Backtracking-1

CombinationSum.swift

@@ -0,0 +1,143 @@
+//
+//  CombinationSum.swift
+//  DSA-Practice
+//
+//  Created by Paridhi Malviya on 2/2/26.
+//
+
+class CombinationSum {
+    func combinationSum(_ candidates: [Int], _ target: Int) -> [[Int]] {
+        var result = [[Int]]()
+        helper(candidates: candidates, idx: 0, target: target, path: [], result: &result)
+        return result
+    }
+
+    //0-1 recursion
+    /*
+     time complexity - 2^(m + n)
+     space complexity - depth of recursion stack - (m+n)
+     */
+    func helper(candidates: [Int], idx: Int, target: Int, path: [Int], result: inout [[Int]]) {
+        //base
+        if (target == 0) {
+            result.append(path)
+            return
+        }
+        if (idx == candidates.count || target < 0) {
+            return
+        }
+
+        //logic
+
+        //recurse
+
+        //no choose
+        helper(candidates: candidates, idx: idx + 1, target: target, path: path, result: &result)
+        var path = path
+        path.append(candidates[idx])
+        //choose
+        helper(candidates: candidates, idx: idx, target: target - candidates[idx], path: path, result: &result)
+    }
+}
+
+class CombinationSumUsingForLoopBasedRecursion {
+    func combinationSum(_ candidates: [Int], _ target: Int) -> [[Int]] {
+        var result = [[Int]]()
+        getCombinations(candidates: candidates, start: 0, target: target, path: [], result: &result)
+        return result
+    }
+
+    //for loop based recursion - time complexty - 2^(m+n)
+    /*
+     here width of the tree is more and height is lesser. Effectvely it's choose, not choose algorithm only.
+     Some places, for loop based recursions is beneficial because it's easier to reach solution.
+     case in point, permutation of string, combination of string
+     */
+    func getCombinations(candidates: [Int], start: Int, target: Int, path: [Int], result: inout [[Int]]) {
+        //base
+        if (target == 0) {
+            result.append(path)
+            return
+        }
+
+        if (target < 0) {
+            return
+        }
+
+        //logic
+        var path = path
+        for i in start..<candidates.count {
+            //action
+            path.append(candidates[i])
+
+            //recurse
+            getCombinations(candidates: candidates, start: i, target: target - candidates[i], path: path,  result: &result)
+
+            //backtrack
+            path.removeLast()
+        }
+    }
+
+
+    /*
+     for loop based recursion - If we want different permutations of the numbers which is summing up to a target then don't pass pivot to the recursive function. Always start from 0.
+     */
+    func getPermutationsWithDifferentArrangements(candidates: [Int], target: Int, path: [Int], result: inout [[Int]]) {
+        //base
+        if (target < 0) {
+            return
+        }
+        if (target == 0) {
+            result.append(path)
+            return
+        }
+
+        //logic
+        var path = path
+        for i in 0..<candidates.count {
+            //action
+            path.append(candidates[i])
+
+            //recurse
+            getPermutationsWithDifferentArrangements(candidates: candidates, target: target - candidates[i], path: path,  result: &result)
+
+            //backtrack
+            path.removeLast()
+        }
+    }
+}
+
+
+//For permutation
+
+class Permutation {
+    func combinationSum(_ candidates: [Int], _ target: Int) -> [[Int]] {
+        var result = [[Int]]()
+        getCombinationsWithDifferentArrangements(candidates: candidates, target: target, path: [],result: &result)
+        return result
+    }
+
+    func getCombinationsWithDifferentArrangements(candidates: [Int], target: Int, path: [Int], result: inout [[Int]]) {
+        //base
+        if (target < 0) {
+            return
+        }
+        if (target == 0) {
+            result.append(path)
+            return
+        }
+
+        //logic
+        var path = path
+        for i in 0..<candidates.count {
+            //action
+            path.append(candidates[i])
+
+            //recurse
+            getCombinationsWithDifferentArrangements(candidates: candidates, target: target - candidates[i], path: path,  result: &result)
+
+            //backtrack
+            path.removeLast()
+        }
+    }
+}

