数组找到第二高的值

Question

I have an array contains 10 integer values. Now I want to find out the second highest number.I should not use any java API. This question was asked by one interviewer to me. He wants the logic.And his requirement is, I should not traverse through the the entire elements. Is there any way where we can achieve the result without traversing? Travesing means going through all the elements in the array. I thought for long time.Finally I gave up. If any one can explain, it would be nice. And also I asked about Sorting. He does not want the array to be sorted.

Answer 1

No, it's completely impossible. If you don't look at all the data, you can't possibly know the second highest value.

You don't have to sort all the data, of course, which may be what your interviewer meant - but you do need to look at every element at least once. Every element has the possibility of changing the result, so needs to be examined.

Answer 2

You cannot know the answer if you don't look at each element at least once. However, if that is not your concern, you could use a Binary Search Tree:

In computer science, a binary search tree (BST), which may sometimes also be called an ordered or sorted binary tree, is a node-based binary tree data structure which has the following properties:[1]

The left subtree of a node contains only nodes with keys less than the node's key. The right subtree of a node contains only nodes with keys greater than or equal to the node's key. Both the left and right subtrees must also be binary search trees.
Source: http://en.wikipedia.org/wiki/Binary_search_tree

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How will you find 2nd biggest element?

Well from how the BST is formed, you know that the biggest element is the rightmost one (starting from the root node, take the right child till you have no place to go any more).

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Now, how to identify the 2nd biggest?
Well, this may not b the most efficient approach, but let's break it down in cases:

1. Biggest Node is Tree root and has no children - There is no 2nd biggest element because there is only one Node in your Tree

2. Biggest Node is Tree root (doesn't have right child) - 2nd biggest element is the biggest element in the left subtree

3. Biggest element is not a Tree root, but not a leaf (has a left child) - 2nd biggest element is his left child

4. Biggest element is not a Tree root, and is a leaf (has no children) - 2nd biggest element is his parent

I'm sure you can figure out the pattern and a simple algorithm now :D

Answer 3

I know this has been answered but I was thinking something like this.

    double maxVal = array[0];
    for (int i=1; i < array.length; i++) {
        if (array[i] > maxVal) {
            maxVal = array[i];
        }
    }

Technically I am not traversing the whole array but n-1 of the length because I assign the first value to the max value. I am sure there are other ways but this one seems the about what the interviewer may want.

Answer 4

Logic is so simple, I have implemented this already in a single for loop.

am giving you my program, If you want the algorithm, I can provide you that also.

public static void main(String[] args) {

    int[] arr={0,12,74,56,2,63,45};
    int f1=1,f2=0,temp=0;
    int num=0;

    for(int i=0;i<arr.length;i++){
        num=arr[i];
        if(f1<num)
        {
            temp=f1;
            f1=num;
            num=temp;
        }
        if(f2<num)
        {
            temp=f2;
            f2=num;
            num=temp;
        }
    }
    System.out.println("First Highest "+f1+" Second Highest "+f2+" Third "+num);

}