rust and zig : add codes for chapter_dynamic_programming (#606)

* rust : add codes for chapter_dynamic_programming

* zig : add codes for chapter_dynamic_programming

* rust : add codes for chapter_backtracking

* Update n_queens.rs

---------

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

codes/rust/chapter_backtracking/permutations_i.rs

@@ -0,0 +1,46 @@
+/*
+ * File: permutations_i.rs
+ * Created Time: 2023-07-15
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 回溯算法：全排列 I */
+fn backtrack(mut state: Vec<i32>, choices: &[i32], selected: &mut [bool], res: &mut Vec<Vec<i32>>) {
+    // 当状态长度等于元素数量时，记录解
+    if state.len() == choices.len() {
+        res.push(state);
+        return;
+    }
+    // 遍历所有选择
+    for i in 0..choices.len() {
+        let choice = choices[i];
+        // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
+        if !selected[i] {
+            // 尝试：做出选择，更新状态
+            selected[i] = true;
+            state.push(choice);
+            // 进行下一轮选择
+            backtrack(state.clone(), choices, selected, res);
+            // 回退：撤销选择，恢复到之前的状态
+            selected[i] = false;
+            state.remove(state.len() - 1);
+        }
+    }
+}
+
+/* 全排列 I */
+fn permutations_i(nums: &mut [i32]) -> Vec<Vec<i32>> {
+    let mut res = Vec::new(); // 状态（子集）
+    backtrack(Vec::new(), nums, &mut vec![false; nums.len()], &mut res);
+    res
+}
+
+/* Driver Code */
+pub fn main() {
+    let mut nums = [ 1, 2, 3 ];
+
+    let res = permutations_i(&mut nums);
+
+    println!("输入数组 nums = {:?}", &nums);
+    println!("所有排列 res = {:?}", &res);
+}