# 35. Search Insert Position

## Description

Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.

You must write an algorithm with O(log n) runtime complexity.

Example 1:

Input: nums = [1,3,5,6], target = 5
Output: 2


Example 2:

Input: nums = [1,3,5,6], target = 2
Output: 1


Example 3:

Input: nums = [1,3,5,6], target = 7
Output: 4


Constraints:

• 1 <= nums.length <= 104
• -104 <= nums[i] <= 104
• nums contains distinct values sorted in ascending order.
• -104 <= target <= 104

## Solutions

Solution 1: Binary Search

Since the array $nums$ is already sorted, we can use the binary search method to find the insertion position of the target value $target$.

The time complexity is $O(\log n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.

• class Solution {
public int searchInsert(int[] nums, int target) {
int left = 0, right = nums.length;
while (left < right) {
int mid = (left + right) >>> 1;
if (nums[mid] >= target) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
}
}

• class Solution {
public:
int searchInsert(vector<int>& nums, int target) {
int left = 0, right = nums.size();
while (left < right) {
int mid = left + right >> 1;
if (nums[mid] >= target)
right = mid;
else
left = mid + 1;
}
return left;
}
};

• class Solution:
def searchInsert(self, nums: List[int], target: int) -> int:
left, right = 0, len(nums)
while left < right:
mid = (left + right) >> 1
if nums[mid] >= target:
right = mid
else:
left = mid + 1
return left


• func searchInsert(nums []int, target int) int {
left, right := 0, len(nums)
for left < right {
mid := (left + right) >> 1
if nums[mid] >= target {
right = mid
} else {
left = mid + 1
}
}
return left
}

• /**
* @param {number[]} nums
* @param {number} target
* @return {number}
*/
var searchInsert = function (nums, target) {
let left = 0;
let right = nums.length;
while (left < right) {
const mid = (left + right) >> 1;
if (nums[mid] >= target) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
};


• use std::cmp::Ordering;
impl Solution {
pub fn search_insert(nums: Vec<i32>, target: i32) -> i32 {
let mut left = 0;
let mut right = nums.len();
while left < right {
let mid = left + (right - left) / 2;
match nums[mid].cmp(&target) {
Ordering::Less => {
left = mid + 1;
}
Ordering::Greater => {
right = mid;
}
Ordering::Equal => {
return mid as i32;
}
}
}
left as i32
}
}


• class Solution {
/**
* @param integer[] $nums * @param integer$target
* @return integer
*/

function searchInsert($nums,$target) {
$key = array_search($target, $nums); if ($key !== false) {
return $key; }$nums[] = $target; sort($nums);
return array_search($target,$nums);
}
}


• function searchInsert(nums: number[], target: number): number {
let [l, r] = [0, nums.length];
while (l < r) {
const mid = (l + r) >> 1;
if (nums[mid] >= target) {
r = mid;
} else {
l = mid + 1;
}
}
return l;
}