problem656

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656. Coin Path (Hard)

Given an array A (index starts at 1) consisting of N integers: A₁, A₂, ..., A_N and an integer B. The integer B denotes that from any place (suppose the index is i) in the array A, you can jump to any one of the place in the array A indexed i+1, i+2, …, i+B if this place can be jumped to. Also, if you step on the index i, you have to pay A_i coins. If A_i is -1, it means you can’t jump to the place indexed i in the array.

Now, you start from the place indexed 1 in the array A, and your aim is to reach the place indexed N using the minimum coins. You need to return the path of indexes (starting from 1 to N) in the array you should take to get to the place indexed N using minimum coins.

If there are multiple paths with the same cost, return the lexicographically smallest such path.

If it's not possible to reach the place indexed N then you need to return an empty array.

Example 1:

Input: [1,2,4,-1,2], 2
Output: [1,3,5]

Example 2:

Input: [1,2,4,-1,2], 1
Output: []

Note:

1. Path Pa₁, Pa₂, ..., Pa_n is lexicographically smaller than Pb₁, Pb₂, ..., Pb_m, if and only if at the first i where Pa_i and Pb_i differ, Pa_i < Pb_i; when no such i exists, then n < m.
2. A₁ >= 0. A₂, ..., A_N (if exist) will in the range of [-1, 100].
3. Length of A is in the range of [1, 1000].
4. B is in the range of [1, 100].

Related Topics

[Array] [Dynamic Programming]

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