LeetCode 975. Odd Even Jump

Description

https://leetcode.com/problems/odd-even-jump/

You are given an integer array A. 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:

  • During odd-numbered jumps (i.e., jumps 1, 3, 5, …), you jump to the index j such that A[i] <= A[j] and A[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 A[i] >= A[j] and A[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 A.length - 1) by jumping some number of times (possibly 0 or more than once).

Return the number of good starting indices.

Example 1:

Input: A = [10,13,12,14,15]
Output: 2
Explanation: 
From starting index i = 0, we can make our 1st jump to i = 2 (since A[2] is the smallest among A[1], A[2], A[3],
A[4] that is greater or equal to A[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: A = [2,3,1,1,4]
Output: 3
Explanation: 
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 A[1] is the smallest value in [A[1], A[2],
A[3], A[4]] that is greater than or equal to A[0].

During our 2nd jump (even-numbered), we jump from i = 1 to i = 2 because A[2] is the largest value in [A[2], A[3],
A[4]] that is less than or equal to A[1]. A[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 A[3] is the smallest value in [A[3], A[4]]
that is greater than or equal to A[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: A = [5,1,3,4,2]
Output: 3
Explanation: 
We can reach the end from starting indices 1, 2, and 4.

Constraints:

  • 1 <= A.length <= 2 * 104
  • 0 <= A[i] < 105

Explanation

Python Solution

class Solution:
    def oddEvenJumps(self, A: List[int]) -> int:
        n = len(A)
        next_higher, next_lower = [0] * n, [0] * n
        
        stack = []
        
        for a, i in sorted([a, i] for i, a in enumerate(A)):
            while stack and stack[-1] < i:
                next_higher[stack.pop()] = i
            stack.append(i)
        
        for a, i in sorted([-a, i] for i, a in enumerate(A)):
            while stack and stack[-1] < i:
                next_lower[stack.pop()] = i
            stack.append(i)        
        
                
        higher, lower = [0] * n, [0] * n
        higher[-1] = lower[-1] = 1
        
        for i in range(n - 1)[::-1]:
            higher[i] = lower[next_higher[i]]
            lower[i] = higher[next_lower[i]]
        
        return sum(higher)
  • Time Complexity: ~N
  • Space Complexity: ~N

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