From 047d89e1e0f40089b1e3266d06e56fd6efa6790d Mon Sep 17 00:00:00 2001
From: Keerthi0910 <chundurikeerthipriya@gmail.com>
Date: Tue, 1 Sep 2026 22:23:31 -0500
Subject: [PATCH 1/3] Create Problem1.java

---
 Problem1.java | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)
 create mode 100644 Problem1.java

diff --git a/Problem1.java b/Problem1.java
new file mode 100644
index 00000000..c2d7c512
--- /dev/null
+++ b/Problem1.java
@@ -0,0 +1,38 @@
+
+// Time complexity is O( 2 ^ (T/M)) where is target is the target  and m is the smallest number inthe candidatest the extra length we get when we keep on choosing smallest number
+//Space complexity is  O(T/M) 
+// combination sum using backtracking
+
+class Solution {
+    List<List<Integer>> result;
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        this.result = new ArrayList<>();
+        helper(candidates, 0, target, new ArrayList<>() );
+
+        return result;
+        
+    }
+
+        private void helper(int[] candidates, int i, int target, List<Integer> path){
+
+            if(target < 0 || i == candidates.length) {
+                return ;
+            }
+
+            if(target == 0){
+                result.add(new ArrayList<>(path));
+                return;
+            }
+  //choose
+            path.add(candidates[i]);
+            helper(candidates, i, target- candidates[i], path);
+            path.remove(path.size()-1);
+            //not choose
+
+            helper(candidates, i+1, target, path);
+
+          
+
+
+        }
+}

From 2683174f67109d3e00a4090ffd1d064df6084b66 Mon Sep 17 00:00:00 2001
From: Keerthi0910 <chundurikeerthipriya@gmail.com>
Date: Tue, 1 Sep 2026 22:25:05 -0500
Subject: [PATCH 2/3] Create Problem2.java

---
 Problem2.java | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Problem2.java

diff --git a/Problem2.java b/Problem2.java
new file mode 100644
index 00000000..8b137891
--- /dev/null
+++ b/Problem2.java
@@ -0,0 +1 @@
+

From fe341f332c00bb86048f9855eaffc5b13fd65261 Mon Sep 17 00:00:00 2001
From: Keerthi0910 <chundurikeerthipriya@gmail.com>
Date: Sat, 5 Sep 2026 21:46:45 -0500
Subject: [PATCH 3/3] Update Problem2.java

---
 Problem2.java | 80 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)

diff --git a/Problem2.java b/Problem2.java
index 8b137891..2c06ad80 100644
--- a/Problem2.java
+++ b/Problem2.java
@@ -1 +1,81 @@
+//space complexity o(n)
+//time complexity o(4^n)
+//using dfs for loop exploring every solution
+class Solution {
 
+    List<String> result = new ArrayList<>();
+
+    public List<String> addOperators(String num, int target) {
+
+        helper(num, 0, "", target, 0, 0);
+
+        return result;
+    }
+
+    private void helper(String num,
+            int i,
+            String path,
+            int target,
+            long totalSum,
+            long prev) {
+
+        if (i == num.length()) {
+
+            if (totalSum == target) {
+                result.add(path);
+            }
+
+            return;
+        }
+
+        long current = 0;
+
+        for (int j = i; j < num.length(); j++) {
+
+            if (j > i && num.charAt(i) == '0') {
+                break;
+            }
+
+            current = current * 10 + (num.charAt(j) - '0');
+
+            String currentString = num.substring(i, j + 1);
+
+            if (i == 0) {
+
+                helper(
+                        num,
+                        j + 1,
+                        currentString,
+                        target,
+                        current,
+                        current);
+
+            } else {
+
+                helper(
+                        num,
+                        j + 1,
+                        path + "+" + currentString,
+                        target,
+                        totalSum + current,
+                        current);
+
+                helper(
+                        num,
+                        j + 1,
+                        path + "-" + currentString,
+                        target,
+                        totalSum - current,
+                        -current);
+
+                helper(
+                        num,
+                        j + 1,
+                        path + "*" + currentString,
+                        target,
+                        totalSum - prev + prev * current,
+                        prev * current);
+            }
+        }
+    }
+}