N Queens Problem in DSA C - Execution Trace

Concept Flow - N Queens Problem

Start with empty board

↓

Place queen in row 0, col 0

↓

Check if safe

↓

Place queen

↓

Move to next row

↓

Repeat placement

↓

If no safe col in row

→Backtrack to previous row

↓

If all rows placed

→Solution found

↓

End or find more solutions

The flow shows placing queens row by row, checking safety, backtracking if needed, until all queens are placed safely.

Execution Sample

DSA C

bool solveNQueens(int row) {
  if (row == N) return true;
  for (int col = 0; col < N; col++) {
    if (isSafe(row, col)) {
      placeQueen(row, col);
      if (solveNQueens(row + 1)) return true;
      removeQueen(row, col);
    }
  }
  return false;
}

This code tries to place queens row by row, backtracking when no safe position is found.

Execution Table

Step	Operation	Row	Column Tried	Action	Board State (Q=queen, .=empty)
1	Try place queen	0	0	Safe, place queen	Q . . . . . . . . . . . . . . .
2	Try place queen	1	0	Not safe, try next	Q . . . . . . . . . . . . . . .
3	Try place queen	1	1	Not safe, try next	Q . . . . . . . . . . . . . . .
4	Try place queen	1	2	Safe, place queen	Q . . . . . Q . . . . . . . . .
5	Try place queen	2	0	Not safe, try next	Q . . . . . Q . . . . . . . . .
6	Try place queen	2	1	Not safe, try next	Q . . . . . Q . . . . . . . . .
7	Try place queen	2	3	Safe, place queen	Q . . . . . Q . . . . Q . . . .
8	Try place queen	3	0	Not safe, try next	Q . . . . . Q . . . . Q . . . .
9	Try place queen	3	1	Safe, place queen	Q . . . . . Q . . . . Q . Q . .
10	All queens placed	N/A	N/A	Solution found	Q . . . . . Q . . . . Q . Q . .
11	Backtrack	3	1	Remove queen	Q . . . . . Q . . . . Q . . . .
12	Try next col	3	2	Not safe, try next	Q . . . . . Q . . . . Q . . . .
13	Try next col	3	3	Not safe, backtrack	Q . . . . . Q . . . . Q . . . .
14	Backtrack	2	3	Remove queen	Q . . . . . Q . . . . . . . . .
15	Try next col	2	4	No column 4, backtrack	Q . . . . . Q . . . . . . . . .
16	Backtrack	1	2	Remove queen	Q . . . . . . . . . . . . . . .
17	Try next col	1	3	Safe, place queen	Q . . . . . . Q . . . . . . . .
18	Try place queen	2	0	Not safe, try next	Q . . . . . . Q . . . . . . . .
19	Try place queen	2	1	Safe, place queen	Q . . . . . . Q . Q . . . . . .
20	Try place queen	3	0	Not safe, try next	Q . . . . . . Q . Q . . . . . .
21	Try place queen	3	1	Not safe, try next	Q . . . . . . Q . Q . . . . . .
22	Try place queen	3	2	Not safe, try next	Q . . . . . . Q . Q . . . . . .
23	Try place queen	3	3	Not safe, backtrack	Q . . . . . . Q . Q . . . . . .
24	Backtrack	2	1	Remove queen	Q . . . . . . Q . . . . . . . .
25	Try next col	2	2	Not safe, try next	Q . . . . . . Q . . . . . . . .
26	Try next col	2	3	Not safe, backtrack	Q . . . . . . Q . . . . . . . .
27	Backtrack	1	3	Remove queen	Q . . . . . . . . . . . . . . .
28	Try next col	1	4	No column 4, backtrack	Q . . . . . . . . . . . . . . .
29	Backtrack	0	0	Remove queen	. . . . . . . . . . . . . . . .
30	Try next col	0	1	Safe, place queen	. Q . . . . . . . . . . . . . .
31	Continue similarly	N/A	N/A	Continue placing queens	Partial board states...
32	Eventually	N/A	N/A	Find all solutions or stop	Final board states
33	End	N/A	N/A	No more columns to try	Final or no solution

💡 All rows processed with safe queen placements or all options exhausted with backtracking

Variable Tracker

Variable	Start	After Step 1	After Step 4	After Step 7	After Step 10	After Step 29	After Step 30	Final
row	0	1	2	3	N (4)	0	1	N or backtracked
col	0	0	3	3	1	0	1	varies
board	[empty]	Q . . . . . . . . . . . . . . .	Q . . . . . Q . . . . . . . . .	Q . . . . . Q . . . . Q . . . .	Q . . . . . Q . . . . Q . Q . .	. . . . . . . . . . . . . . . .	. Q . . . . . . . . . . . . . .	varies with placement

Key Moments - 3 Insights

Why do we backtrack when no safe column is found in a row?

Because placing a queen in the current row is impossible without conflicts, so we remove the queen from the previous row and try a different column there (see steps 13-15 and 25-27 in execution_table).

How do we know if a position is safe for placing a queen?

We check columns, and diagonals for existing queens before placing (implied in 'Safe' or 'Not safe' in execution_table rows like 2, 4, 5).

Why does the algorithm stop when row == N?

Because all N queens have been placed safely on the board, meaning a solution is found (see step 10).

Visual Quiz - 3 Questions

Look at the execution_table at step 10, what is the board state?

A . Q . .\n. . . Q\n. Q . .\n. . . .

B Q . . .\n. . . .\n. . . .\n. . . .

C Q . . .\n. . Q .\n. . . Q\n. Q . .

D . . . .\n. . . .\n. . . .\n. . . .

💡 Hint

Refer to the 'Board State' column at step 10 in execution_table.

At which step does the algorithm first backtrack by removing a queen?

A Step 11

B Step 10

C Step 5

D Step 1

💡 Hint

Look for 'Remove queen' action in execution_table.

If the board size N is increased, how would the variable 'row' change in variable_tracker?

A It would decrease

B It would go up to N instead of 4

C It would stay the same

D It would become negative

💡 Hint

The 'row' variable tracks current row; it goes from 0 to N (see variable_tracker).

Concept Snapshot

N Queens Problem:
- Place N queens on NxN board
- One queen per row, no two queens attack
- Use backtracking: place queen, check safety
- If stuck, remove last queen and try next column
- Stop when all queens placed safely

Full Transcript

The N Queens Problem places N queens on an NxN chessboard so that no two queens threaten each other. The algorithm tries to place a queen in each row, checking if the position is safe by ensuring no other queen is in the same column or diagonal. If a safe position is found, it places the queen and moves to the next row. If no safe position exists in a row, it backtracks by removing the queen from the previous row and tries the next column there. This continues until all queens are placed or all options are exhausted. The execution table shows step-by-step queen placements, safety checks, backtracking, and board states. The variable tracker monitors the current row, column tried, and board configuration after each step. Key moments clarify why backtracking is needed, how safety is checked, and when the algorithm stops. The visual quiz tests understanding of board states, backtracking steps, and variable changes. The snapshot summarizes the problem and backtracking approach in simple terms.