Spiral Matrix

Lesson 39/45

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Data Structures and Algorithms Arrays

Spiral Matrix

Lesson 39/45

Spiral Matrix

Traversing a 2D matrix in a spiral pattern, starting from the top-left and moving inwards in a clockwise direction.

Time

O(N * M)

Space

O(1) (excluding result)

Key Principle 1

Four boundary trackers

Key Principle 2

Layer-by-layer traversal

Key Principle 3

Boundary contraction after each row/col

Key Principle 4

Handles non-square matrices

SPIRAL_MATRIX_LAB
DIM:
Current Step
Initialize boundary pointers: top, bottom, left, right.
Playback
Boundaries ⠿
TOP0
BOTTOM3
LEFT0
RIGHT3
Spiral Logic ⠿
1int top = 0, bottom = m - 1, left = 0, right = n - 1;
2while (top <= bottom && left <= right) {
3    for (int i = left; i <= right; i++) res.push(matrix[top][i]); top++;
4    for (int i = top; i <= bottom; i++) res.push(matrix[i][right]); right--;
5    if (top <= bottom) for (int i = right; i >= left; i--) res.push(matrix[bottom][i]); bottom--;
6    if (left <= right) for (int i = bottom; i >= top; i--) res.push(matrix[i][left]); left++;
7}
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DATA STRUCTURES • ALGORITHMS

Spiral Matrix

Traversing a 2D matrix in a spiral pattern, starting from the top-left and moving inwards in a clockwise direction.

Time

O(N * M)

Space

O(1) (excluding result)

Key Principle 1

Four boundary trackers

Key Principle 2

Layer-by-layer traversal

Key Principle 3

Boundary contraction after each row/col

Key Principle 4

Handles non-square matrices

SPIRAL_MATRIX_LAB
DIM:
Current Step
Initialize boundary pointers: top, bottom, left, right.
Playback
Boundaries ⠿
TOP0
BOTTOM3
LEFT0
RIGHT3
Spiral Logic ⠿
1int top = 0, bottom = m - 1, left = 0, right = n - 1;
2while (top <= bottom && left <= right) {
3    for (int i = left; i <= right; i++) res.push(matrix[top][i]); top++;
4    for (int i = top; i <= bottom; i++) res.push(matrix[i][right]); right--;
5    if (top <= bottom) for (int i = right; i >= left; i--) res.push(matrix[bottom][i]); bottom--;
6    if (left <= right) for (int i = bottom; i >= top; i--) res.push(matrix[i][left]); left++;
7}
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