Package g1501_1600.s1547_minimum_cost_to_cut_a_stick

Class Solution

java.lang.Object
g1501_1600.s1547_minimum_cost_to_cut_a_stick.Solution
public class Solution extends java.lang.Object
1547 - Minimum Cost to Cut a Stick.

Hard

Given a wooden stick of length n units. The stick is labelled from 0 to n. For example, a stick of length 6 is labelled as follows:

Given an integer array cuts where cuts[i] denotes a position you should perform a cut at.

You should perform the cuts in order, you can change the order of the cuts as you wish.

The cost of one cut is the length of the stick to be cut, the total cost is the sum of costs of all cuts. When you cut a stick, it will be split into two smaller sticks (i.e. the sum of their lengths is the length of the stick before the cut). Please refer to the first example for a better explanation.

Return the minimum total cost of the cuts.

Example 1:

Input: n = 7, cuts = [1,3,4,5]

Output: 16

Explanation: Using cuts order = [1, 3, 4, 5] as in the input leads to the following scenario:

The first cut is done to a rod of length 7 so the cost is 7. The second cut is done to a rod of length 6 (i.e. the second part of the first cut), the third is done to a rod of length 4 and the last cut is to a rod of length 3.

The total cost is 7 + 6 + 4 + 3 = 20.

Rearranging the cuts to be [3, 5, 1, 4] for example will lead to a scenario with total cost = 16 (as shown in the example photo 7 + 4 + 3 + 2 = 16).

Example 2:

Input: n = 9, cuts = [5,6,1,4,2]

Output: 22

Explanation: If you try the given cuts ordering the cost will be 25.

There are much ordering with total cost <= 25, for example, the order [4, 6, 5, 2, 1] has total cost = 22 which is the minimum possible.

Constraints:

  • 2 <= n <= 106
  • 1 <= cuts.length <= min(n - 1, 100)
  • 1 <= cuts[i] <= n - 1
  • All the integers in cuts array are distinct.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    minCost(int n, int[] cuts)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minCost

      public int minCost(int n, int[] cuts)