Why Word Search in Grid Using Backtracking in DSA C++?

The Big Idea

What if you could find any hidden word in a puzzle without guessing blindly?

The Scenario

Imagine you have a big crossword puzzle printed on paper. You want to find if a certain word is hidden inside it by looking at every letter one by one and trying to guess if the word starts there.

The Problem

Doing this by hand is slow and tiring. You might miss some letters or paths because the word can be formed by moving in many directions. Checking all possibilities manually is confusing and error-prone.

The Solution

Backtracking helps by trying one letter at a time and moving forward only if the next letter matches. If it doesn't, it goes back and tries a different path. This way, it explores all possible ways efficiently without repeating work.

Before vs After

✗ Before

for (int i = 0; i < rows; i++) {
  for (int j = 0; j < cols; j++) {
    if (grid[i][j] == word[0]) {
      // Manually check all directions
    }
  }
}

✓ After

bool backtrack(int row, int col, int index) {
  if (index == word.length()) return true;
  if (row < 0 || col < 0 || row >= rows || col >= cols || grid[row][col] != word[index]) return false;
  // Mark visited and explore neighbors
  return backtrack(row+1, col, index+1) || backtrack(row-1, col, index+1) || backtrack(row, col+1, index+1) || backtrack(row, col-1, index+1) || backtrack(row+1, col+1, index+1) || backtrack(row+1, col-1, index+1) || backtrack(row-1, col+1, index+1) || backtrack(row-1, col-1, index+1);
}

What It Enables

It enables finding complex words hidden in grids by exploring all paths smartly without missing any possibility.

Real Life Example

Finding words in a word search puzzle game on your phone where words can be hidden horizontally, vertically, or diagonally.

Key Takeaways

Manual search is slow and error-prone.

Backtracking tries all paths efficiently.

It helps find words hidden in any direction in a grid.

Practice

1. What is the main purpose of backtracking in the Word Search in Grid problem?

easy

A. To explore all possible paths to find the word in the grid

B. To sort the grid alphabetically before searching

C. To count the number of words in the grid

D. To replace characters in the grid with special symbols

Solution

1. Step 1: Understand backtracking role

   Backtracking tries all possible paths in the grid to find the word by moving in allowed directions and undoing moves if they don't lead to a solution.

2. Step 2: Eliminate other options

   Sorting, counting words, or replacing characters are not related to backtracking's purpose in this problem.

3. Final Answer:

   To explore all possible paths to find the word in the grid -> Option A

4. Quick Check:

   Backtracking = Explore paths [OK]

Hint: Backtracking means trying all paths and undoing wrong steps [OK]

Common Mistakes:

• Thinking backtracking sorts or modifies the grid
• Confusing backtracking with simple searching
• Ignoring the undo step in backtracking

2. Which of the following is the correct way to check if a cell (row, col) is inside the grid boundaries in C++?

easy

A. if (row == 0 && col == 0)

B. if (row > 0 && row <= rows && col > 0 && col <= cols)

C. if (row >= 0 && row < rows && col >= 0 && col < cols)

D. if (row >= 0 || row < rows || col >= 0 || col < cols)

Solution

1. Step 1: Understand grid indexing

   Grid rows and columns start at 0, so valid indices are from 0 to rows-1 and 0 to cols-1.

2. Step 2: Check boundary condition

   if (row >= 0 && row < rows && col >= 0 && col < cols) correctly checks if row and col are within these ranges using && (and) operator.

3. Final Answer:

   if (row >= 0 && row < rows && col >= 0 && col < cols) -> Option C

4. Quick Check:

   Boundary check = if (row >= 0 && row < rows && col >= 0 && col < cols) [OK]

Hint: Use >= 0 and < size with && to check boundaries [OK]

Common Mistakes:

• Using > 0 instead of >= 0 excludes first row/column
• Using || instead of && allows invalid indices
• Checking only (0,0) cell

3. What will be the output of the following C++ code snippet for word search?

char grid[3][3] = {{'A','B','C'},{'D','E','F'},{'G','H','I'}};
string word = "BE";
// Assume function exist: bool exist(char grid[][], string word)
cout << (exist(grid, word) ? "Found" : "Not Found") << endl;

Assuming exist uses backtracking correctly.

medium

A. Found

B. Not Found

C. Compilation Error

D. Runtime Error

Solution

1. Step 1: Analyze grid and word

   The grid is:
   A B C
   D E F
   G H I
   The word is "BE".

