# 34 Search for a Range – Medium

### Problem:

Given a sorted array of integers, find the starting and ending position of a given target value.

Your algorithm’s runtime complexity must be in the order of O(log n).

If the target is not found in the array, return [-1, -1].

For example, Given [5, 7, 7, 8, 8, 10] and target value 8, return [3, 4].

### Thoughts:

Easy to solve problem if using iteration to find the starting point and ending point. This approach will end up with O(n) running time.

However, there is a better approach which will be O(lgn) using binary search. Still, it’s okay to start with a straight forward method first, then think about optimization or a better approach.

### Solutions:

``````public class Solution {
public int[] searchRange(int[] nums, int target) {
int[] result = searchR(nums, 0, nums.length - 1, target, 0);
return result;
}
private int[] searchR(int[] nums, int start, int end, int target, int direction) {
int[] result = new int[]{-1, -1};
if (start > end) {
return result;
}
int mid = (start + end) /2;
if (nums[mid] < target) {
return searchR(nums, mid + 1, end, target, 0);
}
if (nums[mid] > target) {
return searchR(nums, start, mid - 1, target, 0);
}
// nums[mid] == targe
if (direction != 1) {
int[] left = searchR(nums, start, mid-1, target, -1);
result[0] = left[0] == -1?mid:left[0];
}
if (direction != -1) {
int[] right = searchR(nums, mid+1, end, target, 1);
result[1] = right[1] == -1?mid:right[1];
}

return result;

}
}
``````
``````class Solution {
public int[] searchRange(int[] nums, int target) {
int left = 0;
int right = nums.length - 1;
int[] res = new int[2];
res[0] = -1;
boolean has = false;
while (left <= right) {
int mid = left + (right - left) / 2;
if (nums[mid] < target) {
left ++;
}
else if (nums[mid] == target) {
has = true;
right --;
}
else {
right --;
}
}
if (has) {
res[0] = left;
}
left = 0;
right = nums.length - 1;
while (left <= right) {
int mid = left + (right - left) / 2;
if (nums[mid] <= target) {
left ++;
}
else {
right --;
}
}
if (has) {
res[1] = right;
}
return res;
}
}
``````