First and Last Position Of An Element In A Sorted Array

Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value. If target is not found in the array, return [-1, -1]. You must write an algorithm with O(log n) runtime complexity.

Example 1:

Input: nums = [5,7,7,8,8,10], target = 8 Output: [3,4]

Example 2:

Input: nums = [5,7,7,8,8,10], target = 6 Output: [-1,-1]

Example 3:

Input: nums = [], target = 0 Output: [-1,-1]

Constraints:

• 0 <= nums.length <= 105
• -10^9 <= nums[i] <= 10^9
• nums is a non-decreasing array.
• -10^9 <= target <= 10^9

1. Iterative Solution

class Solution {
    // Method to find the starting position of the target
    //If found in middle, keep the search continued to find if the same element exist on the LEFT of sorted array
    private int findLowerBound(int[] nums, int target) {
        int start = 0, end = nums.length - 1;
        int lowerBound = -1;
        
        while (start <= end) {
            int mid = start + (end - start) / 2;
            if (nums[mid] == target) {
                lowerBound = mid;
                end = mid - 1;  // Narrow down to the left half
            } else if (target < nums[mid]) {
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        
        return lowerBound;
    }
 
    // Method to find the ending position of the target
    //If found in middle, keep the search continued to find if the same element exist on the RIGHT of sorted array.
    private static int findUpperBound(int[] nums, int target) {
        // Handle the case for an empty array
        if (nums.length == 0) return -1;
        
        int start = 0, end = nums.length;
        
        // Binary search loop
        while (start < end) {
            int mid = start + (end - start) / 2;
            if (nums[mid] > target) {
                end = mid; // Narrow down to the left half
            } else {
                start = mid + 1; // Narrow down to the right half
            }
        }
        
        // Check if the element before 'start' is the target
        if (start - 1 >= 0 && nums[start - 1] != target) return -1;
        
        // Return the index of the upper bound
        return start - 1;
    }
 
    // Main method to find the starting and ending position of the target
    public int[] searchRange(int[] nums, int target) {
        int[] res = new int[2];
        res[0] = findLowerBound(nums, target);
        res[1] = findUpperBound(nums, target);
        return res;
    }
}

2. Recursive Solution”

class Solution {
    // Method to find the starting position of the target
    private int findLowerBoundUtil(int[] nums, int target, int start, int end) {
        if (start > end) {
            return -1;
        }
        int mid = start + (end - start) / 2;
        int lowerBound = -1;
        if (nums[mid] == target) {
            int leftRes = findLowerBoundUtil(nums, target, start, mid - 1);
            lowerBound = leftRes != -1 ? leftRes : mid;
        } else if (target < nums[mid]) {
            lowerBound = findLowerBoundUtil(nums, target, start, mid - 1);
        } else {
            lowerBound = findLowerBoundUtil(nums, target, mid + 1, end);
        }
 
        return lowerBound;
    }
 
    // Method to find the ending position of the target
    private int findUpperBoundUtil(int[] nums, int target, int start, int end) {
        if (start > end) {
            return -1;
        }
        int mid = start + (end - start) / 2;
        int upperBound = -1;
        if (nums[mid] == target) {
            int rightRes = findUpperBoundUtil(nums, target, mid + 1, end);
            upperBound = rightRes != -1 ? rightRes : mid;
        } else if (target < nums[mid]) {
            upperBound = findUpperBoundUtil(nums, target, start, mid - 1);
        } else {
            upperBound = findUpperBoundUtil(nums, target, mid + 1, end);
        }
 
        return upperBound;
    }
 
    // Main method to find the starting and ending position of the target
    public int[] searchRange(int[] nums, int target) {
        int[] res = new int[2];
        res[0] = findLowerBoundUtil(nums, target, 0, nums.length - 1);
        res[1] = findUpperBoundUtil(nums, target, 0, nums.length - 1);
        return res;
    }
}