rust : add codes for chapter_backtracking (#594)

* rust : add codes for chapter_backtracking

* Update subset_sum_ii.rs

---------

Co-authored-by: Yudong Jin <krahets@163.com>

codes/rust/Cargo.toml

@@ -22,7 +22,7 @@ path = "chapter_computational_complexity/space_complexity.rs"
 # Run Command: cargo run --bin two_sum
 [[bin]]
 name = "two_sum"
-path = "chapter_computational_complexity/two_sum.rs"
+path = "chapter_searching/two_sum.rs"
 
 # Run Command: cargo run --bin array
 [[bin]]
@@ -194,5 +194,20 @@ path = "chapter_dynamic_programming/climbing_stairs_constraint_dp.rs"
 name = "climbing_stairs_backtrack"
 path = "chapter_dynamic_programming/climbing_stairs_backtrack.rs"
 
+# Run Command: cargo run --bin subset_sum_i_naive
+[[bin]]
+name = "subset_sum_i_naive"
+path = "chapter_backtracking/subset_sum_i_naive.rs"
+
+# Run Command: cargo run --bin subset_sum_i
+[[bin]]
+name = "subset_sum_i"
+path = "chapter_backtracking/subset_sum_i.rs"
+
+# Run Command: cargo run --bin subset_sum_ii
+[[bin]]
+name = "subset_sum_ii"
+path = "chapter_backtracking/subset_sum_ii.rs"
+
 [dependencies]
 rand = "0.8.5"

codes/rust/chapter_backtracking/subset_sum_i.rs

@@ -0,0 +1,50 @@
+/*
+ * File: subset_sum_i.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 回溯算法：子集和 I */
+fn backtrack(mut state: Vec<i32>, target: i32, choices: &[i32], start: usize, res: &mut Vec<Vec<i32>>) {
+    // 子集和等于 target 时，记录解
+    if target == 0 {
+        res.push(state);
+        return;
+    }
+    // 遍历所有选择
+    // 剪枝二：从 start 开始遍历，避免生成重复子集
+    for i in start..choices.len() {
+        // 剪枝一：若子集和超过 target ，则直接结束循环
+        // 这是因为数组已排序，后边元素更大，子集和一定超过 target
+        if target - choices[i] < 0 {
+            break;
+        }
+        // 尝试：做出选择，更新 target, start
+        state.push(choices[i]);
+        // 进行下一轮选择
+        backtrack(state.clone(), target - choices[i], choices, i, res);
+        // 回退：撤销选择，恢复到之前的状态
+        state.pop();
+    }
+}
+
+/* 求解子集和 I */
+fn subset_sum_i(nums: &mut [i32], target: i32) -> Vec<Vec<i32>> {
+    let state = Vec::new(); // 状态（子集）
+    nums.sort(); // 对 nums 进行排序
+    let start = 0; // 遍历起始点
+    let mut res = Vec::new();
+    backtrack(state, target, nums, start, &mut res);
+    res
+}
+
+/* Driver Code */
+pub fn main() {
+    let mut nums = [ 3, 4, 5 ];
+    let target = 9;
+
+    let res = subset_sum_i(&mut nums, target);
+    
+    println!("输入数组 nums = {:?}, target = {}", &nums, target);
+    println!("所有和等于 {} 的子集 res = {:?}", target, &res);
+}

codes/rust/chapter_backtracking/subset_sum_i_naive.rs

@@ -0,0 +1,48 @@
+/*
+ * File: subset_sum_i_naive.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 回溯算法：子集和 I */
+fn backtrack(mut state: Vec<i32>, target: i32, total: i32, choices: &[i32], res: &mut Vec<Vec<i32>>) {
+    // 子集和等于 target 时，记录解
+    if total == target {
+        res.push(state);
+        return;
+    }
+    // 遍历所有选择
+    for i in 0..choices.len() {
+        // 剪枝：若子集和超过 target ，则跳过该选择
+        if total + choices[i] > target {
+            continue;
+        }
+        // 尝试：做出选择，更新元素和 total
+        state.push(choices[i]);
+        // 进行下一轮选择
+        backtrack(state.clone(), target, total + choices[i], choices, res);
+        // 回退：撤销选择，恢复到之前的状态
+        state.pop();
+    }
+}
+
+/* 求解子集和 I（包含重复子集） */
+fn subset_sum_i_naive(nums: &[i32], target: i32) -> Vec<Vec<i32>> {
+    let state = Vec::new(); // 状态（子集）
+    let total = 0;
+    let mut res = Vec::new();
+    backtrack(state, target, total, nums, &mut res);
+    res
+}
+
+/* Driver Code */
+pub fn main() {
+    let nums = [ 3, 4, 5 ];
+    let target = 9;
+
+    let res = subset_sum_i_naive(&nums, target);
+    
+    println!("输入数组 nums = {:?}, target = {}", &nums, target);
+    println!("所有和等于 {} 的子集 res = {:?}", target, &res);
+    println!("请注意，该方法输出的结果包含重复集合");
+}

codes/rust/chapter_backtracking/subset_sum_ii.rs

@@ -0,0 +1,55 @@
+/*
+ * File: subset_sum_ii.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 回溯算法：子集和 II */
+fn backtrack(mut state: Vec<i32>, target: i32, choices: &[i32], start: usize, res: &mut Vec<Vec<i32>>) {
+    // 子集和等于 target 时，记录解
+    if target == 0 {
+        res.push(state);
+        return;
+    }
+    // 遍历所有选择
+    // 剪枝二：从 start 开始遍历，避免生成重复子集
+    // 剪枝三：从 start 开始遍历，避免重复选择同一元素
+    for i in start..choices.len() {
+        // 剪枝一：若子集和超过 target ，则直接结束循环
+        // 这是因为数组已排序，后边元素更大，子集和一定超过 target
+        if target - choices[i] < 0 {
+            break;
+        }
+        // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过
+        if i > start && choices[i] == choices[i - 1] {
+            continue;
+        }
+        // 尝试：做出选择，更新 target, start
+        state.push(choices[i]);
+        // 进行下一轮选择
+        backtrack(state.clone(), target - choices[i], choices, i, res);
+        // 回退：撤销选择，恢复到之前的状态
+        state.pop();
+    }
+}
+
+/* 求解子集和 II */
+fn subset_sum_ii(nums: &mut [i32], target: i32) -> Vec<Vec<i32>> {
+    let state = Vec::new(); // 状态（子集）
+    nums.sort(); // 对 nums 进行排序
+    let start = 0; // 遍历起始点
+    let mut res = Vec::new();
+    backtrack(state, target, nums, start, &mut res);
+    res
+}
+
+/* Driver Code */
+pub fn main() {
+    let mut nums = [ 4, 4, 5 ];
+    let target = 9;
+
+    let res = subset_sum_ii(&mut nums, target);
+    
+    println!("输入数组 nums = {:?}, target = {}", &nums, target);
+    println!("所有和等于 {} 的子集 res = {:?}", target, &res);
+}