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]
when2 <= 2 * i <= n
nums[2 * i + 1] = nums[i] + nums[i + 1]
when2 <= 2 * i + 1 <= n
Returnthe 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.
Constraints:
0 <= n <= 100
Solution: Simulation
Generate the array by the given rules.
Time complexity: O(n)
Space complexity: O(n)
C++
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class Solution { public: int getMaximumGenerated(int n) { vector<int> nums(n + 1); nums[0] = 0; if (n > 0) nums[1] = 1; for (int i = 1; i * 2 <= n; ++i) { nums[2 * i] = nums[i]; if (i * 2 + 1 <= n) nums[2 * i + 1] = nums[i] + nums[i + 1]; } return *max_element(begin(nums), end(nums)); } }; |
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