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描述
You are given an integer n. An 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 3.
Example 2:
Input: n = 2
Output: 1
Explanation: According to the given rules, the maximum between nums[0], nums[1], and nums[2] is 1.
Example 3:
Input: n = 3
Output: 2
Explanation: According to the given rules, the maximum between nums[0], nums[1], nums[2], and nums[3] is 2.
Note:
0 <= n <= 100
解析
根据题意，就是给出一个数字 n ，生成一个 n+1 个数字的列表，找出最大值。生成列表 nums 的过程如下：
- 当索引为 0 的时候，该位置的值为 0
- 当索引为 1 的时候，该位置的值为 1
- 当索引为偶数 i 的时候，该位置的值为 nums[i//2]
- 当索引为奇数 i 的时候，该位置的值为 nums[i//2]+nums[i//2+1]
解答
class Solution(object):
def getMaximumGenerated(self, n):
"""
:type n: int
:rtype: int
"""
if n==0:
return 0
if n==1:
return 1
nums = [0, 1]
for i in range(2, n+1):
if i%2==0:
nums.append(nums[i//2])
else:
nums.append(nums[i//2]+nums[i//2+1])
return max(nums)
运行结果
Runtime: 16 ms, faster than 84.09% of Python online submissions for Get Maximum in Generated Array.
Memory Usage: 13.2 MB, less than 85.23% of Python online submissions for Get Maximum in Generated Array.
解析
另外，可以用递归的方式解决。思路和上面一样。递归的出口就是当 n<=1 的时候返回结果，否则就将 n//2 得到索引位置 p ，当 n 为奇数则求 cal(p)+cal(p+1) ，当 n 为偶数则求 cal(p) ，函数递归结束可得到结果。每个元素通过递归结束得到的结果组成的列表，再通过 max 函数求最大值。
解答
class Solution(object):
def getMaximumGenerated(self, n):
"""
:type n: int
:rtype: int
"""
def cal(n):
if n <= 1: return n
p = n // 2
return cal(p) + cal(p + 1) if n%2 else cal(p)
return max(cal(i) for i in range(n + 1))
运行结果
Runtime: 36 ms, faster than 5.42% of Python online submissions for Get Maximum in Generated Array.
Memory Usage: 13.4 MB, less than 33.73% of Python online submissions for Get Maximum in Generated Array.
原题链接：leetcode.com/problems/ge…
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