33 Search in Rotated Sorted Array

Author: int32bit

README.md

@@ -24,6 +24,7 @@
 + [27 Remove Element](algorithms/RemoveElement)
 + [29 Divide Two Integers(位运算、最小负数绝对值、溢出检测)](algorithms/DivideTwoIntegers)
 + [31 Next Permutation(全排列)](algorithms/NextPermutation)
++ [33 Search in Rotated Sorted Array(二分搜索)](algorithms/SearchinRotatedSortedArray)
 + [34 Search for a Range(二分)](algorithms/SearchforaRange)
 + [35 Search Insert Position(二分查找)](algorithms/SearchInsertPosition)
 + [38 Count and Say(字符串和数字转化详解)](algorithms/CountandSay)

algorithms/FindMinimuminRotatedSortedArray/README.md

@@ -40,4 +40,6 @@ int findMin(vector<int> &nums) {
 
 ## 扩展
 
-当有重复元素存在时，见[Find Minimum in Rotated Sorted Array II](../FindMinimuminRotatedSortedArray2)
+1. 当有重复元素存在时，见[Find Minimum in Rotated Sorted Array II](../FindMinimuminRotatedSortedArray2)
+
+2. [Search in Rotated Sorted Array](../SearchinRotatedSortedArray), 在旋转列表中查找某个数

algorithms/FindMinimuminRotatedSortedArray2/README.md

@@ -41,3 +41,9 @@ int findMin(vector<int> &nums) {
 	return nums[s];
 }
 ```
+
+## 扩展
+
+[Search in Rotated Sorted Array](../SearchinRotatedSortedArray), 从旋转列表中查找某个值
+
+[Find Minimum in Rotated Sorted Array](../FindMinimuminRotatedSortedArray)

algorithms/SearchinRotatedSortedArray/README.md

@@ -0,0 +1,34 @@
+## Search in Rotated Sorted Array
+
+Suppose a sorted array is rotated at some pivot unknown to you beforehand.
+
+(i.e., `0 1 2 4 5 6 7` might become `4 5 6 7 0 1 2`).
+
+You are given a target value to search. If found in the array return its index, otherwise return -1.
+
+You may assume no duplicate exists in the array.
+
+## Solution
+
+既然是有序，自然想到二分搜索, 和[Find Minimum in Rotated Sorted Array](../FindMinimuminRotatedSortedArray)类似:
+
+初始化s = 0, t = n - 1:
+
+* 若a[s] < a[t], 比如`1 2 3 4 5`,则整个列表有序，直接二分搜索即可.
+* `mid = s + ((t - s) >> 1)`, 若`a[mid] == key`, 返回mid，结束
+* `a[mid] < a[t]`, 比如`5 1 [2] 3 4`或`4 5 [1] 2 3`, 则右边一定是有序的:
+
+	+ 若`a[mid] < key <= a[t]`, 二分搜索右边部分即可
+	+ 否则搜索左边， `t = mid - 1`
+
+* `a[mid] > a[t]`, 比如`3 4 [5] 1 2` 或者 `2 3 [4] 5 1`, 则左边一定是有序的:
+
+	+ 若`a[s] <= key < a[mid]`, 二分搜索左边部分
+	+ 否则搜索右边，`s = mid + 1`
+
+## 扩展
+
+1. [Find Minimum in Rotated Sorted Array](../FindMinimuminRotatedSortedArray)
+
+2. [Find Minimum in Rotated Sorted Array II](../FindMinimuminRotatedSortedArray2)
+

algorithms/SearchinRotatedSortedArray/in.txt

@@ -0,0 +1,2 @@
+5 2
+1 2 3 4 5

algorithms/SearchinRotatedSortedArray/solve.c

@@ -0,0 +1,53 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+int binarySearch(int *a, int s, int t, int key)
+{
+	while (s <= t) {
+		int mid = s + ((t - s) >> 1);
+		if (a[mid] == key)
+			return mid;
+		if (a[mid] > key)
+			t = mid - 1;
+		else
+			s = mid + 1;
+	}
+	return -1;
+}
+int search(int *a, int n, int key)
+{
+	int s = 0, t = n - 1;
+	while (s <= t) {
+		if (a[s] < a[t])
+			return binarySearch(a, s, t, key);
+		int mid = s + ((t - s) >> 1);
+		//printf("s = %d, t = %d, mid = %d\n", s, t, mid);
+		if (a[mid] == key)
+			return mid;
+		if (a[mid] < a[t]) {
+			if (a[mid] < key && key <= a[t])
+				return binarySearch(a, mid + 1, t, key);
+			else
+				t = mid - 1;
+		} else { // a[mid] > a[t]
+			if (a[s] <= key && key < a[mid]) // 若key 在s和mid之间
+				return binarySearch(a, s, mid - 1, key);
+			else
+				s = mid + 1;
+		}
+	}
+	return -1;
+}
+void print(int *a, int n)
+{
+	for (int i = 0; i < n; ++i)
+		printf("%d ", a[i]);
+	printf("\n");
+}
+int main(int argc, char **argv)
+{
+	int a[] = {4,5,6,7,8,1,2,3};
+	print(a, 8);
+	printf("%d:%d\n", 8, search(a, 8, 8));
+	return 0;
+}