975. Odd Even Jump

Hard

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446

You are given an integer array `arr`

. From some starting index, you can make a series of jumps. The (1^{st}, 3^{rd}, 5^{th}, ...) jumps in the series are called **odd-numbered jumps**, and the (2^{nd}, 4^{th}, 6^{th}, ...) jumps in the series are called **even-numbered jumps**. Note that the **jumps** are numbered, not the indices.

You may jump forward from index `i`

to index `j`

(with `i < j`

) in the following way:

- During
**odd-numbered jumps**(i.e., jumps 1, 3, 5, ...), you jump to the index`j`

such that`arr[i] <= arr[j]`

and`arr[j]`

is the smallest possible value. If there are multiple such indices`j`

, you can only jump to the**smallest**such index`j`

. - During
**even-numbered jumps**(i.e., jumps 2, 4, 6, ...), you jump to the index`j`

such that`arr[i] >= arr[j]`

and`arr[j]`

is the largest possible value. If there are multiple such indices`j`

, you can only jump to the**smallest**such index`j`

. - It may be the case that for some index
`i`

, there are no legal jumps.

A starting index is **good** if, starting from that index, you can reach the end of the array (index `arr.length - 1`

) by jumping some number of times (possibly 0 or more than once).

Return *the number of good starting indices*.

**Example 1:**

Input:arr = [10,13,12,14,15]Output:2Explanation: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. From starting index i = 1 and i = 2, we can make our 1st jump to i = 3, then we cannot jump any more. From starting index i = 3, we can make our 1st jump to i = 4, so we have reached the end. From starting index i = 4, we have reached the end already. In total, there are 2 different starting indices i = 3 and i = 4, where we can reach the end with some number of jumps.

**Example 2:**

Input:arr = [2,3,1,1,4]Output:3Explanation:From starting index i = 0, we make jumps to i = 1, i = 2, i = 3: 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]. 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 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]. We can't jump from i = 3 to i = 4, so the starting index i = 0 is not good. In a similar manner, we can deduce that: From starting index i = 1, we jump to i = 4, so we reach the end. From starting index i = 2, we jump to i = 3, and then we can't jump anymore. From starting index i = 3, we jump to i = 4, so we reach the end. From starting index i = 4, we are already at the end. In total, there are 3 different starting indices i = 1, i = 3, and i = 4, where we can reach the end with some number of jumps.

**Example 3:**

Input:arr = [5,1,3,4,2]Output:3Explanation:We can reach the end from starting indices 1, 2, and 4.

**Constraints:**

`1 <= arr.length <= 2 * 10`

^{4}`0 <= arr[i] < 10`

^{5}

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