# 1646.get-maximum-in-generated-array

## Statement

• `nums[0] = 0`
• `nums[1] = 1`
• `2 <= 2 * i <= n` 时，`nums[2 * i] = nums[i]`
• `2 <= 2 * i + 1 <= n` 时，`nums[2 * i + 1] = nums[i] + nums[i + 1]`

``````输入：n = 7

nums[0] = 0
nums[1] = 1
nums[(1 * 2) = 2] = nums[1] = 1
nums[(1 * 2) + 1 = 3] = nums[1] + nums[2] = 1 + 1 = 2
nums[(2 * 2) = 4] = nums[2] = 1
nums[(2 * 2) + 1 = 5] = nums[2] + nums[3] = 1 + 2 = 3
nums[(3 * 2) = 6] = nums[3] = 2
nums[(3 * 2) + 1 = 7] = nums[3] + nums[4] = 2 + 1 = 3

``````

``````输入：n = 2

``````

``````输入：n = 3

``````

• `0 <= n <= 100`

You are given an integer `n`. A 0-indexed integer array `nums` of length `n + 1` is generated in the following way:

• `nums[0] = 0`
• `nums[1] = 1`
• `nums[2 * i] = nums[i]` when `2 <= 2 * i <= n`
• `nums[2 * i + 1] = nums[i] + nums[i + 1]` when `2 <= 2 * i + 1 <= n`

Return the maximum integer in the array `nums`​​​.

Example 1:

``````Input: n = 7
Output: 3
Explanation: According to the given rules:
nums[0] = 0
nums[1] = 1
nums[(1 * 2) = 2] = nums[1] = 1
nums[(1 * 2) + 1 = 3] = nums[1] + nums[2] = 1 + 1 = 2
nums[(2 * 2) = 4] = nums[2] = 1
nums[(2 * 2) + 1 = 5] = nums[2] + nums[3] = 1 + 2 = 3
nums[(3 * 2) = 6] = nums[3] = 2
nums[(3 * 2) + 1 = 7] = nums[3] + nums[4] = 2 + 1 = 3
Hence, nums = [0,1,1,2,1,3,2,3], and the maximum is max(0,1,1,2,1,3,2,3) = 3.
``````

Example 2:

``````Input: n = 2
Output: 1
Explanation: According to the given rules, nums = [0,1,1]. The maximum is max(0,1,1) = 1.
``````

Example 3:

``````Input: n = 3
Output: 2
Explanation: According to the given rules, nums = [0,1,1,2]. The maximum is max(0,1,1,2) = 2.
``````

Constraints:

• `0 <= n <= 100`

## Solution

``````class Solution:
def getMaximumGenerated(self, n: int) -> int:
if n == 0:
return 0

f = [0 for i in range(n + 1)]
f[1] = 1

for i in range(1, n + 1):
if (2 * i) <= n:
f[2 * i] = f[i]
if (2 * i + 1) <= n:
f[2 * i + 1] = f[i] + f[i + 1]

return max(f)
``````