837. New 21 Game LeetCode Solution | Easy Approach

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New 21 Game Alice plays the following game, loosely based on the card game “21”.

Alice starts with `0` points and draws numbers while she has less than `k` points. During each draw, she gains an integer number of points randomly from the range `[1, maxPts]`, where `maxPts` is an integer. Each draw is independent and the outcomes have equal probabilities.

Alice stops drawing numbers when she gets `k` or more points.

Return the probability that Alice has `n` or fewer points.

Answers within `10-5` of the actual answer are considered accepted.

Example 1:

```Input: n = 10, k = 1, maxPts = 10
Output: 1.00000
Explanation: Alice gets a single card, then stops.
```

Example 2:

```Input: n = 6, k = 1, maxPts = 10
Output: 0.60000
Explanation: Alice gets a single card, then stops.
In 6 out of 10 possibilities, she is at or below 6 points.
```

Example 3:

```Input: n = 21, k = 17, maxPts = 10
Output: 0.73278
```

Constraints:

• `0 <= k <= n <= 104`
• `1 <= maxPts <= 104`

Time: O(n)
Space: O(n)

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