Get Maximum in Generated Array

Get Maximum in Generated Array - Problem

Array Simulation Easy

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.

Input & Output

Example 1 — Basic Case

$ Input: n = 7

› Output: 3

💡 Note: nums = [0,1,1,2,1,3,2,3]. Generated by rules: nums[2]=nums[1]=1, nums[3]=nums[1]+nums[2]=2, nums[4]=nums[2]=1, nums[5]=nums[2]+nums[3]=3, nums[6]=nums[3]=2, nums[7]=nums[3]+nums[4]=3. Maximum is 3.

Example 2 — Small Input

$ Input: n = 2

› Output: 1

💡 Note: nums = [0,1,1]. nums[2] = nums[1] = 1. Maximum is 1.

Example 3 — Edge Case

$ Input: n = 0

› Output: 0

💡 Note: nums = [0]. Only element is 0, so maximum is 0.

Constraints

0 ≤ n ≤ 100

Visualization

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Asked in

a Amazon 25 M Microsoft 20

The key insight is to recognize this as a simulation problem where we build the array following given rules and track the maximum. The optimal approach tracks the maximum while generating elements in a single pass. Time: O(n), Space: O(n)

Common Approaches

✓ Generate Array Then Find Maximum

⏱️ Time: O(n) Space: O(n)

Build the array by following the generation rules exactly, then iterate through the completed array to find the maximum value.

Track Maximum While Generating

⏱️ Time: O(n) Space: O(n)

Build the array following the generation rules but simultaneously track the maximum value encountered, eliminating the need for a separate maximum search pass.

Generate Array Then Find Maximum — Algorithm Steps

Initialize array with nums[0] = 0 and nums[1] = 1
Generate remaining elements using the given rules
Scan through array to find maximum value

Visualization

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Step-by-Step Walkthrough

Initialize

Set nums[0] = 0, nums[1] = 1

Generate

Fill array using rules for even/odd indices

Find Max

Scan through completed array to find maximum

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int solution(int n) {
    if (n == 0) return 0;
    
    int* nums = (int*)malloc((n + 1) * sizeof(int));
    nums[0] = 0;
    if (n >= 1) nums[1] = 1;
    
    for (int i = 2; i <= n; i++) {
        if (i % 2 == 0) {
            nums[i] = nums[i / 2];
        } else {
            nums[i] = nums[i / 2] + nums[i / 2 + 1];
        }
    }
    
    int max = nums[0];
    for (int i = 1; i <= n; i++) {
        if (nums[i] > max) {
            max = nums[i];
        }
    }
    
    free(nums);
    return max;
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%d\n", solution(n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Generate n elements once, then scan n elements once

✓ Linear Growth

Space Complexity

O(n)

Store the complete array of n+1 elements

⚡ Linearithmic Space

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Medium Frequency

~10 min Avg. Time

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Input & Output

Constraints

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Related Problems

Common Approaches

Generate Array Then Find Maximum — Algorithm Steps

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Code -

Time & Space Complexity

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