Reach the Last Index in the Fewest Jumps
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
You start at index `0` of the integer array `jumps`. From index `i`, choose an integer distance `d` and move to index `i + d`, provided that:
- `0 <= d <= jumps[i]`
- `i + d < jumps.length`
Return the fewest jumps needed to arrive at the final index. Every allowed input guarantees that this index is reachable.
### Examples
**Example 1**
```text
Input: jumps = [4,1,2,1,3,0,1,0]
Output: 2
```
One jump can move from index `0` to index `4`, and the next can move from index `4` to index `7`. A single jump from the starting position cannot reach index `7`.
**Example 2**
```text
Input: jumps = [0]
Output: 0
```
The starting index is already the final index, so no jump is needed.
### Constraints
- `1 <= jumps.length <= 10^4`
- `0 <= jumps[i] <= 1000`
- The final index is reachable from index `0` under the stated jump rules.
Overview: Find the minimum number of jumps to a reachable final array index, where each entry limits the distance of a jump from that position.
