zig : upgrade codes && rust : add codes for chapter_searching and chapter_dynamic_programming. (#591)

* zig : update zig codes

* rust : add codes for linear_search and hashing_search

* rust : add codes for linear_search and hashing_search

* rust : add codes for chapter_dynamic_programming

codes/rust/chapter_dynamic_programming/climbing_stairs_dfs_mem.rs

@@ -0,0 +1,33 @@
+/*
+ * File: climbing_stairs_dfs_mem.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 记忆化搜索 */
+fn dfs(i: usize, mem: &mut [i32]) -> i32 {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if i == 1 || i == 2 { return i as i32};
+    // 若存在记录 dp[i] ，则直接返回之
+    if mem[i] != -1 { return mem[i] };
+    // dp[i] = dp[i-1] + dp[i-2]
+    let count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // 记录 dp[i]
+    mem[i] = count;
+    count
+}
+
+/* 爬楼梯：记忆化搜索 */
+fn climbing_stairs_dfs_mem(n: usize) -> i32 {
+    // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+    let mut mem = vec![-1; n + 1];
+    dfs(n, &mut mem)
+}
+
+/* Driver Code */
+pub fn main() {
+    let n: usize = 9;
+
+    let res = climbing_stairs_dfs_mem(n);
+    println!("爬 {n} 阶楼梯共有 {res} 种方案");
+}