Word Search in Grid Using Backtracking in DSA C++ - Build from Scratch

Word Search in Grid Using Backtracking

📖 Scenario: You are building a simple word search puzzle solver. The puzzle is a grid of letters, and you want to find if a given word exists in the grid by moving horizontally or vertically to adjacent letters.This is like searching for a hidden word in a crossword puzzle.

🎯 Goal: Build a program that checks if a given word can be found in the letter grid by moving up, down, left, or right without revisiting the same cell.

📋 What You'll Learn

Create a 2D grid of characters with exact letters

Create a string variable for the word to search

Implement a backtracking function to search the word in the grid

Print true if the word is found, otherwise false

💡 Why This Matters

🌍 Real World

Word search puzzles and games often require searching for words hidden in grids. This technique helps in solving such puzzles automatically.

💼 Career

Backtracking is a common algorithmic technique used in many software engineering tasks like puzzle solving, constraint satisfaction problems, and pathfinding.

1

Create the letter grid

Create a 2D vector of characters called board with these exact rows:
{'A', 'B', 'C', 'E'},
{'S', 'F', 'C', 'S'},
{'A', 'D', 'E', 'E'}

DSA C++

// Create the 2D vector board with the exact rows
// Your code here

Hint

Use vector> board = {{...}, {...}, {...}}; with the exact letters.

2

Set the word to search

Create a string variable called word and set it to "ABCCED"

DSA C++

#include 
#include 
using namespace std;

vector> board = {
    {'A', 'B', 'C', 'E'},
    {'S', 'F', 'C', 'S'},
    {'A', 'D', 'E', 'E'}
};

// Create the string word with value "ABCCED"
// Your code here

Hint

Use string word = "ABCCED"; to set the word.

3

Implement the backtracking search function

Write a function called bool exist(int row, int col, int index) that uses backtracking to check if the word can be found starting from board[row][col]. Use recursion to check neighbors up, down, left, and right. Mark visited cells by temporarily changing their value to '#' and restore after recursion. Return true if the full word is matched.

DSA C++

#include 
#include 
using namespace std;

vector> board = {
    {'A', 'B', 'C', 'E'},
    {'S', 'F', 'C', 'S'},
    {'A', 'D', 'E', 'E'}
};

string word = "ABCCED";

// Write the bool exist(int row, int col, int index) function here
// Your code here

Hint

Use recursion to check neighbors and mark visited cells with '#' temporarily.

4

Search the word and print the result

Write code to check every cell in board as a starting point. Use the exist function to find if word exists. Print true if found, otherwise false.

DSA C++

#include 
#include 
#include 
using namespace std;

vector> board = {
    {'A', 'B', 'C', 'E'},
    {'S', 'F', 'C', 'S'},
    {'A', 'D', 'E', 'E'}
};

string word = "ABCCED";

bool exist(int row, int col, int index) {
    if (index == word.size()) return true;
    if (row = (int)board.size() || col = (int)board[0].size() || board[row][col] != word[index])
        return false;

    char temp = board[row][col];
    board[row][col] = '#';

    bool found = exist(row + 1, col, index + 1) ||
                 exist(row - 1, col, index + 1) ||
                 exist(row, col + 1, index + 1) ||
                 exist(row, col - 1, index + 1);

    board[row][col] = temp;
    return found;
}

// Write code to search the word in the board and print true or false
// Your code here

Hint

Use nested loops to try every cell as a start. Print "true" if found, else "false".

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