确定数组中的最高和最低编号

Question

I'm trying to solve a problem where I need to write java code to find the two highest and the smallest number in an array given the below conditions:

-Every element is a real number

-Every element is random

Any ideas on the best approach?

Answer 1

You have to examine every number, so your best algorithm is linear in the length of the array.

The standard approach is to just scan the array, keeping track of the two smallest and largest numbers that you've seen so far.

So, given that firstMin , secondMin , firstMax , secondMax are respectively the smallest, second smallest, largest and second largest values that you've seen so far, on the next iteration of the loop:

if (value > firstMax) {
    secondMax = firstMax;
    firstMax = value;
} 
else if (value > secondMax) {
    secondMax = value;
}

if (value < firstMin) {
    secondMin = firstMin; 
    firstMin = value;
}
else if (value < secondMin) {
    secondMin = value;
}

At the end of this block, we maintain the invariant that firstMin , secondMin , firstMax , secondMax are respectively the smallest, second smallest, largest and second largest values that you've seen so far. This proves correctness.

This algorithm is linear in the length of the array and examines each value exactly once and makes the minimum number of comparisons. It is also O(1) in space, and is optimal in that it uses only four extra memory locations for the top and bottom two values.

Answer 2

Have a variable to keep track of the min, second_min, max, and second_max values that you have seen so far.

You can go through the elements of the array one by one, and update your min/max variables accordingly. Here are some cases to consider:

• If current element is smaller than your min, save your min to second_min and update your min.
• If current element is larger than your max, save your max to second_max and update your max
• If current element is smaller then second_min, but larger than min, update second_min only
• If current element is larger then second_max, but smaller than max, update second_max only

Answer 3

Is super-optimized performance necessary? If not,

Arrays.sort( array );

Look at the first and last two elements.

Answer 4

I think the best way is use the array as a heap or a special data structure if you can. Keeping the structure balance and sorted will be most efficient for you. This implies keeping some elements empty at some indixes in your array since the index of the array will be information about your ADT. http://en.wikipedia.org/wiki/Heap_(data_structure)