Frog Jump
<p>A frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.</p>

<p>Given a list of <code>stones</code>&nbsp;positions (in units) in sorted <strong>ascending order</strong>, determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be <code>1</code> unit.</p>

<p>If the frog&#39;s last jump was <code>k</code> units, its next jump must be either <code>k - 1</code>, <code>k</code>, or <code>k + 1</code> units. The frog can only jump in the forward direction.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stones = [0,1,3,5,6,8,12,17]
<strong>Output:</strong> true
<strong>Explanation:</strong> The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stones = [0,1,2,3,4,8,9,11]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= stones.length &lt;= 2000</code></li>
	<li><code>0 &lt;= stones[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>stones[0] == 0</code></li>
	<li><code>stones</code>&nbsp;is sorted in a strictly increasing order.</li>
</ul>
Array; Dynamic Programming
use std::collections::HashMap;

impl Solution {
    #[allow(dead_code)]
    pub fn can_cross(stones: Vec<i32>) -> bool {
        let n = stones.len();
        let mut record = vec![vec![-1; n]; n];
        let mut pos = HashMap::new();
        for (i, &s) in stones.iter().enumerate() {
            pos.insert(s, i);
        }

        Self::dfs(&mut record, 0, 0, n, &pos, &stones)
    }

    #[allow(dead_code)]
    fn dfs(
        record: &mut Vec<Vec<i32>>,
        i: usize,
        k: usize,
        n: usize,
        pos: &HashMap<i32, usize>,
        stones: &Vec<i32>,
    ) -> bool {
        if i == n - 1 {
            return true;
        }

        if record[i][k] != -1 {
            return record[i][k] == 1;
        }

        let k = k as i32;
        for j in k - 1..=k + 1 {
            if j > 0
                && pos.contains_key(&(stones[i] + j))
                && Self::dfs(record, pos[&(stones[i] + j)], j as usize, n, pos, stones)
            {
                record[i][k as usize] = 1;
                return true;
            }
        }

        record[i][k as usize] = 0;
        false
    }
}
