1646. Get Maximum in Generated Array #

Problem #

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.

Constraints:

• 0 <= n <= 100

Problem Summary #

Given an integer n. Generate an array nums of length n + 1 according to the following rules:

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

Return the maximum value in the generated array nums.

Solution Approach #

• Given an array of length n + 1, generate this array according to the generation rules, and find the maximum value in the array.
• This is an easy problem. Generate the array according to the problem statement, and record and update the maximum value while generating it.
• Pay attention to the boundary condition: when n is 0, the array has only one element, 0.

Code #

package leetcode

func getMaximumGenerated(n int) int {
	if n == 0 {
		return 0
	}
	nums, max := make([]int, n+1), 0
	nums[0], nums[1] = 0, 1
	for i := 0; i <= n; i++ {
		if nums[i] > max {
			max = nums[i]
		}
		if 2*i >= 2 && 2*i <= n {
			nums[2*i] = nums[i]
		}
		if 2*i+1 >= 2 && 2*i+1 <= n {
			nums[2*i+1] = nums[i] + nums[i+1]
		}
	}
	return max
}