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0033-Search_in_Rotated_Sorted_Array.cpp
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0033-Search_in_Rotated_Sorted_Array.cpp
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/*******************************************************************************
* 0033-Search_in_Rotated_Sorted_Array.cpp
* Billy.Ljm
* 08 August 2023
*
* =======
* Problem
* =======
* https://leetcode.com/problems/search-in-rotated-sorted-array/
*
* There is an integer array nums sorted in ascending order (with distinct values).
*
* Prior to being passed to your function, nums is possibly rotated at an
* unknown pivot index k (1 <= k < nums.length) such that the resulting array is
* [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]].
* For example, [0,1,2,4,5,6,7] might be rotated at pivot index 3 and become
* [4,5,6,7,0,1,2].
*
* Given the array nums after the possible rotation and an integer target,
* return the index of target if it is in nums, or -1 if it is not in nums.
*
* You must write an algorithm with O(log n) runtime complexity.
*
* ===========
* My Approach
* ===========
* We'll us a modified binary search algorithm. We break the array into two
* halves, one of which will be sorted and the other not sorted due to the
* rotation. We'll check if the target is in the sorted half, otherwise its
* in the other half. This continues until only 1 or 2 elements are left.
*
* This has a time complexity of O(log n), and a space complexity of O(1),
* where n is the length of the array.
******************************************************************************/
#include <iostream>
#include <vector>
using namespace std;
/**
* << operator for vectors
*/
template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
os << "[";
for (int i = 0; i < v.size(); i++) {
os << v[i] << ",";
}
os << "\b]";
return os;
}
/**
* Solution
*/
class Solution {
public:
int search(vector<int>& nums, int target) {
int start = 0, end = nums.size() - 1, mid;
// binary search
while (end - start > 1) {
mid = start + (end - start) / 2;
if (nums[mid] > nums[start]) { // first half is sorted
if (target >= nums[start] and target <= nums[mid]) end = mid;
else start = mid;
}
else { // second half is sorted
if (target >= nums[mid] and target <= nums[end]) start = mid;
else end = mid;
}
}
// check last few elements
if (target == nums[start]) return start;
else if (target == nums[end]) return end;
else return -1;
}
};
/**
* Test cases
*/
int main(void) {
Solution sol;
vector<int> nums;
int target;
// test case 1
nums = { 4,5,6,7,0,1,2 };
target = 0;
std::cout << "search(" << nums << "," << target << ") = ";
std::cout << sol.search(nums, target) << std::endl;
// test case 2
nums = { 4,5,6,7,0,1,2 };
target = 3;
std::cout << "search(" << nums << "," << target << ") = ";
std::cout << sol.search(nums, target) << std::endl;
// test case 3
nums = { 1 };
target = 0;
std::cout << "search(" << nums << "," << target << ") = ";
std::cout << sol.search(nums, target) << std::endl;
return 0;
}