feat: Add rust code for backtracking problems

Author: nikhilmitrax

rust/Backtracking/combinations_of_sum_k.rs

@@ -0,0 +1,41 @@
+pub fn combinations_of_sum_k(nums: Vec<i32>, target: i32) -> Vec<Vec<i32>> {
+    let mut result: Vec<Vec<i32>> = Vec::new();
+    let mut combination: Vec<i32> = Vec::new();
+    
+    combinations_of_sum_k_impl(&mut combination, 0, &nums, target, &mut result);
+    
+    result
+}
+
+fn combinations_of_sum_k_impl(
+    combination: &mut Vec<i32>,
+    start_index: usize,
+    nums: &Vec<i32>,
+    target: i32,
+    result: &mut Vec<Vec<i32>>
+) {
+    // Termination condition: If the target is equal to 0, we found a combination 
+    // that sums to 'k'.
+    if target == 0 {
+        result.push(combination.clone());
+        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 i in start_index..nums.len() {
+        // Add the current number to create a new combination.
+        combination.push(nums[i]);
+        
+        // Recursively explore all paths that branch from this new combination.
+        combinations_of_sum_k_impl(combination, i, nums, target - nums[i], result);
+        
+        // Backtrack by removing the number we just added.
+        combination.pop();
+    }
+}

rust/Backtracking/find_all_permutations.rs

@@ -0,0 +1,37 @@
+pub fn find_all_permutations(nums: Vec<i32>) -> Vec<Vec<i32>> {
+    let mut result: Vec<Vec<i32>> = Vec::new();
+    let mut candidate: Vec<i32> = Vec::new();
+    let mut used: std::collections::HashSet<i32> = std::collections::HashSet::new();
+    
+    find_all_permutations_impl(&nums, &mut candidate, &mut used, &mut result);
+    
+    result
+}
+
+fn find_all_permutations_impl(
+    nums: &Vec<i32>,
+    candidate: &mut Vec<i32>,
+    used: &mut std::collections::HashSet<i32>,
+    result: &mut Vec<Vec<i32>>
+) {
+    // If the current candidate is a complete permutation, add it to the result.
+    if candidate.len() == nums.len() {
+        result.push(candidate.clone());
+        return;
+    }
+    
+    for &num in nums {
+        if !used.contains(&num) {
+            // Add 'num' to the current permutation and mark it as used.
+            candidate.push(num);
+            used.insert(num);
+            
+            // Recursively explore all branches using the updated permutation candidate.
+            find_all_permutations_impl(nums, candidate, used, result);
+            
+            // Backtrack by reversing the changes made.
+            candidate.pop();
+            used.remove(&num);
+        }
+    }
+}

rust/Backtracking/find_all_subsets.rs

@@ -0,0 +1,32 @@
+pub fn find_all_subsets(nums: Vec<i32>) -> Vec<Vec<i32>> {
+    let mut result: Vec<Vec<i32>> = Vec::new();
+    let mut curr_subset: Vec<i32> = Vec::new();
+    
+    find_all_subsets_impl(0, &mut curr_subset, &nums, &mut result);
+    
+    result
+}
+
+fn find_all_subsets_impl(
+    i: usize,
+    curr_subset: &mut Vec<i32>,
+    nums: &Vec<i32>,
+    result: &mut Vec<Vec<i32>>
+) {
+    // Base case: if all elements have been considered, add the
+    // current subset to the output.
+    if i == nums.len() {
+        result.push(curr_subset.clone());
+        return;
+    }
+    
+    // Include the current element and recursively explore all paths
+    // that branch from this subset.
+    curr_subset.push(nums[i]);
+    find_all_subsets_impl(i + 1, curr_subset, nums, result);
+    
+    // Exclude the current element and recursively explore all paths
+    // that branch from this subset.
+    curr_subset.pop();
+    find_all_subsets_impl(i + 1, curr_subset, nums, result);
+}

