Question

I came across this question on a website. As mentioned there, it was asked in amazon interview. I couldn’t figure out a proper solution in given constraint.

Given an array of n integers, find 3 elements such that a[i] < a[j] < a[k] and i < j < k in O(n) time.

Answer 1

So here is how you can solve the problem. You need to iterate over the array three times. On the first iteration mark all the values that have an element greater than them on the right and on the second iteration mark all the elements smaller than them on their left. Now your answer would be with an element that has both:

int greater_on_right[SIZE];
int smaller_on_left[SIZE];
memset(greater_on_rigth, -1, sizeof(greater_on_right));
memset(smaller_on_left, -1, sizeof(greater_on_right));

int n; // number of elements;
int a[n]; // actual elements;
int greatest_value_so_far = a[n- 1];
int greatest_index = n- 1;
for (int i = n -2; i >= 0; --i) {
   if (greatest_value_so_far > a[i]) {
     greater_on_right[i] = greatest_index;
   } else {
     greatest_value_so_far = a[i];
     greatest_index = i;
   }
}

// Do the same on the left with smaller values


for (int i =0;i<n;++i) {
  if (greater_on_right[i] != -1 && smaller_on_left[i] != -1) {
    cout << "Indices:" << smaller_on_left[i] << ", " << i << ", " << greater_on_right[i] << endl;
  }
}

This solution iterates 3 times over the whole array and is therefore linear. I have not provided the whole solution so that you can train yourself on the left to see if you get my idea. I am sorry not to give just some tips but I couldn’t figure out how to give a tip without showing the actual solution.

Hope this solves your problem.