minimum-operations-to-make-the-integer-zero

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Algorithms

You are given two integers <code>num1</code> and <code>num2</code>.

In one operation, you can choose integer <code>i</code> in the range <code>[0, 60]</code> and subtract <code>2i + num2</code> from <code>num1</code>.

Return the integer denoting the minimum number of operations needed to make <code>num1</code> equal to <code>0</code>.

If it is impossible to make <code>num1</code> equal to <code>0</code>, return <code>-1</code>.

&nbsp;
Example 1:

<pre>
Input: num1 = 3, num2 = -2
Output: 3
Explanation: We can make 3 equal to 0 with the following operations:
- We choose i = 2 and subtract 22 + (-2) from 3, 3 - (4 + (-2)) = 1.
- We choose i = 2 and subtract 22&nbsp;+ (-2) from 1, 1 - (4 + (-2)) = -1.
- We choose i = 0 and subtract 20&nbsp;+ (-2) from -1, (-1) - (1 + (-2)) = 0.
It can be proven, that 3 is the minimum number of operations that we need to perform.
</pre>

Example 2:

<pre>
Input: num1 = 5, num2 = 7
Output: -1
Explanation: It can be proven, that it is impossible to make 5 equal to 0 with the given operation.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= num1 &lt;= 109</code></li>
	<li><code>-109&nbsp;&lt;= num2 &lt;= 109</code></li>
</ul>

makeTheIntegerZero

Minimum Operations to Make the Integer Zero

Broken Calculator

broken-calculator

坏了的计算器

Minimum Operations to Reduce X to Zero

minimum-operations-to-reduce-x-to-zero

将 x 减到 0 的最小操作数

Bit Manipulation

Brainteaser

Enumeration

给你两个整数：<code>num1</code> 和 <code>num2</code> 。

在一步操作中，你需要从范围&nbsp;<code>[0, 60]</code> 中选出一个整数 <code>i</code> ，并从 <code>num1</code> 减去 <code>2i + num2</code> 。

请你计算，要想使 <code>num1</code> 等于 <code>0</code> 需要执行的最少操作数，并以整数形式返回。

如果无法使 <code>num1</code> 等于 <code>0</code> ，返回 <code>-1</code> 。

&nbsp;

示例 1：

<pre>
输入：num1 = 3, num2 = -2
输出：3
解释：可以执行下述步骤使 3 等于 0 ：
- 选择 i = 2 ，并从 3 减去 22 + (-2) ，num1 = 3 - (4 + (-2)) = 1 。
- 选择 i = 2 ，并从 1 减去 22 + (-2) ，num1 = 1 - (4 + (-2)) = -1 。
- 选择 i = 0 ，并从 -1 减去 20&nbsp;+ (-2) ，num1 = (-1) - (1 + (-2)) = 0 。
可以证明 3 是需要执行的最少操作数。
</pre>

示例 2：

<pre>
输入：num1 = 5, num2 = 7
输出：-1
解释：可以证明，执行操作无法使 5 等于 0 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= num1 &lt;= 109</code></li>
	<li><code>-109&nbsp;&lt;= num2 &lt;= 109</code></li>
</ul>