From 66857cbfc2743e535996fcc8f22c2b3f8947fba0 Mon Sep 17 00:00:00 2001
From: dhruvil15 <76967484+dhruvil15@users.noreply.github.com>
Date: Thu, 21 May 2026 20:29:32 -0400
Subject: [PATCH] Complete BackTracking-1

---
 Problem70.java | 31 ++++++++++++++++++++++++++++
 Problem71.java | 55 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 86 insertions(+)
 create mode 100644 Problem70.java
 create mode 100644 Problem71.java

diff --git a/Problem70.java b/Problem70.java
new file mode 100644
index 00000000..b27d518e
--- /dev/null
+++ b/Problem70.java
@@ -0,0 +1,31 @@
+// Time Complexity : O(2 ^ (m+n)) where m is the candidates length and n is the target
+// Space Complexity : O(n) 
+
+class Solution {
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        List<List<Integer>> result = new ArrayList<>();
+        helper(candidates, target, 0, new ArrayList<>(), result);
+        return result;
+    }
+
+    private void helper(int[] candidates, int target, int pivot, List<Integer> path, List<List<Integer>> result) {
+        //base
+        if (target < 0 || candidates.length == pivot) {
+            return;
+        }
+
+        if (target == 0) {
+            result.add(new ArrayList<>(path));
+            return;
+        }
+
+        for (int i = pivot; i < candidates.length; i++) {
+            //action
+            path.add(candidates[i]);
+            //recurse
+            helper(candidates, target - candidates[i], i, path, result);
+            //backtrack
+            path.remove(path.size() - 1);
+        }
+    }
+}
\ No newline at end of file
diff --git a/Problem71.java b/Problem71.java
new file mode 100644
index 00000000..8b5dccea
--- /dev/null
+++ b/Problem71.java
@@ -0,0 +1,55 @@
+// Time Complexity : O(4^n)
+// Space Complexity : O(n) 
+
+class Solution {
+    List<String> result;
+    public List<String> addOperators(String num, int target) {
+        
+        this.result = new ArrayList<>();
+
+        helper(num, target, 0, 0, 0, new StringBuilder());
+
+        return result;
+    }
+
+    private void helper(String num, int target, int pivot, long calc, long tail, StringBuilder path){
+
+        if(pivot == num.length()){
+            if(calc == target){
+                result.add(path.toString());
+            }
+        }
+
+        for(int i = pivot; i < num.length(); i++){
+
+            if(num.charAt(pivot) == '0' && i != pivot) break;
+
+            long curr = Long.parseLong(num.substring(pivot, i+1));
+
+            int le = path.length();
+
+            if(pivot == 0){
+                path.append(curr);
+                helper(num, target, i+1, curr, curr, path);
+                path.setLength(le);
+
+            }else{
+
+                // + 
+                path.append("+").append(curr);
+                helper(num, target, i+1, calc + curr, curr, path);
+                path.setLength(le);
+
+                // -
+                path.append("-").append(curr);
+                helper(num, target, i+1, calc - curr, -curr, path);
+                path.setLength(le);
+
+                // * 
+                path.append("*").append(curr);
+                helper(num, target, i+1, calc - tail + (tail * curr), tail * curr, path);
+                path.setLength(le);
+            }
+        }
+    }
+}
\ No newline at end of file