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Program to find minimum time to complete all tasks in python

Suppose we have a list of numbers called nums where each value is determining a unit of time it takes to finish a task. We can skip any non-consecutive tasks, we have to find the minimum time it takes to finish all tasks.

So, if the input is like nums = [11, 6, 8, 16], then the output will be 14, as we can skip the first and last tasks.

To solve this, we will follow these steps:

  • n := size of nums
  • table := make a n x 2 matrix and fill this with 0
  • table[0, 0] := 0
  • table[0, 1] := nums[0]
  • for i in range 1 to n - 1, do
    • table[i, 0] := table[i - 1, 1]
    • table[i, 1] = (minimum of table[i - 1, 0] and table[i - 1][1]) + nums[i]
  • return minimum of table row [n - 1]

Let us see the following implementation to get better understanding:

Example

class Solution:
   def solve(self, nums):
      n = len(nums)
      table = [[0] * 2 for _ in range(n)]

      table[0][0] = 0
      table[0][1] = nums[0]

      for i in range(1, n):
         table[i][0] = table[i - 1][1]
         table[i][1] = min(table[i - 1][0], table[i - 1][1]) + nums[i]

      return min(table[n - 1])

ob = Solution()
nums = [11, 6, 8, 16]
print(ob.solve(nums))

Input

[11, 6, 8, 16]

Output

14