feat: add the section of the introduction to dynamic programming (#571)

* add the section of the introduction to
dynamic programming

* add a code comments.

codes/java/chapter_dynamic_programming/climbing_stairs_dfs_mem.java

@@ -0,0 +1,41 @@
+/**
+ * File: climbing_stairs_dfs_mem.java
+ * Created Time: 2023-06-30
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_dynamic_programming;
+
+import java.util.Arrays;
+
+public class climbing_stairs_dfs_mem {
+    /* 记忆化搜索 */
+    public static int dfs(int i, int[] mem) {
+        // 已知 dp[1] 和 dp[2] ，返回之
+        if (i == 1 || i == 2)
+            return 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]
+        int 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 */
+    public static int climbingStairsDFSMem(int n) {
+        // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+        int[] mem = new int[n + 1];
+        Arrays.fill(mem, -1);
+        return dfs(n, mem);
+    }
+
+    public static void main(String[] args) {
+        int n = 9;
+
+        int res = climbingStairsDFSMem(n);
+        System.out.println(String.format("爬 %d 阶楼梯共有 %d 种方案", n, res));
+    }
+}