From c6bc10a1015fadf86ddafbf6928d821c07ec99a8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E7=8E=8B=E4=BD=9C=E5=8B=8B?=
 <59754483+Zuoxun@users.noreply.github.com>
Date: Sat, 7 Oct 2023 21:32:35 +0800
Subject: [PATCH] Add Min cost climbing stairs dp in C code (#828)
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* Update vector.h

增加功能列表：
获取向量的第 i 个元素
设置向量的第 i 个元素
向量扩容
向量缩容
向量插入元素
向量删除元素
向量交换元素
向量是否为空
向量是否已满
向量是否相等
对向量内部进行排序（升序/降序）
对向量某段数据排序（升序/降序）

* Create hanota.c

* 新增binary_search_recur.c

* Update vector.h

* Delete codes/c/chapter_divide_and_conquer directory

* Update vector.h

* Create binary_search_recur.c

* Delete codes/chapter_divide_and_conquer directory

* Update vector.h

* Create min_cost_climbing_stairs_dp.c

* Update min_cost_climbing_stairs_dp.c

* Update min_cost_climbing_stairs_dp.c

* RollBack vector.h

* Update min_cost_climbing_stairs_dp.c

* Update min_cost_climbing_stairs_dp.c

* Create CMakeLists.txt

* Update min_cost_climbing_stairs_dp.c
---
 .../CMakeLists.txt                            |  1 +
 .../min_cost_climbing_stairs_dp.c             | 63 +++++++++++++++++++
 2 files changed, 64 insertions(+)
 create mode 100644 codes/c/chapter_dynamic_programming/CMakeLists.txt
 create mode 100644 codes/c/chapter_dynamic_programming/min_cost_climbing_stairs_dp.c

diff --git a/codes/c/chapter_dynamic_programming/CMakeLists.txt b/codes/c/chapter_dynamic_programming/CMakeLists.txt
new file mode 100644
index 000000000..b3a0d5771
--- /dev/null
+++ b/codes/c/chapter_dynamic_programming/CMakeLists.txt
@@ -0,0 +1 @@
+add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c)
diff --git a/codes/c/chapter_dynamic_programming/min_cost_climbing_stairs_dp.c b/codes/c/chapter_dynamic_programming/min_cost_climbing_stairs_dp.c
new file mode 100644
index 000000000..c98dd4502
--- /dev/null
+++ b/codes/c/chapter_dynamic_programming/min_cost_climbing_stairs_dp.c
@@ -0,0 +1,63 @@
+/**
+ * File: min_cost_climbing_stairs_dp.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* 求最小值 */
+int min(int a, int b) {
+    return a < b ? a : b;
+}
+
+/* 爬楼梯最小代价：动态规划 */
+int minCostClimbingStairsDP(int cost[], int costSize) {
+    int n = costSize - 1;
+    if (n == 1 || n == 2)
+        return cost[n];
+    // 初始化 dp 表，用于存储子问题的解
+    int dp[n + 1];
+    // 初始状态：预设最小子问题的解
+    dp[1] = cost[1];
+    dp[2] = cost[2];
+    // 状态转移：从较小子问题逐步求解较大子问题
+    for (int i = 3; i <= n; i++) {
+        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];
+    }
+    return dp[n];
+}
+
+/* 爬楼梯最小代价：空间优化后的动态规划 */
+int minCostClimbingStairsDPComp(int cost[], int costSize) {
+    int n = costSize - 1;
+    if (n == 1 || n == 2)
+        return cost[n];
+    int a = cost[1], b = cost[2];
+    for (int i = 3; i <= n; i++) {
+        int tmp = b;
+        b = min(a, tmp) + cost[i];
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+int main() {
+    int cost[] = {0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1};
+    int costSize = sizeof(cost) / sizeof(cost[0]);
+    printf("输入楼梯的代价列表为 [");
+    for (int i = 0; i < costSize; i++) {
+        if (i != costSize - 1) printf("%d, ", cost[i]);
+        else printf("%d", cost[i]);
+    }
+    printf("]\n");
+
+    int res = minCostClimbingStairsDP(cost, costSize);
+    printf("爬完楼梯的最低代价为 %d\n", res);
+
+    res = minCostClimbingStairsDPComp(cost, costSize);
+    printf("爬完楼梯的最低代价为 %d\n", res);
+
+    return 0;
+}