Question

1646. Get Maximum in Generated Array

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Description

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

Solutions

Solution 1

class Solution:
  def getMaximumGenerated(self, n: int) -> int:
    if n < 2:
      return n
    nums = [0] * (n + 1)
    nums[1] = 1
    for i in range(2, n + 1):
      nums[i] = nums[i >> 1] if i % 2 == 0 else nums[i >> 1] + nums[(i >> 1) + 1]
    return max(nums)

class Solution {
  public int getMaximumGenerated(int n) {
    if (n < 2) {
      return n;
    }
    int[] nums = new int[n + 1];
    nums[1] = 1;
    for (int i = 2; i <= n; ++i) {
      nums[i] = i % 2 == 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
    }
    return Arrays.stream(nums).max().getAsInt();
  }
}

class Solution {
public:
  int getMaximumGenerated(int n) {
    if (n < 2) {
      return n;
    }
    int nums[n + 1];
    nums[0] = 0;
    nums[1] = 1;
    for (int i = 2; i <= n; ++i) {
      nums[i] = i % 2 == 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
    }
    return *max_element(nums, nums + n + 1);
  }
};

func getMaximumGenerated(n int) int {
  if n < 2 {
    return n
  }
  nums := make([]int, n+1)
  nums[1] = 1
  for i := 2; i <= n; i++ {
    if i%2 == 0 {
      nums[i] = nums[i/2]
    } else {
      nums[i] = nums[i/2] + nums[i/2+1]
    }
  }
  return slices.Max(nums)
}

function getMaximumGenerated(n: number): number {
  if (n === 0) {
    return 0;
  }
  const nums: number[] = new Array(n + 1).fill(0);
  nums[1] = 1;
  for (let i = 2; i < n + 1; ++i) {
    nums[i] = i % 2 === 0 ? nums[i >> 1] : nums[i >> 1] + nums[(i >> 1) + 1];
  }
  return Math.max(...nums);
}