## 1824. Minimum Sideway Jumps

There is a **3 lane road** of length `n`

that consists of `n + 1`

**points** labeled from `0`

to `n`

. A frog **starts** at point `0`

in the **second **lane** **and wants to jump to point `n`

. However, there could be obstacles along the way.

You are given an array `obstacles`

of length `n + 1`

where each `obstacles[i]`

(**ranging from 0 to 3**) describes an obstacle on the lane `obstacles[i]`

at point `i`

. If `obstacles[i] == 0`

, there are no obstacles at point `i`

. There will be **at most one** obstacle in the 3 lanes at each point.

- For example, if
`obstacles[2] == 1`

, then there is an obstacle on lane 1 at point 2.

The frog can only travel from point `i`

to point `i + 1`

on the same lane if there is not an obstacle on the lane at point `i + 1`

. To avoid obstacles, the frog can also perform a **side jump** to jump to **another** lane (even if they are not adjacent) at the **same** point if there is no obstacle on the new lane.

- For example, the frog can jump from lane 3 at point 3 to lane 1 at point 3.

Return* the minimum number of side jumps the frog needs to reach any lane at point n starting from lane *

`2`

at point 0.**Note:** There will be no obstacles on points `0`

and `n`

.

**Example 1:**

Input:obstacles = [0,1,2,3,0]Output:2Explanation:The optimal solution is shown by the arrows above. There are 2 side jumps (red arrows). Note that the frog can jump over obstacles only when making side jumps (as shown at point 2).

**Example 2:**

Input:obstacles = [0,1,1,3,3,0]Output:0Explanation:There are no obstacles on lane 2. No side jumps are required.

**Example 3:**

Input:obstacles = [0,2,1,0,3,0]Output:2Explanation:The optimal solution is shown by the arrows above. There are 2 side jumps.

**Constraints:**

`obstacles.length == n + 1`

`1 <= n <= 5 * 10`

^{5}`0 <= obstacles[i] <= 3`

`obstacles[0] == obstacles[n] == 0`

## Rust Solution

```
struct Solution;
impl Solution {
fn min_side_jumps(obstacles: Vec<i32>) -> i32 {
let n = obstacles.len();
let mut dp: Vec<Vec<i32>> = vec![vec![0, 0, 0]; n];
dp[0][0] = 1;
dp[0][2] = 1;
for i in 1..n {
for j in 0..3 {
if obstacles[i] == (j + 1) as i32 {
dp[i][j] = std::i32::MAX;
} else {
let mut min = std::i32::MAX;
for k in 0..3 {
if !(obstacles[i - 1] == (k + 1) as i32 || obstacles[i] == (k + 1) as i32) {
min = min.min(dp[i - 1][k] + if k == j { 0 } else { 1 });
}
}
dp[i][j] = min;
}
}
}
*dp[n - 1].iter().min().unwrap()
}
}
#[test]
fn test() {
let obstacles = vec![0, 1, 2, 3, 0];
let res = 2;
assert_eq!(Solution::min_side_jumps(obstacles), res);
let obstacles = vec![0, 1, 1, 3, 3, 0];
let res = 0;
assert_eq!(Solution::min_side_jumps(obstacles), res);
let obstacles = vec![0, 2, 1, 0, 3, 0];
let res = 2;
assert_eq!(Solution::min_side_jumps(obstacles), res);
}
```

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