rust/Backtracking/n_queens.rs

@@ -0,0 +1,54 @@
+pub fn n_queens(n: i32) -> i32 {
+    let mut result = 0;
+    let mut diagonals_set = std::collections::HashSet::new();
+    let mut anti_diagonals_set = std::collections::HashSet::new();
+    let mut cols_set = std::collections::HashSet::new();
+    
+    n_queens_impl(0, &mut diagonals_set, &mut anti_diagonals_set, &mut cols_set, n, &mut result);
+    
+    result
+}
+
+fn n_queens_impl(
+    r: i32, 
+    diagonals_set: &mut std::collections::HashSet<i32>, 
+    anti_diagonals_set: &mut std::collections::HashSet<i32>, 
+    cols_set: &mut std::collections::HashSet<i32>, 
+    n: i32,
+    result: &mut i32
+) {
+    // Termination condition: If we have reached the end of the rows,
+    // we've placed all 'n' queens.
+    if r == n {
+        *result += 1;
+        return;
+    }
+    
+    for c in 0..n {
+        let curr_diagonal = r - c;
+        let curr_anti_diagonal = r + c;
+        
+        // If there are queens on the current column, diagonal or
+        // anti-diagonal, skip this square.
+        if cols_set.contains(&c) || 
+           diagonals_set.contains(&curr_diagonal) || 
+           anti_diagonals_set.contains(&curr_anti_diagonal) {
+            continue;
+        }
+        
+        // Place the queen by marking the current column, diagonal, and
+        // anti-diagonal as occupied.
+        cols_set.insert(c);
+        diagonals_set.insert(curr_diagonal);
+        anti_diagonals_set.insert(curr_anti_diagonal);
+        
+        // Recursively move to the next row to continue placing queens.
+        n_queens_impl(r + 1, diagonals_set, anti_diagonals_set, cols_set, n, result);
+        
+        // Backtrack by removing the current column, diagonal, and
+        // anti-diagonal from the hash sets.
+        cols_set.remove(&c);
+        diagonals_set.remove(&curr_diagonal);
+        anti_diagonals_set.remove(&curr_anti_diagonal);
+    }
+}

rust/Backtracking/phone_keypad_combinations.rs

@@ -0,0 +1,54 @@
+use std::collections::HashMap;
+
+pub fn phone_keypad_combinations(digits: String) -> Vec<String> {
+    if digits.is_empty() {
+        return Vec::new();
+    }
+    
+    let mut keypad_map = HashMap::new();
+    keypad_map.insert('2', "abc");
+    keypad_map.insert('3', "def");
+    keypad_map.insert('4', "ghi");
+    keypad_map.insert('5', "jkl");
+    keypad_map.insert('6', "mno");
+    keypad_map.insert('7', "pqrs");
+    keypad_map.insert('8', "tuv");
+    keypad_map.insert('9', "wxyz");
+    
+    let mut result: Vec<String> = Vec::new();
+    let mut curr_combination: Vec<char> = Vec::new();
+    
+    let digits_chars: Vec<char> = digits.chars().collect();
+    phone_keypad_combinations_impl(0, &mut curr_combination, &digits_chars, &keypad_map, &mut result);
+    
+    result
+}
+
+fn phone_keypad_combinations_impl(
+    i: usize,
+    curr_combination: &mut Vec<char>,
+    digits: &Vec<char>,
+    keypad_map: &HashMap<char, &str>,
+    result: &mut Vec<String>
+) {
+    // Termination condition: if all digits have been considered, add the
+    // current combination to the output list.
+    if curr_combination.len() == digits.len() {
+        result.push(curr_combination.iter().collect());
+        return;
+    }
+    
+    let digit = digits[i];
+    if let Some(letters) = keypad_map.get(&digit) {
+        for letter in letters.chars() {
+            // Add the current letter.
+            curr_combination.push(letter);
+            
+            // Recursively explore all paths that branch from this combination.
+            phone_keypad_combinations_impl(i + 1, curr_combination, digits, keypad_map, result);
+            
+            // Backtrack by removing the letter we just added.
+            curr_combination.pop();
+        }
+    }
+}