From 256327124fd4cd3bb2ea96b8463df12e39b3d79b Mon Sep 17 00:00:00 2001
From: sainathek <erukullasainath@gmail.com>
Date: Thu, 26 Mar 2026 10:42:23 -0400
Subject: [PATCH] Done Backtracking-1

---
 problem1.java | 51 +++++++++++++++++++++++++++++++
 problem2.java | 83 +++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 134 insertions(+)
 create mode 100644 problem1.java
 create mode 100644 problem2.java

diff --git a/problem1.java b/problem1.java
new file mode 100644
index 00000000..121104b6
--- /dev/null
+++ b/problem1.java
@@ -0,0 +1,51 @@
+
+/**
+Time Complexity = Exponential, approximately O(2^N)
+Explanation:
+For each element, we either choose it or skip it.
+This results in exploring all possible combinations recursively.
+
+Space Complexity = O(Target)
+Explanation:
+The recursion stack and the current path list can grow up to
+target / smallest candidate value.
+
+Did this code successfully run on LeetCode : Yes
+
+Any problem you faced while coding this :
+Initially struggled to decide when to move the index forward and
+when to stay on the same index to allow reuse of elements.
+Fixed it by using:
+- idx + 1 for "not choose"
+- same idx for "choose"
+*/
+
+import java.util.*;
+
+class Solution {
+
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        List<List<Integer>> result = new ArrayList<>();
+        helper(candidates, 0, target, new ArrayList<>(), result);
+        return result;
+    }
+
+    private void helper(int[] candidates, int idx, int target, List<Integer> path, List<List<Integer>> result) {
+        // Base cases
+        if (idx == candidates.length || target < 0) {
+            return;
+        }
+        if (target == 0) {
+            result.add(new ArrayList<>(path));
+            return;
+        }
+        // Not choose current element
+        helper(candidates, idx + 1, target, path, result);
+
+        // Choose current element
+        path.add(candidates[idx]);
+        helper(candidates, idx, target - candidates[idx], path, result);
+        // Backtrack
+        path.remove(path.size() - 1);
+    }
+}
diff --git a/problem2.java b/problem2.java
new file mode 100644
index 00000000..1a80ed63
--- /dev/null
+++ b/problem2.java
@@ -0,0 +1,83 @@
+    /**
+    Time Complexity : Exponential, approximately O(4^N)
+    Explanation:
+    At each position, we try different partitions of the number
+    and for each partition we try three operators:
+        +, -, *
+    So the total number of recursive states grows exponentially.
+
+    Space Complexity : O(N)
+    Explanation:
+    Recursion depth can go up to N and StringBuilder path also holds
+    up to N characters/operators along one recursive path.
+
+    Did this code successfully run on LeetCode : Yes
+
+    Any problem you faced while coding this :
+    Initially the difficult part was handling multiplication,
+    because multiplication has higher precedence than + and -.
+    Fixed it by keeping track of the previous operand using 'tail'.
+    So when '*' is used:
+        calc = calc - tail + tail * curr
+    Also had to carefully handle numbers with leading zeros
+    like "05", which are not valid.
+    */
+    class Solution {
+
+
+
+        List<String> res;
+    
+        public List<String> addOperators(String num, int target) {
+    
+            this.res = new LinkedList<>();
+            helper(num, 0, 0L, 0L, new StringBuilder(), target);
+            return res;
+        }
+    
+        private void helper(String num, int pivot, long calc, long tail, StringBuilder path, int target) {
+    
+            // Base case
+            if (pivot == num.length()) {
+                if (calc == target) {
+                    res.add(path.toString());
+                }
+                return;
+            }
+    
+            // Try every possible next number
+            for (int i = pivot; i < num.length(); i++) {
+    
+                // Skip numbers with leading zero
+                if (num.charAt(pivot) == '0' && pivot != i) break;
+    
+                long curr = Long.parseLong(num.substring(pivot, i + 1));
+    
+                if (pivot == 0) {
+                    // First number, no operator before it
+                    int pl = path.length();
+                    path.append(curr);
+                    helper(num, i + 1, curr, curr, path, target);
+                    path.setLength(pl);
+                } else {
+                    // Addition
+                    int pl = path.length();
+                    path.append("+").append(curr);
+                    helper(num, i + 1, calc + curr, curr, path, target);
+                    path.setLength(pl);
+    
+                    // Subtraction
+                    pl = path.length();
+                    path.append("-").append(curr);
+                    helper(num, i + 1, calc - curr, -curr, path, target);
+                    path.setLength(pl);
+    
+                    // Multiplication
+                    pl = path.length();
+                    path.append("*").append(curr);
+                    helper(num, i + 1, calc - tail + tail * curr, tail * curr, path, target);
+                    path.setLength(pl);
+                }
+            }
+        }
+    }
\ No newline at end of file