Spiral Matrix Traversal in DSA C - Execution Trace

Concept Flow - Spiral Matrix Traversal

Initialize boundaries: top, bottom, left, right

↓

Traverse from left to right along top row

↓

Move top boundary down

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Traverse from top to bottom along right column

↓

Move right boundary left

↓

Traverse from right to left along bottom row

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Move bottom boundary up

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Traverse from bottom to top along left column

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Move left boundary right

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Check if boundaries crossed

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Repeat or End

We keep four boundaries and move inward in a spiral: top row left to right, right column top to bottom, bottom row right to left, left column bottom to top, then shrink boundaries and repeat until all elements are visited.

Execution Sample

DSA C

int top = 0, bottom = rows - 1;
int left = 0, right = cols - 1;
while (top <= bottom && left <= right) {
  // Traverse and print edges
  // Update boundaries
}

This code traverses the matrix edges in spiral order by updating boundaries after each edge traversal.

Execution Table

Step	Operation	Nodes in List	Pointer Changes	Visual State
1	Initialize boundaries	N/A	top=0, bottom=2, left=0, right=2	[[1,2,3],[4,5,6],[7,8,9]]
2	Traverse top row left to right	Elements visited: 1,2,3	top=0 -> top=1	[[1,2,3],[4,5,6],[7,8,9]] Visited: 1->2->3
3	Traverse right column top to bottom	Elements visited: 6,9	right=2 -> right=1	[[1,2,3],[4,5,6],[7,8,9]] Visited: 1->2->3->6->9
4	Traverse bottom row right to left	Elements visited: 8,7	bottom=2 -> bottom=1	[[1,2,3],[4,5,6],[7,8,9]] Visited: 1->2->3->6->9->8->7
5	Traverse left column bottom to top	Elements visited: 4	left=0 -> left=1	[[1,2,3],[4,5,6],[7,8,9]] Visited: 1->2->3->6->9->8->7->4
6	Traverse top row left to right (inner layer)	Elements visited: 5	top=1 -> top=2	[[1,2,3],[4,5,6],[7,8,9]] Visited: 1->2->3->6->9->8->7->4->5
7	Check boundaries	All elements visited	top=2, bottom=1, left=1, right=1 (top > bottom)	Traversal ends

💡 top boundary crossed bottom boundary (top=2 > bottom=1), traversal complete

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
top	0	1	1	1	1	2	2
bottom	2	2	2	1	1	1	1
left	0	0	0	0	1	1	1
right	2	2	1	1	1	1	1
Visited Elements	[]	[1,2,3]	[1,2,3,6,9]	[1,2,3,6,9,8,7]	[1,2,3,6,9,8,7,4]	[1,2,3,6,9,8,7,4,5]	[1,2,3,6,9,8,7,4,5]

Key Moments - 3 Insights

Why do we update the 'top' boundary after traversing the top row?

Because after visiting the top row, that row is fully processed and should not be visited again. Updating 'top' moves the boundary down, as shown in execution_table step 2.

Why does the traversal stop when 'top' becomes greater than 'bottom'?

Because it means all rows have been visited. The boundaries crossed, so no more elements remain inside the current boundaries. This is shown in execution_table step 7.

Why do we traverse the left column from bottom to top instead of top to bottom?

To maintain the spiral order. After traversing bottom row right to left, we go up the left column to complete the outer layer before moving inward, as shown in execution_table step 5.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'right' after step 3?

A 1

B 2

C 0

D 3

💡 Hint

Check the 'Pointer Changes' column in step 3 where right boundary is updated.

At which step does the traversal visit the element '5'?

A Step 5

B Step 6

C Step 4

D Step 7

💡 Hint

Look at the 'Elements visited' column in execution_table for step 6.

If the matrix had 4 columns instead of 3, which boundary would be updated last in the first full spiral cycle?

A top

B bottom

C left

D right

💡 Hint

Refer to the concept_flow where left boundary is updated after traversing left column.

Concept Snapshot

Spiral Matrix Traversal:
- Use four boundaries: top, bottom, left, right
- Traverse edges in order: top row, right column, bottom row, left column
- After each edge, update the corresponding boundary inward
- Repeat until boundaries cross (top > bottom or left > right)
- Visits all elements in spiral order without repeats

Full Transcript

Spiral Matrix Traversal uses four boundaries to track the current edges of the matrix to visit. We start with top row from left to right, then right column top to bottom, bottom row right to left, and left column bottom to top. After each edge traversal, we move the boundary inward to avoid revisiting elements. This repeats until the top boundary crosses the bottom or the left crosses the right, meaning all elements have been visited. The execution table shows each step with visited elements and boundary updates. Key moments clarify why boundaries move and when traversal stops. The visual quiz tests understanding of boundary updates and element visits.