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/zig/chapter_dynamic_programming/climbing_stairs_dfs_mem.zig

@@ -0,0 +1,39 @@
+// File: climbing_stairs_dfs_mem.zig
+// Created Time: 2023-07-15
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+
+// 记忆化搜索
+fn dfs(i: usize, mem: []i32) i32 {
+    // 已知 dp[1] 和 dp[2] ，返回之
+    if (i == 1 or i == 2) {
+        return @intCast(i);
+    }
+    // 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]
+    var count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // 记录 dp[i]
+    mem[i] = count;
+    return count;
+}
+
+// 爬楼梯：记忆化搜索
+fn climbing_stairs_dfs_mem(comptime n: usize) i32 {
+    // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+    var mem = [_]i32{ -1 } ** (n + 1);
+    return dfs(n, &mem);
+}
+
+// Driver Code
+pub fn main() !void {
+    comptime var n: usize = 9;
+
+    var res = climbing_stairs_dfs_mem(n);
+    std.debug.print("爬 {} 阶楼梯共有 {} 种方案\n", .{ n, res });
+
+    _ = try std.io.getStdIn().reader().readByte();
+}