排序数组并找到复杂度为O（n）的和

Question

We have sorted array arr[]={2,4,5,7,8,12,16,18,20} .

We need to find out pair of elements whose addition is 12 , with complexity O(n) .

Could anyone help on it?

Answer 1

No solution for you unfortunately, just some things to think about that should lead you in the right direction:

Keeping in mind that the array is sorted, which of the following are true?

   arr[x+1] + arr[y] < arr[x] + arr[y]
or arr[x+1] + arr[y] > arr[x] + arr[y]

   arr[x] + arr[y-1] < arr[x] + arr[y]
or arr[x] + arr[y-1] > arr[x] + arr[y]

If you think about the answers to these long enough (and maybe draw it), a solution should follow.

Hint for how to start:

Let x = 0, y = n-1.
...

Answer 2

Try this:

Since the array is sorted, take the sum of the first element (arr[0]) and the last element(arr[8]). If the sum is greater than 12, then we need to lower the sum, so we replace the largest number by the next largest number(in this case, arr[7]); If the sum is less than 12, we need to increase the sum, so we replace the smallest number by the next smallest number, (in this case, replace arr[0] with arr[1]). Keep repeating this process until you get the sum you want or the two numbers you are summing up is from the same index in the array.