## Problem

Problem ID: 34

Title: Find First and Last Position of Element in Sorted Array

Difficulty: Medium

Description: Given an array of integers nums sorted in ascending order, find the starting and ending position of a given target value.

## Thoughts

I have always struggled with implementing binary search well and found this problem very challenging (22 failed submissions).

IMO, The main challenges with implementing binary search are:

• Ensuring that the left and right index are inside the range of the array
• Preventing an infinite loop

## Solution

### Explanation

First position: We can think of finding the first position of the element as moving the right pointer as far left as possible while the value is more than or equal to the target. We can achieve this with m = (l+r)/2 and r = m. This ensures that the right pointer will always progress towards the left.

Last Position: Similarly, the last position of the element is the position of the left pointer after moving as far right as possible while the value is less than or equal to the target. We can achieve this with m = (l+r+1)/2 and l = m. This ensures that the left pointer will always progress towards the right.

Preventing infinite loop: With l = m + 1 (first position) and r = m - 1 (last position) we can ensure that the search space will always be reduced when the main pointer is not making any progression.

### Implementation

class Solution {
public:
// [1, 2, 3, 3, 3, 4, 5]
int first(const vector<int>& nums, int target) {
int l = 0;
int r = nums.size() - 1;
while (l < r) {
int m = (l+r)/2;
int m_val = nums[m];
if (m_val >= target) {
r = m;
} else {
l = m + 1;
}
}
return nums[r] == target ? l : -1;
}
int last(const vector<int>& nums, int target) {
int l = 0;
int r = nums.size() - 1;
while (l < r) {
int m = (l+r+1)/2;
int m_val = nums[m];
if (m_val <= target) {
l = m;
} else {
r = m -1;
}
}
return nums[l] == target ? l : -1;
}
vector<int> searchRange(vector<int>& nums, int target) {
if (nums.empty()) return {-1, -1};
return {first(nums, target), last(nums,target)};
}
};