31. Search in Rotated Sorted Array

In a rotated sorted array, at least one side of any midpoint is fully sorted. Identify that side; check whether target lies in its range; if yes search there, otherwise search the other half.

Approach

For each step, compare nums[l] with nums[mid]:

• If nums[l] <= nums[mid], the left half [l..mid] is sorted.
  • If nums[l] <= target < nums[mid], search left (r = mid - 1).
  • Else search right (l = mid + 1).
• Else the right half [mid..r] is sorted.
  • If nums[mid] < target <= nums[r], search right.
  • Else search left.

import java.util.*;

class Solution {
    public int search(int[] nums, int target) {
        int l = 0, r = nums.length - 1;
        while (l <= r) {
            int mid = (l + r) / 2;
            if (nums[mid] == target) return mid;
            if (nums[l] <= nums[mid]) {
                if (nums[l] <= target && target < nums[mid]) r = mid - 1;
                else l = mid + 1;
            } else {
                if (nums[mid] < target && target <= nums[r]) l = mid + 1;
                else r = mid - 1;
            }
        }
        return -1;
    }
}