991. Broken Calculator

On a broken calculator that has a number showing on its display, we can perform two operations:

• Double: Multiply the number on the display by 2, or;

• Decrement: Subtract 1 from the number on the display.

Initially, the calculator is displaying the number X.

Return the minimum number of operations needed to display the number Y.

Example 1:

Input: X = 2, Y = 3
Output: 2
Explanation: Use double operation and then decrement operation {2 -> 4 -> 3}.

Example 2:

Input: X = 5, Y = 8
Output: 2
Explanation: Use decrement and then double {5 -> 4 -> 8}.

Example 3:

Input: X = 3, Y = 10
Output: 3
Explanation:  Use double, decrement and double {3 -> 6 -> 5 -> 10}.

Example 4:

Input: X = 1024, Y = 1
Output: 1023
Explanation: Use decrement operations 1023 times.

Note:

1. 1 <= X <= 10^9

2. 1 <= Y <= 10^9

// Y -> X
int brokenCalc(int X, int Y) { // time: O(log(Y / X)); space: O(1)
    int res = 0;
    while (Y > X) {
        Y = (Y % 2) ? (Y + 1) : (Y / 2);
        ++res;
    }
    res += (X - Y);
    return res;
}

// X -> Y
int brokenCalc(int X, int Y) { // time: O(log(Y / X)); space: O(1)
    int multiplier = 1, res = 0;
    while (X * multiplier < Y) {
        multiplier *= 2;
        ++res;
    }
    int diff = X * multiplier - Y;
    while (diff > 0) {
        res += diff / multiplier;
        diff -= diff / multiplier * multiplier;
        multiplier /= 2;
    }
    return res;
}