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34. Find First and Last Position of Element in Sorted Array

Description

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
  • -109 <= nums[i] <= 109
  • nums is a non-decreasing array.
  • -109 <= target <= 109

Solutions

We can perform two binary searches to find the left boundary and the right boundary.

The time complexity is $O(\log n)$, where $n$ is the length of the array $\textit{nums}$. The space complexity is $O(1)$.

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class Solution:
    def searchRange(self, nums: List[int], target: int) -> List[int]:
        l = bisect_left(nums, target)
        r = bisect_left(nums, target + 1)
        return [-1, -1] if l == r else [l, r - 1]

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class Solution {
    public int[] searchRange(int[] nums, int target) {
        int l = search(nums, target);
        int r = search(nums, target + 1);
        return l == r ? new int[] {-1, -1} : new int[] {l, r - 1};
    }

    private int search(int[] nums, int x) {
        int left = 0, right = nums.length;
        while (left < right) {
            int mid = (left + right) >>> 1;
            if (nums[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

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class Solution {
public:
    vector<int> searchRange(vector<int>& nums, int target) {
        int l = lower_bound(nums.begin(), nums.end(), target) - nums.begin();
        int r = lower_bound(nums.begin(), nums.end(), target + 1) - nums.begin();
        if (l == r) {
            return {-1, -1};
        }
        return {l, r - 1};
    }
};

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func searchRange(nums []int, target int) []int {
    l := sort.SearchInts(nums, target)
    r := sort.SearchInts(nums, target+1)
    if l == r {
        return []int{-1, -1}
    }
    return []int{l, r - 1}
}

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function searchRange(nums: number[], target: number): number[] {
    const search = (x: number): number => {
        let [left, right] = [0, nums.length];
        while (left < right) {
            const mid = (left + right) >> 1;
            if (nums[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    };
    const l = search(target);
    const r = search(target + 1);
    return l === r ? [-1, -1] : [l, r - 1];
}

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impl Solution {
    pub fn search_range(nums: Vec<i32>, target: i32) -> Vec<i32> {
        let n = nums.len();
        let search = |x| {
            let mut left = 0;
            let mut right = n;
            while left < right {
                let mid = left + (right - left) / 2;
                if nums[mid] < x {
                    left = mid + 1;
                } else {
                    right = mid;
                }
            }
            left
        };
        let l = search(target);
        let r = search(target + 1);
        if l == r {
            return vec![-1, -1];
        }
        vec![l as i32, (r - 1) as i32]
    }
}

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/**
 * @param {number[]} nums
 * @param {number} target
 * @return {number[]}
 */
var searchRange = function (nums, target) {
    function search(x) {
        let left = 0,
            right = nums.length;
        while (left < right) {
            const mid = (left + right) >> 1;
            if (nums[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
    const l = search(target);
    const r = search(target + 1);
    return l == r ? [-1, -1] : [l, r - 1];
};

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class Solution {
    /**
     * @param Integer[] $nums
     * @param Integer $target
     * @return Integer[]
     */
    function searchRange($nums, $target) {
        $search = function ($x) use ($nums) {
            $left = 0;
            $right = count($nums);
            while ($left < $right) {
                $mid = intdiv($left + $right, 2);
                if ($nums[$mid] >= $x) {
                    $right = $mid;
                } else {
                    $left = $mid + 1;
                }
            }
            return $left;
        };

        $l = $search($target);
        $r = $search($target + 1);
        return $l === $r ? [-1, -1] : [$l, $r - 1];
    }
}

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class Solution {
    fun searchRange(nums: IntArray, target: Int): IntArray {
        val left = this.search(nums, target)
        val right = this.search(nums, target + 1)
        return if (left == right) intArrayOf(-1, -1) else intArrayOf(left, right - 1)
    }

    private fun search(nums: IntArray, target: Int): Int {
        var left = 0
        var right = nums.size
        while (left < right) {
            val middle = (left + right) / 2
            if (nums[middle] < target) {
                left = middle + 1
            } else {
                right = middle
            }
        }
        return left
    }
}

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