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Snail Traversal
Transform a 1D array into a 2D matrix following the snail traversal core interview pattern efficiently and safely.
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Medium · Snail Traversal core interview pattern
Answer-first summary
Transform a 1D array into a 2D matrix following the snail traversal core interview pattern efficiently and safely.
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Start by validating input dimensions to ensure rowsCount * colsCount equals the array length. Fill the matrix column by column, alternating top-to-bottom and bottom-to-top directions. Track the current column and direction to handle the snail traversal pattern without errors.
Problem Statement
Write a function that converts a 1D array into a 2D array arranged in snail traversal order. Snail traversal begins at the top-left of the matrix, proceeds down the first column, up the next column, and continues alternating column directions until all values are placed. If the total elements do not match rowsCount * colsCount, return an empty array to indicate invalid input.
For example, given nums = [19, 10, 3, 7, 9, 8, 5, 2, 1, 17, 16, 14, 12, 18, 6, 13, 11, 20, 4, 15], rowsCount = 5, and colsCount = 4, the snail traversal should produce a matrix where columns alternate top-to-bottom and bottom-to-top placement. Invalid dimensions or empty arrays should safely return [].
Examples
Example 1
Input: nums = [19, 10, 3, 7, 9, 8, 5, 2, 1, 17, 16, 14, 12, 18, 6, 13, 11, 20, 4, 15] rowsCount = 5 colsCount = 4
Output: [ [19,17,16,15], [10,1,14,4], [3,2,12,20], [7,5,18,11], [9,8,6,13] ]
Example details omitted.
Example 2
Input: nums = [1,2,3,4] rowsCount = 1 colsCount = 4
Output: [[1, 2, 3, 4]]
Example details omitted.
Example 3
Input: nums = [1,3] rowsCount = 2 colsCount = 2
Output: []
2 multiplied by 2 is 4, and the original array [1,3] has a length of 2; therefore, the input is invalid.
Constraints
- 0 <= nums.length <= 250
- 1 <= nums[i] <= 1000
- 1 <= rowsCount <= 250
- 1 <= colsCount <= 250
Solution Approach
Input Validation
Check if nums.length equals rowsCount * colsCount. Return an empty array immediately for mismatches. This prevents index errors and ensures only valid transformations proceed.
Matrix Construction with Direction Tracking
Initialize a 2D array of size rowsCount x colsCount. Use a boolean to track whether the current column is filled top-to-bottom or bottom-to-top. Iterate through nums, filling each column according to the direction, then flip the boolean for the next column.
Column-wise Filling
For each column, compute row indices based on the current direction. Assign array values sequentially while switching direction each column. This preserves the snail traversal pattern exactly as required by the problem.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(N) |
| Space | O(N) |
Time complexity is O(N) because every element is visited once. Space complexity is O(N) due to the resulting 2D array holding all elements from the original array.
What Interviewers Usually Probe
- Ask about handling invalid input arrays that do not match rowsCount * colsCount.
- Check if the candidate correctly alternates column directions for snail traversal.
- Expect discussion on efficient O(N) column-wise filling without redundant operations.
Common Pitfalls or Variants
Common pitfalls
- Not validating the input length before constructing the matrix.
- Filling all columns in the same direction, breaking the snail pattern.
- Incorrectly computing row indices for bottom-to-top traversal.
Follow-up variants
- Snail traversal row-wise instead of column-wise with alternating directions.
- Generating the traversal order as a flat 1D output instead of a 2D matrix.
- Handling dynamic resizing or non-rectangular matrices with padding.
FAQ
What is the core pattern for snail traversal in this problem?
The core pattern alternates column directions, filling top-to-bottom then bottom-to-top for each subsequent column.
What should I return if rowsCount and colsCount do not match the array length?
Return an empty array to indicate invalid input and avoid out-of-bounds errors.
Can I implement snail traversal row-wise instead of column-wise?
Yes, but you must maintain the alternating direction pattern, just applied to rows instead of columns.
What is the time complexity of the snail traversal implementation?
It is O(N) since each element is placed exactly once into the 2D matrix.
How do I handle bottom-to-top traversal correctly?
Compute row indices in reverse order for columns marked as bottom-to-top, and then flip direction for the next column.
Solution
Solution 1
#### TypeScript
declare global {
interface Array<T> {
snail(rowsCount: number, colsCount: number): number[][];
}
}
Array.prototype.snail = function (rowsCount: number, colsCount: number): number[][] {
if (rowsCount * colsCount !== this.length) {
return [];
}
const ans: number[][] = Array.from({ length: rowsCount }, () => Array(colsCount));
for (let h = 0, i = 0, j = 0, k = 1; h < this.length; ++h) {
ans[i][j] = this[h];
i += k;
if (i === rowsCount || i === -1) {
i -= k;
k = -k;
++j;
}
}
return ans;
};
/**
* const arr = [1,2,3,4];
* arr.snail(1,4); // [[1,2,3,4]]
*/