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65 lines
4.1 KiB
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<p>You are given an integer array <code>arr</code>. From some starting index, you can make a series of jumps. The (1<sup>st</sup>, 3<sup>rd</sup>, 5<sup>th</sup>, ...) jumps in the series are called <strong>odd-numbered jumps</strong>, and the (2<sup>nd</sup>, 4<sup>th</sup>, 6<sup>th</sup>, ...) jumps in the series are called <strong>even-numbered jumps</strong>. Note that the <strong>jumps</strong> are numbered, not the indices.</p>
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<p>You may jump forward from index <code>i</code> to index <code>j</code> (with <code>i < j</code>) in the following way:</p>
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<ul>
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<li>During <strong>odd-numbered jumps</strong> (i.e., jumps 1, 3, 5, ...), you jump to the index <code>j</code> such that <code>arr[i] <= arr[j]</code> and <code>arr[j]</code> is the smallest possible value. If there are multiple such indices <code>j</code>, you can only jump to the <strong>smallest</strong> such index <code>j</code>.</li>
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<li>During <strong>even-numbered jumps</strong> (i.e., jumps 2, 4, 6, ...), you jump to the index <code>j</code> such that <code>arr[i] >= arr[j]</code> and <code>arr[j]</code> is the largest possible value. If there are multiple such indices <code>j</code>, you can only jump to the <strong>smallest</strong> such index <code>j</code>.</li>
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<li>It may be the case that for some index <code>i</code>, there are no legal jumps.</li>
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</ul>
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<p>A starting index is <strong>good</strong> if, starting from that index, you can reach the end of the array (index <code>arr.length - 1</code>) by jumping some number of times (possibly 0 or more than once).</p>
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<p>Return <em>the number of <strong>good</strong> starting indices</em>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> arr = [10,13,12,14,15]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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From starting index i = 0, we can make our 1st jump to i = 2 (since arr[2] is the smallest among arr[1], arr[2], arr[3], arr[4] that is greater or equal to arr[0]), then we cannot jump any more.
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From starting index i = 1 and i = 2, we can make our 1st jump to i = 3, then we cannot jump any more.
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From starting index i = 3, we can make our 1st jump to i = 4, so we have reached the end.
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From starting index i = 4, we have reached the end already.
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In total, there are 2 different starting indices i = 3 and i = 4, where we can reach the end with some number of
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jumps.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> arr = [2,3,1,1,4]
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<strong>Output:</strong> 3
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<strong>Explanation:</strong>
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From starting index i = 0, we make jumps to i = 1, i = 2, i = 3:
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During our 1st jump (odd-numbered), we first jump to i = 1 because arr[1] is the smallest value in [arr[1], arr[2], arr[3], arr[4]] that is greater than or equal to arr[0].
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During our 2nd jump (even-numbered), we jump from i = 1 to i = 2 because arr[2] is the largest value in [arr[2], arr[3], arr[4]] that is less than or equal to arr[1]. arr[3] is also the largest value, but 2 is a smaller index, so we can only jump to i = 2 and not i = 3
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During our 3rd jump (odd-numbered), we jump from i = 2 to i = 3 because arr[3] is the smallest value in [arr[3], arr[4]] that is greater than or equal to arr[2].
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We can't jump from i = 3 to i = 4, so the starting index i = 0 is not good.
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In a similar manner, we can deduce that:
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From starting index i = 1, we jump to i = 4, so we reach the end.
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From starting index i = 2, we jump to i = 3, and then we can't jump anymore.
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From starting index i = 3, we jump to i = 4, so we reach the end.
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From starting index i = 4, we are already at the end.
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In total, there are 3 different starting indices i = 1, i = 3, and i = 4, where we can reach the end with some
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number of jumps.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> arr = [5,1,3,4,2]
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<strong>Output:</strong> 3
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<strong>Explanation:</strong> We can reach the end from starting indices 1, 2, and 4.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= arr.length <= 2 * 10<sup>4</sup></code></li>
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<li><code>0 <= arr[i] < 10<sup>5</sup></code></li>
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</ul>
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