Good evening! Here's our prompt for today.
Understanding the Matrix Shift Problem
Suppose you have a matrix where each row and column is sorted in ascending order. Your task is to apply two specific types of shifts, described below, and locate a given element x
in the transformed matrix.
Shift Types
Left Circular Shift (l):
- Definition: Moves the first column to the last position, shifting all other columns one step left.
Example:
Before:
PYTHON1[ 2 [1, 2, 3], 3 [4, 5, 6], 4 [7, 8, 9] 5]
After:
PYTHON1[ 2 [2, 3, 1], 3 [5, 6, 4], 4 [8, 9, 7] 5]
Visual Explanation: Imagine the columns on a circular conveyor belt. The first column wraps to the end, while others shift left.
Top Circular Shift (u):
- Definition: Moves the first row to the last position, shifting all other rows one step up.
Example:
Before:
PYTHON1[ 2 [1, 2, 3], 3 [4, 5, 6], 4 [7, 8, 9] 5]
After:
PYTHON1[ 2 [4, 5, 6], 3 [7, 8, 9], 4 [1, 2, 3] 5]
Visual Explanation: Picture the rows on a circular escalator. The first row descends to the bottom, while others shift up.
Applying the Shifts to a Specific Example
Let's consider a sequence of shifts like [l,u,l,u,u]
and apply them to the given matrix:
1matrix = [
2 [ 1, 2, 3, 4, 5],
3 [ 6, 7, 8, 9,10],
4 [11,12,13,14,15],
5 [16,17,18,19,20]
6]
After applying these rotations, the matrix transforms to:
1matrix = [
2 [9 ,10, 6, 7, 8],
3 [14,15,11,12,13],
4 [19,20,16,17,18],
5 [ 4, 5, 1, 2, 3]
6]
Here's an illustration to help visualize the problem:

Your Task
Given this final matrix and a specific value x
, how can you efficiently find the location of this element in the array and return it?
Constraints
- Matrix Size: Up to
10^5 x 10^5
- Time Complexity:
O(nlogn)
- Memory Complexity:
O(1)
- Element Existence: The value
x
is in the matrix. - Minimum Elements: At least 1 element in the matrix.
- Sorting Order: Always sorted in all rows and columns.
- Uniqueness: Contains unique elements.
Considering these constraints and the above example, can you develop a method to locate the specified element in the transformed matrix?
Try to solve this here or in Interactive Mode.
How do I practice this challenge?
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var assert = require('assert');
​
function findElementInMatrix(matrix, x) {
// Your Code Here
}
​
try {
let matrix = [
[9, 10, 6, 7, 8],
[14, 15, 11, 12, 13],
[19, 20, 16, 17, 18],
[4, 5, 1, 2, 3],
];
let result = findElementInMatrix(matrix, 17);
assert(result.length === 2, 'Return type must be of length 2');
assert(result[0] === 2, 'Wrong Answer');
assert(result[1] === 3, 'Wrong Answer');
​
console.log(
'PASSED: The below matrix should result in `(2,3)`.
​
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