From ef87bd494a906b050ab6fdca8b040cf93db1eb4f 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 21:47:05 +0800
Subject: [PATCH] Add Binary search recur in C code (#820)
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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

* Create CMakeLists.txt

* Update vector.h

* RollBack vector.h

* Update CMakeLists.txt

* Update binary_search_recur.c

* Update binary_search_recur.c

---------

Co-authored-by: Yudong Jin <krahets@163.com>
---
 .../chapter_divide_and_conquer/CMakeLists.txt |  1 +
 .../binary_search_recur.c                     | 47 +++++++++++++++++++
 2 files changed, 48 insertions(+)
 create mode 100644 codes/c/chapter_divide_and_conquer/binary_search_recur.c

diff --git a/codes/c/chapter_divide_and_conquer/CMakeLists.txt b/codes/c/chapter_divide_and_conquer/CMakeLists.txt
index 04f0bf4f1..34e23f6de 100644
--- a/codes/c/chapter_divide_and_conquer/CMakeLists.txt
+++ b/codes/c/chapter_divide_and_conquer/CMakeLists.txt
@@ -1 +1,2 @@
+add_executable(binary_search_recur binary_search_recur.c)
 add_executable(hanota hanota.c)
diff --git a/codes/c/chapter_divide_and_conquer/binary_search_recur.c b/codes/c/chapter_divide_and_conquer/binary_search_recur.c
new file mode 100644
index 000000000..72b579bf5
--- /dev/null
+++ b/codes/c/chapter_divide_and_conquer/binary_search_recur.c
@@ -0,0 +1,47 @@
+/**
+ * File: binary_search_recur.c
+ * Created Time: 2023-10-01
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* 二分查找：问题 f(i, j) */
+int dfs(int nums[], int target, int i, int j) {
+    // 若区间为空，代表无目标元素，则返回 -1
+    if (i > j) {
+        return -1;
+    }
+    // 计算中点索引 m
+    int m = (i + j) / 2;
+    if (nums[m] < target) {
+        // 递归子问题 f(m+1, j)
+        return dfs(nums, target, m + 1, j);
+    } else if (nums[m] > target) {
+        // 递归子问题 f(i, m-1)
+        return dfs(nums, target, i, m - 1);
+    } else {
+        // 找到目标元素，返回其索引
+        return m;
+    }
+}
+
+/* 二分查找 */
+int binarySearch(int nums[], int target, int numsSize) {
+    int n = numsSize;
+    // 求解问题 f(0, n-1)
+    return dfs(nums, target, 0, n - 1);
+}
+
+/* Driver Code */
+int main() {
+    int target = 6;
+    int nums[] = {1, 3, 6, 8, 12, 15, 23, 26, 31, 35};
+    int numsSize = sizeof(nums) / sizeof(nums[0]);
+
+    // 二分查找（双闭区间）
+    int index = binarySearch(nums, target, numsSize);
+    printf("目标元素 6 的索引 = %d\n", index);
+    
+    return 0;
+}