jump-game-ix

You are given an integer array nums.

From any index i, you can jump to another index j under the following rules:

• Jump to index j where j > i is allowed only if nums[j] < nums[i].


• Jump to index j where j < i is allowed only if nums[j] > nums[i].

For each index i, find the maximum value in nums that can be reached by following any sequence of valid jumps starting at i.

Return an array ans where ans[i] is the maximum value reachable starting from index i.

Example 1:

Input: nums = [2,1,3]

Output: [2,2,3]

Explanation:

• For i = 0: No jump increases the value.


• For i = 1: Jump to j = 0 as nums[j] = 2 is greater than nums[i].


• For i = 2: Since nums[2] = 3 is the maximum value in nums, no jump increases the value.

Thus, ans = [2, 2, 3].

Example 2:

Input: nums = [2,3,1]

Output: [3,3,3]

Explanation:

• For i = 0: Jump forward to j = 2 as nums[j] = 1 is less than nums[i] = 2, then from i = 2 jump to j = 1 as nums[j] = 3 is greater than nums[2].


• For i = 1: Since nums[1] = 3 is the maximum value in nums, no jump increases the value.


• For i = 2: Jump to j = 1 as nums[j] = 3 is greater than nums[2] = 1.

Thus, ans = [3, 3, 3].

Constraints:

• 1 <= nums.length <= 105


• 1 <= nums[i] <= 109​​​​​​​