Odd Even Jump Problem
Description
LeetCode Problem 975.
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:
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Input: arr = [10,13,12,14,15]
Output: 2
Explanation:
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:
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Input: arr = [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 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:
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Input: arr = [5,1,3,4,2]
Output: 3
Explanation: We can reach the end from starting indices 1, 2, and 4.
Constraints:
- 1 <= arr.length <= 2 * 10^4
- 0 <= arr[i] < 10^5
Sample C++ Code
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class Solution {
public:
int oddEvenJumps(vector<int>& A) {
vector<pair<int,int>> bound(A.size()); // odd/even jump
bound.back() = {1, 1};
map<int, int> indx;
int total = 0;
for (int i = A.size() - 1; i >= 0; --i) {
auto upper = indx.lower_bound(A[i]); // return 1st elem s.t. >= val
auto lower = indx.upper_bound(A[i]); // return 1st elem s.t. > val
if (upper != indx.end()) {
bound[i].first = bound[upper->second].second;
}
if (lower != indx.begin()) {
--lower;
bound[i].second = bound[lower->second].first;
}
total += bound[i].first; // if it works when starting at index `i`
indx[A[i]] = i;
}
return total;
}
};