Shuffle the Array - Practice Coding Problems

Shuffle the Array - Problem

Array Easy

Shuffle the Array is a fundamental array manipulation problem that tests your understanding of index mapping and pattern recognition.

You're given an array nums containing exactly 2n elements, structured as two equal halves: [x₁, x₂, ..., xₙ, y₁, y₂, ..., yₙ]. The first half contains the x-values and the second half contains the corresponding y-values.

Your task is to interleave these two halves to create a new array in the format: [x₁, y₁, x₂, y₂, ..., xₙ, yₙ].

Example: If nums = [2, 5, 1, 3, 4, 7] where n = 3, the x-values are [2, 5, 1] and y-values are [3, 4, 7]. The shuffled result should be [2, 3, 5, 4, 1, 7].

Input & Output

example_1.py — Basic Case

$ Input: nums = [2,5,1,3,4,7], n = 3

› Output: [2,3,5,4,1,7]

💡 Note: The first half [2,5,1] represents x-values, second half [3,4,7] represents y-values. Interleaving gives us [x₁,y₁,x₂,y₂,x₃,y₃] = [2,3,5,4,1,7]

example_2.py — Minimum Case

$ Input: nums = [1,2,3,4], n = 2

› Output: [1,3,2,4]

💡 Note: With n=2, x-values are [1,2] and y-values are [3,4]. The shuffle pattern gives [1,3,2,4]

example_3.py — Single Pair

$ Input: nums = [1,1], n = 1

› Output: [1,1]

💡 Note: Edge case with only one pair: x₁=1, y₁=1, so result is [1,1]

Constraints

1 ≤ n ≤ 500
nums.length == 2n
1 ≤ nums[i] ≤ 10³
Array contains exactly 2n elements

Visualization

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Understanding the Visualization

Split the Deck

Identify the two halves: X-cards [2,5,1] and Y-cards [3,4,7]

Recognize the Pattern

Each position in result follows: even positions get X-cards, odd positions get Y-cards

Perform Perfect Shuffle

Interleave one card from each pile: X₁,Y₁,X₂,Y₂,X₃,Y₃

Complete the Shuffle

Final arrangement: [2,3,5,4,1,7] - perfectly interleaved!

Key Takeaway

🎯 Key Insight: The shuffle follows a predictable mathematical pattern - each element at position i maps to position 2*i, and its pair at i+n maps to 2*i+1. This allows us to solve the problem optimally in a single pass!

Asked in

a Amazon 15 G Google 12 ⊞ Microsoft 8 f Meta 6

The optimal solution uses pattern recognition to directly map elements: for each index i from 0 to n-1, place nums[i] at result[2*i] and nums[i+n] at result[2*i+1]. This achieves O(n) time and O(n) space complexity with elegant, bug-free code.

Common Approaches

Approach	Time	Space	Notes
✓ Optimal Pattern Recognition	O(n)	O(n)	Directly map array elements using mathematical pattern i → (2i, 2i+1)

Optimal Pattern Recognition — Algorithm Steps

Create a result array of size 2n
Iterate through indices 0 to n-1 (first half)
For each index i, place nums[i] at result[2*i]
Place nums[i+n] at result[2*i+1]
Return the result array

Visualization

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Step-by-Step Walkthrough

Identify Pattern

Recognize that element at index i goes to position 2*i

Map X Values

Place nums[i] at result[2*i] for each i from 0 to n-1

Map Y Values

Place nums[i+n] at result[2*i+1] for each i from 0 to n-1

Complete in One Pass

Both mappings happen simultaneously in a single loop

Code -

solution.c — C

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

int* shuffle(int* nums, int numsSize, int n, int* returnSize) {
    *returnSize = 2 * n;
    int* result = (int*)malloc(2 * n * sizeof(int));
    
    for (int i = 0; i < n; i++) {
        result[2 * i] = nums[i];      // Place x_i
        result[2 * i + 1] = nums[i + n];  // Place y_i
    }
    
    return result;
}

int main() {
    int nums[] = {2, 5, 1, 3, 4, 7};
    int returnSize;
    int* result = shuffle(nums, 6, 3, &returnSize);
    
    for (int i = 0; i < returnSize; i++) {
        printf("%d ", result[i]);
    }
    free(result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

We iterate through n elements once, performing constant time operations for each pair

✓ Linear Growth

Space Complexity

O(n)

We create a new result array of size 2n to store the shuffled elements

⚡ Linearithmic Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Optimal Pattern Recognition — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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