Get Maximum in Generated Array - Practice Coding Problems

Get Maximum in Generated Array - Problem

Array Simulation Easy

You are given an integer n and need to generate a special array following specific rules, then find the maximum value in it.

The array nums of length n + 1 is generated using these rules:

nums[0] = 0 (base case)
nums[1] = 1 (base case)
For even indices: nums[2 * i] = nums[i] when 2 ≤ 2 * i ≤ n
For odd indices: nums[2 * i + 1] = nums[i] + nums[i + 1] when 2 ≤ 2 * i + 1 ≤ n

Goal: Return the maximum integer in the generated array.

Example: For n = 7, we generate: [0, 1, 1, 2, 2, 3, 3, 4] and return 4.

Input & Output

example_1.py — Basic Case

$ Input: n = 7

› Output: 4

💡 Note: Generated array: [0,1,1,2,2,3,3,4]. 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]=4. Maximum is 4.

example_2.py — Small Case

$ Input: n = 2

› Output: 1

💡 Note: Generated array: [0,1,1]. We have nums[0]=0, nums[1]=1, nums[2]=nums[1]=1. Maximum is 1.

example_3.py — Edge Case

$ Input: n = 0

› Output: 0

💡 Note: Generated array: [0]. Only nums[0]=0 exists, so maximum is 0.

Constraints

0 ≤ n ≤ 100
The generated array will have exactly n + 1 elements
All values in the array will be non-negative integers

Visualization

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Understanding the Visualization

Root Generation

Start with nums[0]=0 and nums[1]=1 as the foundation

Even Index Rule

For even indices like 2,4,6: copy value from nums[i/2]

Odd Index Rule

For odd indices like 3,5,7: sum nums[i//2] + nums[i//2+1]

Maximum Discovery

Scan completed array to find the largest generated value

Key Takeaway

🎯 Key Insight: This problem is pure simulation - no complex algorithms needed! Just follow the rules step by step to build the array, then find the maximum. The pattern creates a binary tree-like structure where values propagate down through specific mathematical relationships.

Asked in

a Amazon 25 G Google 20 ⊞ Microsoft 15 f Meta 12

The optimal approach uses direct simulation to build the array following the given rules in O(n) time. We initialize base cases nums[0]=0 and nums[1]=1, then for each index i from 2 to n, apply the appropriate rule: nums[2*i] = nums[i] for even indices and nums[2*i+1] = nums[i] + nums[i+1] for odd indices. Finally, we scan through the completed array to find the maximum value.

Common Approaches

Approach	Time	Space	Notes
✓ Simulation Approach	O(n)	O(n)	Build the array step by step following the given rules, then find maximum

Simulation Approach — Algorithm Steps

Initialize array of size n+1 with nums[0]=0 and nums[1]=1
For each index i from 2 to n, apply the appropriate rule based on whether i is even or odd
If i is even: nums[i] = nums[i/2]
If i is odd: nums[i] = nums[i//2] + nums[i//2 + 1]
Scan through the completed array to find maximum value

Visualization

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Step-by-Step Walkthrough

Initialize Base Cases

Set nums[0] = 0 and nums[1] = 1

Apply Even Rule

For even indices: nums[2*i] = nums[i]

Apply Odd Rule

For odd indices: nums[2*i+1] = nums[i] + nums[i+1]

Find Maximum

Scan through completed array to find max value

Code -

solution.c — C

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

int getMaximumGenerated(int n) {
    if (n == 0) return 0;
    if (n == 1) return 1;
    
    int* nums = (int*)malloc((n + 1) * sizeof(int));
    nums[0] = 0;
    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 maxVal = nums[0];
    for (int i = 1; i <= n; i++) {
        if (nums[i] > maxVal) {
            maxVal = nums[i];
        }
    }
    
    free(nums);
    return maxVal;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(n)

We visit each index exactly once to generate values, then scan once more to find maximum

✓ Linear Growth

Space Complexity

O(n)

We store the entire generated array of size n+1

⚡ Linearithmic Space

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Medium Frequency

~12 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Simulation Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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