[DFS] Add a solution to Expression Add Operators

DFS/ExpressionAddOperators.swift

@@ -0,0 +1,50 @@
+/**
+ * Question Link: https://leetcode.com/problems/expression-add-operators/
+ * Primary idea: Classic Depth-first Search, terminates at when position encounters the 
+ *               length of the string num, add to result when eval is equal to target
+ * 
+ * Note: 
+ * 1. String cast to Integer will make character loss, e.g. "05" -> 5
+ * 2. Multiplication's priority is higher than addiction
+ *
+ * Time Complexity: O(n!), Space Complexity: O(n)
+ *
+ */
+
+class ExpressionAddOperators {
+    func addOperators(_ num: String, _ target: Int) -> [String] {
+        var res = [String]()
+        let numChars = Array(num.characters)
+
+        guard numChars.count > 0 else {
+            return res
+        }
+
+        dfs(&res, "", numChars, target, 0, 0, 0)
+
+        return res
+    }
+
+    private func dfs(_ res: inout [String], _ temp: String, _ numChars: [Character], _ target: Int, _ pos: Int, _ eval: Int, _ mul: Int) {
+        if pos == numChars.count {
+            if eval == target {
+                res.append(temp)
+            }
+            return
+        }
+
+        for i in pos ..< numChars.count {
+            if i != pos && numChars[pos] == "0" {
+                break
+            }
+            let curt = Int(String(numChars[pos ..< i + 1]))!
+            if pos == 0 {
+                dfs(&res, temp + String(curt), numChars, target, i + 1, curt, curt)
+            } else {
+                dfs(&res, temp + "+" + String(curt), numChars, target, i + 1, eval + curt, curt)
+                dfs(&res, temp + "-" + String(curt), numChars, target, i + 1, eval - curt, -curt)
+                dfs(&res, temp + "*" + String(curt), numChars, target, i + 1, eval - mul + mul * curt, mul * curt)
+            }
+        }
+    }
+}