### Max Leaps in Jump Game (Main Thread)

Here is the interview question prompt, presented for reference.

We have an array that model square blocks on a city street. On each block is a non-negative whole number.

Ever heard of hopscotch? Picture that as an array:

`[1, 3, 2, 2, 1]`

Now, in hopscotch, you need to jump in patterns from the start to the end of the boxes. We can model that behavior in the above array-- so we begin at the first index and see the number `1`.

Let also assume that each integer in the array represents a maximum jump length from that index. So at index `0`, we encounter the value `1`, and thus can jump `1` time to the next block. This lets us make our way over to index `1` (which contains `3`).

``````arr = [1, 3, 2, 2, 1]
idx    0, 1, 2, 3, 4
``````

However, with numbers greater than `1`, we don't always have to take the maximum leap. At index `1`, since the max jump is `3`, we can choose to jump either `1`, `2`, or `3` squares (but no more than that).

Example 1

Following this logic, can you write an algorithm that determines if we are able to make it until the very end? In our example of `[1, 3, 2, 2, 1]`, we can make the following moves:

1. `1` leap from index `0` to `1`
2. `3` leaps that get us from index `1` to `4`

Since we can get to index `4`, we would return `true`.

Example 2

On the other hand, here's an example that wouldn't work:

`[2, 1, 0, 1, 4]`

Regardless of whether we jump once or twice at the first element, we have to end up at index `2`. Then, because the max jump at index `2` is `0`, we can never progress beyond that, and thus would return `false`.

### Constraints

• Length of the array <= `100000`
• The values of the array will be between `0` and `1000000000`
• Expected time complexity : `O(n)`
• Expected space complexity : `O(1)`

You can see the full challenge with visuals at this link.

Challenges • Asked over 5 years ago by Jake from AlgoDaily

Jake from AlgoDaily Commented on Nov 30, 2017:

This is the main discussion thread generated for Max Leaps in Jump Game.

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