From 119091c060dab56709fe218a694c4398e320739a Mon Sep 17 00:00:00 2001
From: MeghaN28 <n.megha82@gmail.com>
Date: Tue, 11 Aug 2026 11:41:47 -0700
Subject: [PATCH] Backtrack

---
 CombinationSumForBacktrack.java     |  43 +++++++++++
 CombinationSumRecurseBacktrack.java |  56 ++++++++++++++
 Evaluateexp.java                    | 110 ++++++++++++++++++++++++++++
 3 files changed, 209 insertions(+)
 create mode 100644 CombinationSumForBacktrack.java
 create mode 100644 CombinationSumRecurseBacktrack.java
 create mode 100644 Evaluateexp.java

diff --git a/CombinationSumForBacktrack.java b/CombinationSumForBacktrack.java
new file mode 100644
index 00000000..1640702c
--- /dev/null
+++ b/CombinationSumForBacktrack.java
@@ -0,0 +1,43 @@
+import java.util.*;
+
+class Solution {
+
+    List<List<Integer>> res;
+
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+
+        res = new ArrayList<>();
+
+        helper(candidates, target, new ArrayList<>(), 0);
+
+        return res;
+    }
+
+    private void helper(int[] candidates,
+                        int target,
+                        List<Integer> path,
+                        int indx) {
+
+        if (target < 0) {
+            return;
+        }
+
+        if (target == 0) {
+            res.add(new ArrayList<>(path));
+            return;
+        }
+
+        for (int i = indx; i < candidates.length; i++) {
+
+            path.add(candidates[i]);
+
+            helper(candidates,
+                   target - candidates[i],
+                   path,
+                   i);
+
+            // backtrack
+            path.remove(path.size() - 1);
+        }
+    }
+}
\ No newline at end of file
diff --git a/CombinationSumRecurseBacktrack.java b/CombinationSumRecurseBacktrack.java
new file mode 100644
index 00000000..8763efa4
--- /dev/null
+++ b/CombinationSumRecurseBacktrack.java
@@ -0,0 +1,56 @@
+
+// Time Complexity : O(2^n+m)
+// Space Complexity : Recursion stack space
+// Did this code successfully run on Leetcode :Yes
+// Any problem you faced while coding this :no
+
+
+// Your code here along with comments explaining your approach
+// this is similar to the coin change problem
+// we need to find the combinations of the numbers which adds up to the target 
+// no need of permutations, only the combinations and add to the res and return it
+// we can do normal deep copy, for loop, backtrack anything.
+import java.util.*;
+
+class Solution {
+
+    List<List<Integer>> res;
+
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+
+        res = new ArrayList<>();
+
+        helper(candidates, target, new ArrayList<>(), 0);
+
+        return res;
+    }
+
+    private void helper(int[] candidates,
+                        int target,
+                        List<Integer> path,
+                        int indx) {
+
+        if (target < 0 || indx == candidates.length) {
+            return;
+        }
+
+        if (target == 0) {
+            res.add(new ArrayList<>(path));
+            return;
+        }
+
+        // Skip current number
+        helper(candidates, target, path, indx + 1);
+
+        // Take current number
+        path.add(candidates[indx]);
+
+        helper(candidates,
+               target - candidates[indx],
+               path,
+               indx);
+
+        // Backtrack
+        path.remove(path.size() - 1);
+    }
+}
\ No newline at end of file
diff --git a/Evaluateexp.java b/Evaluateexp.java
new file mode 100644
index 00000000..97ceaf28
--- /dev/null
+++ b/Evaluateexp.java
@@ -0,0 +1,110 @@
+// Time Complexity :O(4^N)
+// Space Complexity : Recursion stack space
+// Did this code successfully run on Leetcode : yes
+// Any problem you faced while coding this : no , just that 2 level tree
+
+
+// Your code here along with comments explaining your approach
+// Do 2 level tree recursion . first only for the numbers
+// next for the operators
+// for each operator do a seperate recursion, when it comes to * and % maintain a tail
+// Strin builder + backtracking to avoid new space everytime.
+import java.util.*;
+
+public class Evaluateexp {
+    List<String> res;
+
+    public List<String> addOperators(String num, int target) {
+        this.res = new ArrayList<>();
+
+        helper(num, 0, 0L, new StringBuilder(), 0L, target);
+
+        return res;
+    }
+
+    private void helper(String num, int pivot, long calc,
+                         StringBuilder path, long tail, int target) {
+
+        if (pivot == num.length()) {
+            if (calc == target) {
+                res.add(path.toString());
+            }
+            return;
+        }
+
+        for (int i = pivot; i < num.length(); i++) {
+
+            // Don't allow numbers with leading zeros
+            if (num.charAt(pivot) == '0' && i != pivot) {
+                break;
+            }
+
+            long curr = Long.parseLong(
+                num.substring(pivot, i + 1)
+            );
+
+            int len = path.length();
+
+            if (pivot == 0) {
+                path.append(curr);
+
+                helper(
+                    num,
+                    i + 1,
+                    curr,
+                    path,
+                    curr,
+                    target
+                );
+
+                path.setLength(len);
+            } else {
+
+                // +
+                path.append("+");
+                path.append(curr);
+
+                helper(
+                    num,
+                    i + 1,
+                    calc + curr,
+                    path,
+                    curr,
+                    target
+                );
+
+                path.setLength(len);
+
+                // -
+                path.append("-");
+                path.append(curr);
+
+                helper(
+                    num,
+                    i + 1,
+                    calc - curr,
+                    path,
+                    -curr,
+                    target
+                );
+
+                path.setLength(len);
+
+                // *
+                path.append("*");
+                path.append(curr);
+
+                helper(
+                    num,
+                    i + 1,
+                    calc - tail + (tail * curr),
+                    path,
+                    tail * curr,
+                    target
+                );
+
+                path.setLength(len);
+            }
+        }
+    }
+}
\ No newline at end of file