Search In a Big Sorted Array

Description

Given a big sorted array with positive integers sorted by ascending order. The array is so big so that you can not get the length of the whole array directly, and you can only access the kth number byArrayReader.get(k)(or ArrayReader->get(k) for C++). Find the first index of a target number. Your algorithm should be in O(log k), where k is the first index of the target number.

Return -1, if the number doesn't exist in the array.

Notice

If you accessed an inaccessible index (outside of the array), ArrayReader.get will return2,147,483,647.

Example

Given[1, 3, 6, 9, 21, ...], and target =3, return1.

Given[1, 3, 6, 9, 21, ...], and target =4, return-1.

Challenge

O(log k), k is the first index of the given target number.

Related problems

First Position of Target

Implementation

Link: http://lintcode.com/en/problem/strstr/

/**
 * Definition of ArrayReader:
 * 
 * class ArrayReader {
 * public:
 *     int get(int index) {
 *          // return the number on given index, 
 *          // return -1 if index does not exist.
 *     }
 * };
 */
class Solution {
public:
    /**
     * @param reader: An instance of ArrayReader.
     * @param target: An integer
     * @return: An integer which is the first index of target.
     */
    int searchBigSortedArray(ArrayReader *reader, int target) {
        // write your code here
        int end = 1;
        while (reader->get(end) < target) {
            end *= 2;
        }

        int start = 0;
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            int val = reader->get(mid);
            if (val == target) {
                end = mid;
            } else if (val < target) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (reader->get(start) == target) {
            return start;
        } else if (reader->get(end) == target) {
            return end;
        }
        return -1;
    }
};