2. Step 2: Check if "BE" can be formed

   Starting at 'B' (0,1), next letter 'E' must be adjacent (up, down, left, right). Adjacent cells to 'B' are 'A'(0,0), 'C'(0,2), 'E'(1,1). 'E' is adjacent, so path B->E exists.

3. Step 3: Confirm backtracking finds the word

   Backtracking will find "BE" successfully.

4. Final Answer:

   Found -> Option A

5. Quick Check:

   Word "BE" exists in grid = Found [OK]

Hint: Check adjacency of letters in grid for word presence [OK]

Common Mistakes:

• Ignoring adjacency rules
• Assuming diagonal moves allowed (usually not)
• Confusing output with error

4. Identify the bug in this backtracking snippet for word search:

bool backtrack(int r, int c, int index) {
  if (index == word.length()) return true;
  if (r < 0 || r >= rows || c < 0 || c >= cols) return false;
  if (grid[r][c] != word[index]) return false;
  grid[r][c] = '#';
  bool found = backtrack(r+1, c, index+1) || backtrack(r-1, c, index+1) || backtrack(r, c+1, index+1) || backtrack(r, c-1, index+1);
  return found;
}

medium

A. Incorrect boundary checks

B. Wrong base case condition

C. Using '||' instead of '&&' in recursive calls

D. Missing restoring grid[r][c] after recursion

Solution

1. Step 1: Understand backtracking marking

   The code marks visited cells by setting grid[r][c] = '#'.

2. Step 2: Check if grid is restored after recursion

   After recursive calls, the original character should be restored to allow other paths. This code does not restore it.

3. Step 3: Identify the bug

   Missing restoration causes wrong results or blocks other paths.

4. Final Answer:

   Missing restoring grid[r][c] after recursion -> Option D

5. Quick Check:

   Restore grid after recursion = Fix bug [OK]

Hint: Always undo changes after recursive calls in backtracking [OK]

Common Mistakes:

• Not restoring visited cells
• Wrong base case logic
• Incorrect boundary conditions

5. Given a 4x4 grid:

char grid[4][4] = {
  {'C','A','T','F'},
  {'B','G','E','S'},
  {'I','T','A','E'},
  {'S','E','R','T'}
};

Which of the following words can be found using backtracking moving only up, down, left, or right?
Select the correct option.

hard

A. "CATS"

B. "TEA"

C. "FEST"

D. "BAT"

Solution

1. Step 1: Check "CATS"

   "CATS" starts at (0,0) 'C', next 'A' at (0,1), next 'T' at (0,2), but no adjacent 'S' to 'T' at (0,2). Adjacent: 'A'(0,1), 'F'(0,3), 'E'(1,2). No path exists.

2. Step 2: Check "TEA"

   "TEA" letters: T, E, A.
   Possible path: (2,1) 'T' -> (3,1) 'E' -> (2,2) 'A' ? From 'E'(3,1) to 'A'(2,2) is diagonal, invalid.
   Try other 'T's: (0,2) 'T' -> (1,2) 'E' down -> (2,2) 'A' down. Valid path.

3. Step 3: Check "FEST" and "BAT"

   "FEST" letters not found in order with adjacency.
   "BAT" letters: B(1,0), A(2,2), T(0,2) no continuous path.

4. Final Answer:

   "TEA" -> Option B

5. Quick Check:

   Check adjacency for each word = "TEA" found [OK]

Hint: Trace letter adjacency step-by-step for each word [OK]

Common Mistakes:

• Assuming diagonal moves allowed
• Not checking letter order carefully
• Ignoring multiple occurrences of letters