Coding Interview Questions

Questions: All numbers in an array with length n+1 are in range from 1 to n, so there is at least one duplication in the array. How to find any a duplication? Please don't modify the input array.
Analysis: The simple solution is to utilize hash tables. When scanning the array, array elements are inserted into the hash table one by one. In this way, it's easy to find a duplication with the hash table, which costs O(n) space....

Question: Given an array where two neighboring elements are adjacent (in absolute difference 1), can you write an algorithm to search an element in the array and return its position? If the element appears multiple times, please return the first occurrence...

Problem: Integers in an array are unique and increasingly sorted. Please write a function/method to find an integer from the array who equals to its index. For example, in the array {-3, -1, 1, 3, 5}, the number 3 equals its index 3.
Analysis: If we scan all integers in the array from beginning to end, we may check whether every element equals its index. Obviously, this solution costs O(n) time....

Question: A board has n*m cells, and there is a gift with some value (value is greater than 0) in every cell. You can get gifts starting from the top-left cell, and move right or down in each step, and finally reach the cell at the bottom-right cell...