1646 Get Maximum in Generated Array

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

  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

其实这题有点迷，一看上去，是不是斐波那契数列？然后再看了看，是不是heap？各种想，怎么省空间，算值。然后一看n最大只是100。那，就真的很简单了，其实不懂这题想考什么。规律从第一个例子里就能看出来。T:O(n), S:O(n)

public int getMaximumGenerated(int n) {
    if (n < 0 || n > 100) {
        return -1;
    }

    if (n < 2) {
        return n;
    }

    int max = 0;
    int[] holder = new int[n + 1];
    holder[0] = 0;
    holder[1] = 1;

    for (int i = 2; i <= n; i++) {
        if (i % 2 == 0) {
            holder[i] = holder[i / 2];
        } else {
            holder[i] = holder[i / 2] + holder[i / 2 + 1];
        }

        max = Math.max(max, holder[i]);
    }

    return max;
}