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+# 17-letter-combinations-of-a-phone-number
+
+Given a string containing digits from 2–9 inclusive, return all possible letter combinations that the number could represent. Return the answer in any order.
+
+A mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters.
+
+### Example 1:
+**Input:** `digits = "23"`  
+**Output:** `["ad","ae","af","bd","be","bf","cd","ce","cf"]`
+
+### Example 2:
+**Input:** `digits = ""`  
+**Output:** `[]`
+
+### Example 3:
+**Input:** `digits = "2"`  
+**Output:** `["a","b","c"]`
+
+---
+
+### Constraints:
+- `0 <= digits.length <= 4`
+- `digits[i]` is a digit in the range `['2', '9']`.
diff --git a/leet-code/17-letter-combinations-of-a-phone-number/index.js b/leet-code/17-letter-combinations-of-a-phone-number/index.js
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+/**
+ * @param {string} digits
+ * @return {string[]}
+ */
+var letterCombinations = function(digits) {
+    // store the distinct combinations of chracters
+    const combinations = [];
+    // short circuit if there are no digits to consider
+    if (digits === "") return combinations
+    // lookup alphabetic characters by number
+    const lettersByNumber = {
+        2: 'abc',
+        3: 'def',
+        4: 'ghi',
+        5: 'jkl',
+        6: 'mno',
+        7: 'pqrs',
+        8: 'tuv',
+        9: 'wxyz'
+    }
+    // explore all possible combinations using backtracking
+    function search(index, workingMemory) {
+        // combinations can't exceed the length of digits used
+        const isValidCombination = index === digits.length;
+        if (isValidCombination) {
+            // add the combination
+            combinations.push(workingMemory)
+            return;
+        }
+        // lookup the letters corresponding to the current number
+        const letters = lettersByNumber[digits[index]]
+        // add each character to working memory and continue searching for combinations
+        for (var j = 0; j < letters.length; j++) {
+            // increment the index to process the next digit
+            search(index + 1, workingMemory + letters[j])
+        }
+    }
+    // start at the first digit and no working memory
+    search(0, "")
+    // return the alphabetic combinations
+    return combinations;
+};
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