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# Problem statement

Given an array of integers `nums`

which is sorted in ascending order, and an integer `target`

, write a function to search `target`

in `nums`

. If `target`

exists, then return its index. Otherwise, return `-1`

.

You must write an algorithm with `O(log n)`

runtime complexity.

## Example 1

```
Input: nums = [-1,0,3,5,9,12], target = 9
Output: 4
Explanation: 9 exists in nums and its index is 4
```

## Example 2

```
Input: nums = [-1,0,3,5,9,12], target = 2
Output: -1
Explanation: 2 does not exist in nums so return -1
```

## Constraints

`1 <= nums.length <= 10^4`

.`-10^4 < nums[i], target < 10^4`

.- All the integers in
`nums`

are unique. `nums`

is sorted in ascending order.

# Solution: Divide and Conquer

Since `nums`

is sorted in ascending order you can divide it into subparts to find the `target`

. You can use the middle elements of `nums`

to divide the subparts. `target`

might equal to that element, on the left subpart or in the right subpart.

## Code

```
#include <vector>
#include <iostream>
using namespace std;
int search(vector<int>& nums, int target) {
int left = 0;
int right = nums.size() - 1;
while (left <= right) {
int mid = left + (right - left) / 2;
if (nums[mid] == target) {
return mid;
} else if (nums[mid] > target) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return -1;
}
int main() {
vector<int> nums{-1,0,3,5,9,12};
cout << search(nums, 9) << endl;
cout << search(nums, 2) << endl;
}
```

```
Output:
4
-1
```

## Complexity

- Runtime:
`O(logN)`

where`N = nums.length`

. - Extra space:
`O(1)`

.

# Implementation notes

`mid`

is actually`(right + left) / 2`

. But`(right + left)`

might be too big to be overflow before the division. To avoid that overflow you can rewrite the expression to`mid = left + (right - left) / 2`

.

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