) / 3));
    return dp[n];

                        Solution in Python : 
class Solution:
    def solve(self, n):
        if n <= 1:
            return n
        return min(1 + int(n % 3) + self.solve(n // 3), 1 + int(n % 2) + self.solve(n // 2))

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