ExpressionAddOperators.swift

@@ -0,0 +1,119 @@
+//
+//  ExpressionAddOperators.swift
+//  DSA-Practice
+//
+//  Created by Paridhi Malviya on 4/8/26.
+//
+
+/*
+ It has 2 layers of recursion.
+
+ + - *
+ there are 4 possibilities -
+ 1. Not putting any operator at all.
+ 2. putting +
+ 3. putting -
+ 4. putting *
+        1234
+ 1    12     123  1234 (outer layer)
+
+ */
+
+class ExpressionAddOperators {
+    func addOperators(_ num: String, _ target: Int) -> [String] {
+        var result = [String]()
+        var path = [Character]()
+        helper(Array(num), start: 0, target, calculated: 0, tail: 0, path: path, result: &result)
+        return result
+    }
+
+    func helper(_ numArr: [Character], start: Int, _ target: Int, calculated: Int, tail: Int, path: [Character], result: inout [String]) {
+        //the start pointer went out of bounds
+        if (start == numArr.count) {
+            if (calculated == target) {
+                result.append(String(path))
+            }
+            return
+        }
+        //logic
+        for i in start..<numArr.count {
+            if (start != i && numArr[start] == "0") {
+                continue
+            }
+            let substr = numArr[start...i]
+            let currNum = Int(String(substr))! //1, 12, 123, 1234, .... 2, 23, 234....
+            let strCount = substr.count //used while backtracking
+
+            /* at first level, we have only numbers. Fron next levels, we have expressions
+            */
+            if (start == 0) {
+                // path.append(String(currNum))
+                helper(numArr, start: i + 1, target, calculated: currNum, tail: currNum, path: path + substr, result: &result) // 23
+                // path.removeLast(path.count - strCount)
+            } else {
+                //how to put all the characters after the substring and append it to the path
+                //if it't not first level. It's further levels. We have 3 options
+
+                //+
+                helper(numArr, start: i + 1, target, calculated: calculated + currNum, tail: currNum, path: path + "+" + substr, result: &result)
+
+                //-
+                helper(numArr, start: i + 1, target, calculated: calculated - currNum, tail: -currNum, path: path + "-" + substr, result: &result)
+
+                //*
+                helper(numArr, start: i + 1, target, calculated: calculated - tail + tail * currNum, tail: tail * currNum, path: path + "*" + substr, result: &result)
+            }
+        }
+    }
+
+    //MARK: using backtracking
+    func addOperatorsB(_ num: String, _ target: Int) -> [String] {
+        var result = [String]()
+        var path: [Character] = []
+        helperB(Array(num), start: 0, target, calculated: 0, tail: 0, path: &path, result: &result)
+        return result
+    }
+
+    func helperB(_ numArr: [Character], start: Int, _ target: Int, calculated: Int, tail: Int, path: inout [Character], result: inout [String]) {
+        //the start pointer went out of bounds
+        if (start == numArr.count) {
+            if (calculated == target) {
+                result.append(String(path))
+            }
+            return
+        }
+        //logic
+        for i in start..<numArr.count {
+            if (start != i && numArr[start] == "0") {
+                continue
+            }
+            let substr = numArr[start...i]
+            let currNum = Int(String(substr))! //1, 12, 123, 1234, .... 2, 23, 234....
+            let strCount = substr.count //used while backtracking
+
+            /* at first level, we have only numbers. Fron next levels, we have expressions
+            */
+            if (start == 0) {
+                path += substr
+                // path.append(Array(substr)
+                helperB(numArr, start: i + 1, target, calculated: currNum, tail: currNum, path: &path, result: &result) // 23
+                path.removeLast(strCount)
+            } else {
+                //to put all the operators after the substring and append it to the path
+                //if it't not first level. It's further levels. We have 3 options
+                //+
+                path = path + "+" + substr
+                helperB(numArr, start: i + 1, target, calculated: calculated + currNum, tail: currNum, path: &path, result: &result)
+                path.removeLast(strCount + 1)
+                //-
+                path = path + "-" + substr
+                helperB(numArr, start: i + 1, target, calculated: calculated - currNum, tail: -currNum, path: &path, result: &result)
+                path.removeLast(strCount + 1)
+                //*
+                path = path + "*" + substr
+                helperB(numArr, start: i + 1, target, calculated: calculated - tail + tail * currNum, tail: tail * currNum, path: &path, result: &result)
+                path.removeLast(strCount + 1)
+            }
+        }
+    }
+}