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# 1529. Bulb Switcher IV

There is a room with `n` bulbs, numbered from `0` to `n-1`, arranged in a row from left to right. Initially all the bulbs are turned off.

Your task is to obtain the configuration represented by `target` where `target[i]` is '1' if the i-th bulb is turned on and is '0' if it is turned off.

You have a switch to flip the state of the bulb, a flip operation is defined as follows:

• Choose any bulb (index `i`) of your current configuration.
• Flip each bulb from index `i` to `n-1`.

When any bulb is flipped it means that if it is 0 it changes to 1 and if it is 1 it changes to 0.

Return the minimum number of flips required to form `target`.

Example 1:

```Input: target = "10111"
Output: 3
Explanation: Initial configuration "00000".
flip from the third bulb:  "00000" -> "00111"
flip from the first bulb:  "00111" -> "11000"
flip from the second bulb:  "11000" -> "10111"
We need at least 3 flip operations to form target.```

Example 2:

```Input: target = "101"
Output: 3
Explanation: "000" -> "111" -> "100" -> "101".
```

Example 3:

```Input: target = "00000"
Output: 0
```

Example 4:

```Input: target = "001011101"
Output: 5
```

Constraints:

• `1 <= target.length <= 10^5`
• `target[i] == '0'` or `target[i] == '1'`

Medium

Normal

Unknown

### Problem Solution

1529-Bulb-Switcher-IV