Array Painting

2000ms

262144K

Description:

You are given an array of $$$n$$$ integers, where each integer is either $$$0$$$, $$$1$$$, or $$$2$$$. Initially, each element of the array is blue.

Your goal is to paint each element of the array red. In order to do so, you can perform operations of two types:

pay one coin to choose a blue element and paint it red;
choose a red element which is not equal to $$$0$$$ and a blue element adjacent to it, decrease the chosen red element by $$$1$$$, and paint the chosen blue element red.

What is the minimum number of coins you have to spend to achieve your goal?

The first line contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 2$$$).

Print one integer — the minimum number of coins you have to spend in order to paint all elements red.

3
0 2 0

4
0 0 1 1

7
0 1 0 0 1 0 2

In the first example, you can paint all elements red with having to spend only one coin as follows:

paint the $$$2$$$-nd element red by spending one coin;
decrease the $$$2$$$-nd element by $$$1$$$ and paint the $$$1$$$-st element red;
decrease the $$$2$$$-nd element by $$$1$$$ and paint the $$$3$$$-rd element red.

In the second example, you can paint all elements red spending only two coins as follows:

paint the $$$4$$$-th element red by spending one coin;
decrease the $$$4$$$-th element by $$$1$$$ and paint the $$$3$$$-rd element red;
paint the $$$1$$$-st element red by spending one coin;
decrease the $$$3$$$-rd element by $$$1$$$ and paint the $$$2$$$-nd element red.

Informação

Provedor Codeforces

Código CF1849D