You have some number of sticks with positive integer lengths. These lengths are given as an array sticks
, where sticks[i]
is the length of the i^{th}
stick.
You can connect any two sticks of lengths x
and y
into one stick by paying a cost of x + y
. You must connect all the sticks until there is only one stick remaining.
Return the minimum cost of connecting all the given sticks into one stick in this way.
Example 1:
Input: sticks = [2,4,3]
Output: 14
Explanation: You start with sticks = [2,4,3].
1. Combine sticks 2 and 3 for a cost of 2 + 3 = 5. Now you have sticks = [5,4].
2. Combine sticks 5 and 4 for a cost of 5 + 4 = 9. Now you have sticks = [9].
There is only one stick left, so you are done. The total cost is 5 + 9 = 14.
Example 2:
Input: sticks = [1,8,3,5]
Output: 30
Explanation: You start with sticks = [1,8,3,5].
1. Combine sticks 1 and 3 for a cost of 1 + 3 = 4. Now you have sticks = [4,8,5].
2. Combine sticks 4 and 5 for a cost of 4 + 5 = 9. Now you have sticks = [9,8].
3. Combine sticks 9 and 8 for a cost of 9 + 8 = 17. Now you have sticks = [17].
There is only one stick left, so you are done. The total cost is 4 + 9 + 17 = 30.
Example 3:
Input: sticks = [5]
Output: 0
Explanation: There is only one stick, so you don't need to do anything.
The total cost is 0.
Constraints:
1 <= sticks.length <= 10^{4}
1 <= sticks[i] <= 10^{4}

