feat: Add C code for the section of intro to DP (#771)

* Add dynamic programming C language code

* Add dynamic programming chapter C language code

* Modifying errors in files

codes/c/chapter_dynamic_programming/climbing_stairs_dfs_mem.c

@@ -0,0 +1,44 @@
+/**
+ * File: climbing_stairs_dfs_mem.c
+ * Created Time: 2023-09-19
+ * Author: huawuque404 (huawuque404@163.com)
+ */
+
+#include "../utils/common.h"
+
+/* 记忆化搜索 */
+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 */
+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 = (int *)malloc((n + 1) * sizeof(int));
+    for (int i = 0; i <= n; i++) {
+        mem[i] = -1;
+    }
+    int result = dfs(n, mem);
+    free(mem);
+    return result;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+    
+    int res = climbingStairsDFSMem(n);
+    printf("爬 %d 阶楼梯共有 %d 种方案\n", n, res);
+
+    return 0;
+}