CareerCup

This is very famous problem asked by Amazon thousand number of times. It is a min-heap problem.
They also presented once to me like this:
We have a strcat(s1,s2) that is 3rd party function. Every time you run this function, you need to pay cost s1.length()+s2.length() to 3rd party. You have to minimize this cost.
Suppose you have arrayp[ = {3,4,6,9},
If you start adding bigger numbers first, the cost is (9+6) + ((9+6)+4) + ((9+6+4)+3). You can see that 9 occurred most number of times. So, cost is more. Instead, if you start with 2 smallest numbers, cost will be calculated like this:
1. (3+4=7), now we have {7,6,9}
2. Take min 2 from these (6+7)=13, now we have (13,9)
3. Take min. 2 from these. and final sum is 22.
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So, every time it is about taking minimum 2 numbers, adding them and putting the resultant sum back in set (or array). Again find 2 min. numbers, add them...
Repeat this process until you have a single element (or let's say you have 2 elements and sum them.).
So, algo goes like this:

int getMinCost(int a[], int n)
{
1. Create min heap (lets say pq) and push all elements of array into min heap (STL priority queue acts like min heap so you can use that).
2. int sum=0;
      // heap size is n initially (number of array elements)
         while(n>1) {
             
             top1= pq.top(); top2 =pq.top();
             sum+=top1+top2;
	     pq.push_back(top1+top2);
             // priority queue runs heapify() itself.
             n--;
  	}
	return sum;
 }