From d5e902131a453d83b955383fc53edbb90830a844 Mon Sep 17 00:00:00 2001
From: kalyan <kalyan.ng22@gmail.com>
Date: Sat, 8 Nov 2025 10:34:31 -0600
Subject: [PATCH] Backtracking-1 solutions

---
 CombinationSum.java      | 71 ++++++++++++++++++++++++++++++++++++++++
 ExpressionOperators.java | 57 ++++++++++++++++++++++++++++++++
 2 files changed, 128 insertions(+)
 create mode 100644 CombinationSum.java
 create mode 100644 ExpressionOperators.java

diff --git a/CombinationSum.java b/CombinationSum.java
new file mode 100644
index 00000000..f1184682
--- /dev/null
+++ b/CombinationSum.java
@@ -0,0 +1,71 @@
+// Time Complexity : O(2^(m+n)) where m is the length of candidates ad n is the target value.
+// Space Complexity : O(n)
+// Did this code successfully run on Leetcode : Yes
+// Approach : I followed 0/1 recursion with backtracking and while the base condition is met, before storing the result we store a deep
+// copy of it so that the rest of recursion happens without any issues. In no choose condition, index needs to be increased while in
+// choose condition we dont have to increase index as it can have duplicates as well to reach the target sum. Once we find the result or we
+// reach the end of the recursive function, we remove the last element in the path so that it can continue recursion.
+
+
+class Solution {
+    List<List<Integer>> result;
+
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        this.result = new ArrayList<>();
+        helper(candidates, target, 0, new ArrayList<>());
+        return result;
+    }
+
+    private void helper(int[] candidates, int target, int index, List<Integer> path) {
+
+        if (target == 0) {
+            result.add(new ArrayList<>(path)); //copy of path
+            return;
+        }
+        if (target < 0 || index == candidates.length) {
+            return;
+        }
+        //no choose
+        helper(candidates, target, index + 1, path);
+
+        //choose
+        path.add(candidates[index]); //add to path first
+        helper(candidates, target - candidates[index], index, path);
+
+        //backtracking
+        path.remove(path.size() - 1);
+    }
+}
+
+
+
+//for loop based recursion
+
+class Solution {
+    List<List<Integer>> result;
+
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        this.result = new ArrayList<>();
+        helper(candidates, target, 0, new ArrayList<>());
+        return result;
+    }
+
+    private void helper(int[] candidates, int target, int index, List<Integer> path) {
+
+        if (target == 0) {
+            result.add(new ArrayList<>(path)); //copy of path
+            return;
+        }
+        if (target < 0 || index == candidates.length) {
+            return;
+        }
+
+        for (int i = index; i < candidates.length; i++) {
+            path.add(candidates[i]);
+            helper(candidates, target - candidates[i], i, path);
+            //backtracking
+            path.remove(path.size() - 1);
+        }
+
+    }
+}
\ No newline at end of file
diff --git a/ExpressionOperators.java b/ExpressionOperators.java
new file mode 100644
index 00000000..7f86e9e2
--- /dev/null
+++ b/ExpressionOperators.java
@@ -0,0 +1,57 @@
+// Time Complexity : O(4^(n)) .
+// Space Complexity : O(n)
+// Did this code successfully run on Leetcode : Yes
+// Approach : Used for loop recursion to solve this problem. First we need to achieve all possible combination of numbers and at each combination
+// we have to calculate +,-,* for the combinations. We maintain a curr and tail values as we need higher precedence operator in * case
+// by using the previous value. After exploring the path, we backtracking it and set the path length to previous step one.
+
+
+class Solution {
+    List<String> result;
+    public List<String> addOperators(String num, int target) {
+        this.result = new ArrayList<>();
+        helper(num, target, new StringBuilder(), 0, 0, 0);
+        return result;
+    }
+
+    private void helper(String num, int target, StringBuilder path, int pivot, long calc, long tail){
+        if(pivot == num.length()){ //base case
+            if(calc == target){
+                result.add(path.toString());
+            }
+        }
+
+        for(int i = pivot; i < num.length(); i++){
+
+            if(num.charAt(pivot) == '0' && i != pivot) continue; // 0 precedence case
+
+            long curr = Long.parseLong(num.substring(pivot, i+1));
+
+            int le = path.length();
+
+            if(pivot == 0){//at 0th level we dont have to perform operations
+                path.append(curr);
+                helper(num, target,path, i+1, curr, curr);
+                path.setLength(le);//backtrack
+
+            }else{
+
+                // + case
+                path.append("+").append(curr);
+                helper(num, target, path, i+1, calc + curr, curr);
+                path.setLength(le);//backtrack
+
+                // - case
+                path.append("-").append(curr);
+                helper(num, target, path, i+1, calc - curr, -curr);
+                path.setLength(le);//backtrack
+
+                // * case
+                path.append("*").append(curr);
+                helper(num, target, path, i+1, calc - tail + (tail * curr), tail * curr);
+                path.setLength(le);//backtrack
+            }
+        }
+    }
+
+}
\ No newline at end of file