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_dynamic_programming/unbounded_knapsack.rs

@@ -0,0 +1,60 @@
+/*
+ * File: unbounded_knapsack.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 完全背包：动态规划 */
+fn unbounded_knapsack_dp(wgt: &[i32], val: &[i32], cap: usize) -> i32 {
+    let n = wgt.len();
+    // 初始化 dp 表
+    let mut dp = vec![vec![0; cap + 1]; n + 1];
+    // 状态转移
+    for i in 1..=n {
+        for c in 1..=cap {
+            if wgt[i - 1] > c as i32 {
+                // 若超过背包容量，则不选物品 i
+                dp[i][c] = dp[i - 1][c];
+            } else {
+                // 不选和选物品 i 这两种方案的较大值
+                dp[i][c] = std::cmp::max(dp[i - 1][c], dp[i][c - wgt[i - 1] as usize] + val[i - 1]);
+            }
+        }
+    }
+    return dp[n][cap];
+}
+
+/* 完全背包：状态压缩后的动态规划 */
+fn unbounded_knapsack_dp_comp(wgt: &[i32], val: &[i32], cap: usize) -> i32 {
+    let n = wgt.len();
+    // 初始化 dp 表
+    let mut dp = vec![0; cap + 1];
+    // 状态转移
+    for i in 1..=n {
+        for c in 1..=cap {
+            if wgt[i - 1] > c as i32 {
+                // 若超过背包容量，则不选物品 i
+                dp[c] = dp[c];
+            } else {
+                // 不选和选物品 i 这两种方案的较大值
+                dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);
+            }
+        }
+    }
+    dp[cap]
+}
+
+/* Driver Code */
+pub fn main() {
+    let wgt = [ 1, 2, 3 ];
+    let val = [ 5, 11, 15 ];
+    let cap: usize = 4;
+
+    // 动态规划
+    let res = unbounded_knapsack_dp(&wgt, &val, cap);
+    println!("不超过背包容量的最大物品价值为 {res}");
+
+    // 状态压缩后的动态规划
+    let res = unbounded_knapsack_dp_comp(&wgt, &val, cap);
+    println!("不超过背包容量的最大物品价值为 {res}");
+}