Minimum Cost of Ropes

Problem Statement:

Given an array, arr[] of rope lengths, connect all ropes into a single rope with the minimum total cost. The cost to connect two ropes is the sum of their lengths. 

• Example:

  Input: arr[] = [4, 3, 2, 6]
  Output: 29
  Explanation: We can connect the ropes in following ways.
  1) First connect ropes of lengths 2 and 3. Which makes the array [4, 5, 6]. Cost of this operation 2 + 3 = 5. 
  2) Now connect ropes of lengths 4 and 5. Which makes the array [9, 6]. Cost of this operation 4 + 5 = 9.
  3) Finally connect the two ropes and all ropes have connected. Cost of this operation 9 + 6 =15. Total cost is 5 + 9 + 15 = 29. This is the optimized cost for connecting ropes. 
  Other ways of connecting ropes would always have same or more cost. For example, if we connect 4 and 6 first (we get three rope of 3, 2 and 10), then connect 10 and 3 (we get two rope of 13 and 2). Finally we connect 13 and 2. Total cost in this way is 10 + 13 + 15 = 38.
  
  Input: arr[] = [4, 2, 7, 6, 9]
  Output: 62 
  Explanation: First, connect ropes 4 and 2, which makes the array [6, 7, 6, 9]. Cost of this operation 4 + 2 = 6. 
  Next, add ropes 6 and 6, which results in [12, 7, 9]. Cost of this operation 6 + 6 = 12.
  Then, add 7 and 9, which makes the array [12,16]. Cost of this operation 7 + 9 = 16. And
  finally, add these two which gives [28]. Hence, the total cost is 6 + 12 + 16 + 28 = 62.
  
  Input: arr[] = [10]
  Output: 0
  Explanation: Since there is only one rope, no connections are needed, so the cost is 0.

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