Add kotlin code for dynamic programming (#1099)

* feat(kotlin): add kotlin code for dynamic programming.

* Update knapsack.kt

codes/kotlin/chapter_dynamic_programming/climbing_stiars_dfs_mem.kt

@@ -0,0 +1,38 @@
+/**
+ * File: climbing_stairs_dfs_mem.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import java.util.*
+
+/* 记忆化搜索 */
+fun dfs(i: Int, mem: IntArray): Int {
+    // 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]
+    val 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 */
+fun climbingStairsDFSMem(n: Int): Int {
+    // mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+    val mem = IntArray(n + 1)
+    Arrays.fill(mem, -1)
+    return dfs(n, mem)
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    val res: Int = climbingStairsDFSMem(n)
+    println("爬 $n 阶楼梯共有 $res 种方案")
+}