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| 1 | +<h2><a href="https://leetcode.com/problems/frog-jump-ii/">2498. Frog Jump II</a></h2><h3>Medium</h3><hr><p>You are given a <strong>0-indexed</strong> integer array <code>stones</code> sorted in <strong>strictly increasing order</strong> representing the positions of stones in a river.</p> |
| 2 | + |
| 3 | +<p>A frog, initially on the first stone, wants to travel to the last stone and then return to the first stone. However, it can jump to any stone <strong>at most once</strong>.</p> |
| 4 | + |
| 5 | +<p>The <strong>length</strong> of a jump is the absolute difference between the position of the stone the frog is currently on and the position of the stone to which the frog jumps.</p> |
| 6 | + |
| 7 | +<ul> |
| 8 | + <li>More formally, if the frog is at <code>stones[i]</code> and is jumping to <code>stones[j]</code>, the length of the jump is <code>|stones[i] - stones[j]|</code>.</li> |
| 9 | +</ul> |
| 10 | + |
| 11 | +<p>The <strong>cost</strong> of a path is the <strong>maximum length of a jump</strong> among all jumps in the path.</p> |
| 12 | + |
| 13 | +<p>Return <em>the <strong>minimum</strong> cost of a path for the frog</em>.</p> |
| 14 | + |
| 15 | +<p> </p> |
| 16 | +<p><strong class="example">Example 1:</strong></p> |
| 17 | +<img alt="" src="https://assets.leetcode.com/uploads/2022/11/14/example-1.png" style="width: 600px; height: 219px;" /> |
| 18 | +<pre> |
| 19 | +<strong>Input:</strong> stones = [0,2,5,6,7] |
| 20 | +<strong>Output:</strong> 5 |
| 21 | +<strong>Explanation:</strong> The above figure represents one of the optimal paths the frog can take. |
| 22 | +The cost of this path is 5, which is the maximum length of a jump. |
| 23 | +Since it is not possible to achieve a cost of less than 5, we return it. |
| 24 | +</pre> |
| 25 | + |
| 26 | +<p><strong class="example">Example 2:</strong></p> |
| 27 | +<img alt="" src="https://assets.leetcode.com/uploads/2022/11/14/example-2.png" style="width: 500px; height: 171px;" /> |
| 28 | +<pre> |
| 29 | +<strong>Input:</strong> stones = [0,3,9] |
| 30 | +<strong>Output:</strong> 9 |
| 31 | +<strong>Explanation:</strong> |
| 32 | +The frog can jump directly to the last stone and come back to the first stone. |
| 33 | +In this case, the length of each jump will be 9. The cost for the path will be max(9, 9) = 9. |
| 34 | +It can be shown that this is the minimum achievable cost. |
| 35 | +</pre> |
| 36 | + |
| 37 | +<p> </p> |
| 38 | +<p><strong>Constraints:</strong></p> |
| 39 | + |
| 40 | +<ul> |
| 41 | + <li><code>2 <= stones.length <= 10<sup>5</sup></code></li> |
| 42 | + <li><code>0 <= stones[i] <= 10<sup>9</sup></code></li> |
| 43 | + <li><code>stones[0] == 0</code></li> |
| 44 | + <li><code>stones</code> is sorted in a strictly increasing order.</li> |
| 45 | +</ul> |
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