Target Number with Operations - Google Top Interview Questions

Problem Statement :

Given positive integers start and end (start < end), return the minimum number of operations needed to convert start to end using these operations:

Increment by 1

Multiply by 2


start < end < 2 ** 31

Example 1


start = 2

end = 9




We can multiply 2 to get 4, and then again to get 8, then add 1 to get 9.

Solution :


                        Solution in C++ :

int solve(int start, int end) {
    int ops = 0;
    for (; start * 2 <= end; ops++) {
        if (end % 2)
            end /= 2;
    return ops + end - start;

                        Solution in Java :

class Solution {
    public int solve(int start, int end) {
        int ops = 0;
        while (end / 2 >= start) {
            ops += 1 + (end % 2);
            end /= 2;
        return ops + end - start;

                        Solution in Python : 
class Solution:
    def solve(self, start, end):
        c = 0
        if start <= 0:
            return None
        while end != start:
            if end & 1:  # Odd number
                end -= 1
                res = end // 2
                if res < start:
                    c += end - start
                    return c
                end = res
            c += 1
        return c

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