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

@@ -2,8 +2,8 @@ import gradio as gr
 from itertools import permutations
 
 def solve_cryptarithm(equation):
-    # Parse the words from the equation"
-    left, right = equation.split(" == ")
+    # Parse the words from the equation
+    left, right = equation.split(" = ")
     words = left.split(" + ") + [right]
     
     # Extract unique letters
@@ -51,24 +51,30 @@ def solve_cryptarithm(equation):
     
     # Start DFS and find solution
     if dfs(0, letter_to_digit, used_digits):
-        return {letter: letter_to_digit[letter] for letter in unique_letters}
+        # 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 "= "
+        return formatted_result
     else:
         return "No solution found"
 
 def process_input(equations):
-    results = {}
+    results = []
     for equation in equations.splitlines():
-        result = solve_cryptarithm(equation)
-        results[equation] = result
-    return results
+        result = solve_cryptarithm(equation.strip())
+        results.append(result)
+    return "\n\n".join(results)
 
 
 interface = gr.Interface(
     fn=process_input,
-    inputs=gr.Textbox(label="Enter Cryptarithm Equations (one per line)", placeholder="E.g., SEND + MORE == MONEY"),
-    outputs="json",
+    inputs=gr.Textbox(label="Enter Cryptarithm Equations (one per line)", placeholder="E.g., SEND + 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."
+    description="Enter cryptarithm equations (like SEND + MORE = MONEY) one per line to find solutions. Each letter represents a unique digit from 0-9."
 )
 
 interface.launch()