Implement new method: Depth First Search (DFS)

Update:

- Implemented Depth First Search (DFS) to explore possible digit assignments for each letter, with pruning to discard any paths that can't yield a valid solution. This optimization speeds up runtime by eliminating unfeasible assignments early.
- Added backtracking to revert and try alternative assignments if a partial solution doesn’t lead to a valid final solution.

How This Works:
- The solver first extracts all unique letters from the puzzle.
- DFS explores each possible digit for these letters.
- Pruning: The solver skips digits already in use and only continues exploring if the partial assignment can still lead to a valid solution.
- Backtracking: If a particular assignment fails, the solver backtracks to try the next possible digit, ensuring all potential solutions are explored efficiently.

app.py

@@ -2,7 +2,7 @@ import gradio as gr
 from itertools import permutations
 
 def solve_cryptarithm(equation):
-    # Parse the words from the equation
+    # Parse the words from the equation "SEND + MORE = MONEY"
     left, right = equation.split(" = ")
     words = left.split(" + ") + [right]
     
@@ -17,6 +17,7 @@ def solve_cryptarithm(equation):
     
     # Depth-First Search with Pruning
     def dfs(index, letter_to_digit, used_digits):
+        # If we've assigned all letters, check if equation holds
         if index == len(unique_letters):
             left_sum = sum(word_to_number(word, letter_to_digit) for word in words[:-1])
             right_val = word_to_number(words[-1], letter_to_digit)
@@ -52,29 +53,40 @@ def solve_cryptarithm(equation):
     # Start DFS and find solution
     if dfs(0, letter_to_digit, used_digits):
         # Format the solution as per the user's requirements
-        formatted_result = "Input: " + equation + "\n\n"
-        for word in words:
-            formatted_result += " ".join(str(letter_to_digit[char]) for char in word) + "  "
-            if word != words[-1]:
-                formatted_result += "+ " if word != words[-2] else "= "
+        formatted_result = f"Input: {equation}\n\n"
+        
+        # Convert each word to its number representation
+        for i, word in enumerate(words):
+            formatted_result += " ".join(str(letter_to_digit[char]) for char in word)
+            if i < len(words) - 2:
+                formatted_result += " + "
+            elif i == len(words) - 2:
+                formatted_result += " = "
+        
         return formatted_result
     else:
-        return "No solution found"
+        return f"No solution found for: {equation}"
 
 def process_input(equations):
     results = []
     for equation in equations.splitlines():
-        result = solve_cryptarithm(equation.strip())
-        results.append(result)
+        equation = equation.strip()
+        if equation:  # Ensure it's not an empty line
+            result = solve_cryptarithm(equation)
+            results.append(result)
     return "\n\n".join(results)
 
-
+# Set up Gradio interface
 interface = gr.Interface(
     fn=process_input,
-    inputs=gr.Textbox(label="Enter Cryptarithm Equations (one per line)", placeholder="E.g., SEND + MORE = MONEY"),
+    inputs=gr.Textbox(
+        label="Enter Cryptarithm Equations (one per line)", 
+        placeholder="E.g., SEND + MORE = MONEY\nSEND + MORE = MONEY"
+    ),
     outputs="text",
     title="Cryptarithm Solver",
     description="Enter cryptarithm equations (like SEND + MORE = MONEY) one per line to find solutions. Each letter represents a unique digit from 0-9."
 )
 
+# Launch Gradio app
 interface.launch()