Java Chapter 14: Backtracking

java/Backtracking/CombinationsOfSumK.java

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+import java.util.ArrayList;
+import java.util.List;
+
+public class CombinationsOfSumK {
+    public List<List<Integer>> combinationsOfSumK(int[] nums, int target) {
+        List<List<Integer>> res = new ArrayList<>();
+        dfs(new ArrayList<>(), 0, nums, target, res);
+        return res;
+    }
+
+    private void dfs(List<Integer> combination, int startIndex, int[] nums, int target, List<List<Integer>> res) {
+        // Termination condition: If the target is equal to 0, we found a combination 
+        // that sums to 'k'.
+        if (target == 0) {
+            res.add(new ArrayList<>(combination));
+            return;
+        }
+        // Termination condition: If the target is less than 0, no more valid 
+        // combinations can be created by adding it to the current combination.
+        if (target < 0) {
+            return;
+        }
+        // Starting from start_index, explore all combinations after adding nums[i].
+        for (int i = startIndex; i < nums.length; i++) {
+            // Add the current number to create a new combination.
+            combination.add(nums[i]);
+            // Recursively explore all paths that branch from this new combination.
+            dfs(combination, i, nums, target - nums[i], res);
+            // Backtrack by removing the number we just added.
+            combination.remove(combination.size() - 1);
+        }
+    }
+}

java/Backtracking/FindAllPermutations.java

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+import java.util.ArrayList;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Set;
+
+public class FindAllPermutations {
+    public List<List<Integer>> findAllPermutations(int[] nums) {
+        List<List<Integer>> res = new ArrayList<>();
+        backtrack(nums, new ArrayList<>(), new HashSet<>(), res);
+        return res;
+    }
+
+    private void backtrack(int[] nums, List<Integer> candidate, Set<Integer> used, List<List<Integer>> res) {
+        // If the current candidate is a complete permutation, add it to the
+        // result.
+        if (candidate.size() == nums.length) {
+            res.add(new ArrayList<>(candidate));
+            return;
+        }
+        for (int num : nums) {
+            if (!used.contains(num)) {
+                // Add 'num' to the current permutation and mark it as used.
+                candidate.add(num);
+                used.add(num);
+                // Recursively explore all branches using the updated
+                // permutation candidate.
+                backtrack(nums, candidate, used, res);
+                // Backtrack by reversing the changes made.
+                candidate.remove(candidate.size() - 1);
+                used.remove(num);
+            }
+        }
+    }
+}

java/Backtracking/FindAllSubsets.java

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+import java.util.ArrayList;
+import java.util.List;
+
+public class FindAllSubsets {
+    public List<List<Integer>> findAllSubsets(int[] nums) {
+        List<List<Integer>> res = new ArrayList<>();
+        backtrack(0, new ArrayList<>(), nums, res);
+        return res;
+    }
+
+    private void backtrack(int i, List<Integer> currSubset, int[] nums, List<List<Integer>> res) {
+        // Base case: if all elements have been considered, add the
+        // current subset to the output.
+        if (i == nums.length) {
+            res.add(new ArrayList<>(currSubset));
+            return;
+        }
+        // Include the current element and recursively explore all paths
+        // that branch from this subset.
+        currSubset.add(nums[i]);
+        backtrack(i + 1, currSubset, nums, res);
+        // Exclude the current element and recursively explore all paths
+        // that branch from this subset.
+        currSubset.remove(currSubset.size() - 1);
+        backtrack(i + 1, currSubset, nums, res);
+    }
+}

java/Backtracking/NQueens.java

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+import java.util.HashSet;
+import java.util.Set;
+
+public class NQueens {
+    int res = 0;
+
+    public int nQueens(int n) {
+        dfs(0, new HashSet<>(), new HashSet<>(), new HashSet<>(), n);
+        return res;
+    }
+
+    private void dfs(int r, Set<Integer> diagonalsSet, Set<Integer> antiDiagonalsSet, Set<Integer> colsSet, int n) {
+        // Termination condition: If we have reached the end of the rows,
+        // we've placed all 'n' queens.
+        if (r == n) {
+            res++;
+            return;
+        }
+        for (int c = 0; c < n; c++) {
+            int currDiagonal = r - c;
+            int currAntiDiagonal = r + c;
+            // If there are queens on the current column, diagonal or
+            // anti-diagonal, skip this square.
+            if (colsSet.contains(c) || diagonalsSet.contains(currDiagonal) || antiDiagonalsSet.contains(currAntiDiagonal)) {
+                continue;
+            }
+            // Place the queen by marking the current column, diagonal, and
+            // anti−diagonal as occupied.
+            colsSet.add(c);
+            diagonalsSet.add(currDiagonal);
+            antiDiagonalsSet.add(currAntiDiagonal);
+            // Recursively move to the next row to continue placing queens.
+            dfs(r + 1, diagonalsSet, antiDiagonalsSet, colsSet, n);
+            // Backtrack by removing the current column, diagonal, and
+            // anti−diagonal from the hash sets.
+            colsSet.remove(c);
+            diagonalsSet.remove(currDiagonal);
+            antiDiagonalsSet.remove(currAntiDiagonal);
+        }
+    }
+}

java/Backtracking/PhoneKeypadCombinations.java

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+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+
+public class PhoneKeypadCombinations {
+    public List<Stirng> phoneKeypadCombinations(String digits) {
+        Map<Character, String> keypadMap = new HashMap<>();
+        keypadMap.put('2', "abc");
+        keypadMap.put('3', "def");
+        keypadMap.put('4', "ghi");
+        keypadMap.put('5', "jkl");
+        keypadMap.put('6', "mno");
+        keypadMap.put('7', "pqrs");
+        keypadMap.put('8', "tuv");
+        keypadMap.put('9', "wxyz");
+        List<String> result = new ArrayList<>();
+        backtrack(0, new ArrayList<>(), digits, keypadMap, result);
+        return result;
+    }
+
+    private void backtrack(int i, List<Character> currCombination, String digits, Map<Character, String> keypadMap, List<String> result) {
+        // Termination condition: if all digits have been considered, add the
+        // current combination to the output list.
+        if (currCombination.size() == digits.length()) {
+            StringBuilder sb = new StringBuilder();
+            for (char c: currCombination) {
+                sb.append(c);
+            }
+            result.add(sb.toString());
+            return;
+        }
+        for (char letter: keypadMap.get(digits.charAt(i)).toCharArray()) {
+            // Add the current letter.
+            currCombination.add(letter);
+            // Recursively explore all paths that branch from this combination.
+            backtrack(i + 1, currCombination, digits, keypadMap, result);
+            // Backtrack by removing the letter we just added.
+            currCombination.remove(currCombination.size() - 1);
+        }
+    }
+}