{ "data": { "question": { "questionId": "1017", "questionFrontendId": "975", "categoryTitle": "Algorithms", "boundTopicId": 2823, "title": "Odd Even Jump", "titleSlug": "odd-even-jump", "content": "
You are given an integer array arr
. From some starting index, you can make a series of jumps. The (1st, 3rd, 5th, ...) jumps in the series are called odd-numbered jumps, and the (2nd, 4th, 6th, ...) 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:
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
.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
.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.
\n\n\n
Example 1:
\n\n\nInput: arr = [10,13,12,14,15]\nOutput: 2\nExplanation: \nFrom 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.\nFrom starting index i = 1 and i = 2, we can make our 1st jump to i = 3, then we cannot jump any more.\nFrom starting index i = 3, we can make our 1st jump to i = 4, so we have reached the end.\nFrom starting index i = 4, we have reached the end already.\nIn total, there are 2 different starting indices i = 3 and i = 4, where we can reach the end with some number of\njumps.\n\n\n
Example 2:
\n\n\nInput: arr = [2,3,1,1,4]\nOutput: 3\nExplanation: \nFrom starting index i = 0, we make jumps to i = 1, i = 2, i = 3:\nDuring 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].\nDuring 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\nDuring 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].\nWe can't jump from i = 3 to i = 4, so the starting index i = 0 is not good.\nIn a similar manner, we can deduce that:\nFrom starting index i = 1, we jump to i = 4, so we reach the end.\nFrom starting index i = 2, we jump to i = 3, and then we can't jump anymore.\nFrom starting index i = 3, we jump to i = 4, so we reach the end.\nFrom starting index i = 4, we are already at the end.\nIn total, there are 3 different starting indices i = 1, i = 3, and i = 4, where we can reach the end with some\nnumber of jumps.\n\n\n
Example 3:
\n\n\nInput: arr = [5,1,3,4,2]\nOutput: 3\nExplanation: We can reach the end from starting indices 1, 2, and 4.\n\n\n
\n
Constraints:
\n\n1 <= arr.length <= 2 * 104
0 <= arr[i] < 105
给定一个整数数组 A
,你可以从某一起始索引出发,跳跃一定次数。在你跳跃的过程中,第 1、3、5... 次跳跃称为奇数跳跃,而第 2、4、6... 次跳跃称为偶数跳跃。
你可以按以下方式从索引 i
向后跳转到索引 j
(其中 i < j
):
j
,使得 A[i] <= A[j]
,A[j]
是可能的最小值。如果存在多个这样的索引 j
,你只能跳到满足要求的最小索引 j
上。j
,使得 A[i] >= A[j]
,A[j]
是可能的最大值。如果存在多个这样的索引 j
,你只能跳到满足要求的最小索引 j
上。i
,可能无法进行合乎要求的跳跃。)如果从某一索引开始跳跃一定次数(可能是 0 次或多次),就可以到达数组的末尾(索引 A.length - 1
),那么该索引就会被认为是好的起始索引。
返回好的起始索引的数量。
\n\n\n\n
示例 1:
\n\n输入:[10,13,12,14,15]\n输出:2\n解释: \n从起始索引 i = 0 出发,我们可以跳到 i = 2,(因为 A[2] 是 A[1],A[2],A[3],A[4] 中大于或等于 A[0] 的最小值),然后我们就无法继续跳下去了。\n从起始索引 i = 1 和 i = 2 出发,我们可以跳到 i = 3,然后我们就无法继续跳下去了。\n从起始索引 i = 3 出发,我们可以跳到 i = 4,到达数组末尾。\n从起始索引 i = 4 出发,我们已经到达数组末尾。\n总之,我们可以从 2 个不同的起始索引(i = 3, i = 4)出发,通过一定数量的跳跃到达数组末尾。\n\n\n
示例 2:
\n\n输入:[2,3,1,1,4]\n输出:3\n解释:\n从起始索引 i=0 出发,我们依次可以跳到 i = 1,i = 2,i = 3:\n\n在我们的第一次跳跃(奇数)中,我们先跳到 i = 1,因为 A[1] 是(A[1],A[2],A[3],A[4])中大于或等于 A[0] 的最小值。\n\n在我们的第二次跳跃(偶数)中,我们从 i = 1 跳到 i = 2,因为 A[2] 是(A[2],A[3],A[4])中小于或等于 A[1] 的最大值。A[3] 也是最大的值,但 2 是一个较小的索引,所以我们只能跳到 i = 2,而不能跳到 i = 3。\n\n在我们的第三次跳跃(奇数)中,我们从 i = 2 跳到 i = 3,因为 A[3] 是(A[3],A[4])中大于或等于 A[2] 的最小值。\n\n我们不能从 i = 3 跳到 i = 4,所以起始索引 i = 0 不是好的起始索引。\n\n类似地,我们可以推断:\n从起始索引 i = 1 出发, 我们跳到 i = 4,这样我们就到达数组末尾。\n从起始索引 i = 2 出发, 我们跳到 i = 3,然后我们就不能再跳了。\n从起始索引 i = 3 出发, 我们跳到 i = 4,这样我们就到达数组末尾。\n从起始索引 i = 4 出发,我们已经到达数组末尾。\n总之,我们可以从 3 个不同的起始索引(i = 1, i = 3, i = 4)出发,通过一定数量的跳跃到达数组末尾。\n\n\n
示例 3:
\n\n输入:[5,1,3,4,2]\n输出:3\n解释: \n我们可以从起始索引 1,2,4 出发到达数组末尾。\n\n\n
\n\n
提示:
\n\n1 <= A.length <= 20000
0 <= A[i] < 100000
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