> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/0991-broken-calculator.md).

# 0991. Broken Calculator

<https://leetcode.com/problems/broken-calculator>

## Description

There is a broken calculator that has the integer `startValue` on its display initially. In on operation you can:

* multiply the number on the display by `2`, or
* subtract `1` from the number on the display.

Given two integers `startValue` and `target`, return *the minimum number of operations needed to display* `target` *on the calculator*.

**Example 1:**

```
**Input:** startValue = 2, target = 3
**Output:** 2
**Explanation:** Use double operation and then decrement operation {2 -> 4 -> 3}.
```

**Example 2:**

```
**Input:** startValue = 5, target = 8
**Output:** 2
**Explanation:** Use decrement and then double {5 -> 4 -> 8}.
```

**Example 3:**

```
**Input:** startValue = 3, target = 10
**Output:** 3
**Explanation:** Use double, decrement and double {3 -> 6 -> 5 -> 10}.
```

**Example 4:**

```
**Input:** startValue = 1024, target = 1
**Output:** 1023
**Explanation:** Use decrement operations 1023 times.
```

**Constraints:**

* `1 <= x, y <= 109`

## ac

```java
```