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- Grokkin from #ai/chatgpt4 - Great, let's dissect the example of generating mnemonics for the phone number "23". The final mnemonics list contains ['ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf'], and here's how we got there step-by-step: - ```javascript # Let's simulate the backtracking algorithm with a simple example phone number "23" # We will go step-by-step to see how the algorithm explores all the possible mnemonics # Digit to letter mapping digit_to_letters = { "0": ["0"], "1": ["1"], "2": ["a", "b", "c"], "3": ["d", "e", "f"], "4": ["g", "h", "i"], "5": ["j", "k", "l"], "6": ["m", "n", "o"], "7": ["p", "q", "r", "s"], "8": ["t", "u", "v"], "9": ["w", "x", "y", "z"], } # Phone number to find mnemonics for phone_number = "23" # List to store the final mnemonics mnemonics = [] # Function to perform backtracking def backtrack(start, path): if start == len(phone_number): mnemonics.append("".join(path)) return for letter in digit_to_letters[phone_number[start]]: path.append(letter) backtrack(start + 1, path) path.pop() # Start backtracking backtrack(0, []) mnemonics ``` - ### Step-by-Step Explanation 1. **Initial Call**: `backtrack(0, [])` - `start = 0`, `path = []` - We look at the first digit "2", which maps to ["a", "b", "c"] 2. **First Level of Recursion**: - `backtrack(1, ["a"])` - `start = 1`, `path = ["a"]` - Now we look at the second digit "3", which maps to ["d", "e", "f"] - We append "d" to `path` and go deeper: `backtrack(2, ["a", "d"])` - **Second Level of Recursion**: - `backtrack(2, ["a", "d"])` - `start = 2`, `path = ["a", "d"]` - We've reached the end (`start == len(phone_number)`), so we add "ad" to `mnemonics` - We backtrack and pop "d" from `path`, now `path = ["a"]` - Continue with the next letter "e": `backtrack(2, ["a", "e"])` - This continues until we have added "ad", "ae", "af" to `mnemonics` - We backtrack again to `path = ["a"]` and pop "a" so that `path = []` - Continue with the next letter "b": `backtrack(1, ["b"])` - This pattern repeats until all mnemonics are generated. - ### Key Moments in the Algorithm - **Appending to `path`**: We add a letter corresponding to the current digit to the `path`. - **Recursive Call**: We go deeper into the next level of the decision tree by calling `backtrack(start + 1, path)`. - **Backtrack**: We undo the last decision by popping the last letter from `path`. - **Stopping Criterion**: We stop when `start` reaches the length of the phone number and save the mnemonic. In essence, the algorithm is like a tree-traversal mechanism where each node represents a letter for a digit. You traverse each path from root to leaf, and each leaf becomes a mnemonic. The backtracking is the act of climbing back up the tree to the last decision point whenever you reach a leaf, so you can continue down a new path. Does this step-by-step breakdown help clarify how backtracking works in this problem? Would you like to explore anything else?