From 857da0557d807146e6f3ce0123a8a02761d1aae3 Mon Sep 17 00:00:00 2001
From: Hriday-A <hriday.agarwal20103@gmail.com>
Date: Sun, 17 May 2026 19:36:07 -0500
Subject: [PATCH] Backtracking Assignment completed

---
 combination_sum.java         | 57 ++++++++++++++++++++++++++++++++++++
 expression_and_operator.java | 40 +++++++++++++++++++++++++
 2 files changed, 97 insertions(+)
 create mode 100644 combination_sum.java
 create mode 100644 expression_and_operator.java

diff --git a/combination_sum.java b/combination_sum.java
new file mode 100644
index 00000000..581cea3e
--- /dev/null
+++ b/combination_sum.java
@@ -0,0 +1,57 @@
+//Time Complexity - O(n*2 ^ (m+n))
+//Space Complexity - O(n^2)
+// class Solution {
+//     List<List<Integer>> result;
+//     public List<List<Integer>> combinationSum(int[] candidates, int target) {
+//         this.result= new ArrayList<>();
+//         helper(candidates,target,new ArrayList<>(),0);
+//         return result;
+//     }
+//     private void helper(int[] candidates,int target, List<Integer> path,int i){
+//         //base
+//         if(target==0) {
+//             result.add(new ArrayList<>(path));
+//             return;
+//         }
+//         if(target<0 || i==candidates.length) return; 
+//         //logic
+//         //0
+//         helper(candidates,target,new ArrayList<>(path),i+1);
+//         //action
+//         path.add(candidates[i]);
+//         // System.out.println(path);
+//         //1
+//         //recurse
+//         helper(candidates,target-candidates[i],new ArrayList<>(path),i);
+//     }
+// }
+
+//Time Complexity - O(2 ^ (m+n))
+//Space Complexity - O(n)
+class Solution {
+    List<List<Integer>> result;
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        this.result= new ArrayList<>();
+        helper(candidates,target,new ArrayList<>(),0);
+        return result;
+    }
+    private void helper(int[] candidates,int target, List<Integer> path,int i){
+        //base
+        if(target==0) {
+            result.add(new ArrayList<>(path));
+            return;
+        }
+        if(target<0 || i==candidates.length) return; 
+        //logic
+        //0
+        helper(candidates,target,path,i+1);
+        //action
+        path.add(candidates[i]);
+        // System.out.println(path);
+        //1
+        //recurse
+        helper(candidates,target-candidates[i],path,i);
+        //backtrack
+        path.remove(path.size()-1);
+    }
+}
\ No newline at end of file
diff --git a/expression_and_operator.java b/expression_and_operator.java
new file mode 100644
index 00000000..ff55e550
--- /dev/null
+++ b/expression_and_operator.java
@@ -0,0 +1,40 @@
+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){
+        //base 
+        if(pivot==num.length()) {
+            if(calc == target){
+                result.add(path.toString());
+            }
+        }
+        //logic 
+        for(int i=pivot;i<num.length();i++){
+            if(num.charAt(pivot) == '0' && i != pivot) break; // preoccuring zero
+            long curr = Long.parseLong(num.substring(pivot,i+1));
+            int le = path.length(); // stack variable 
+            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); // why - sign ?? 
+                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