Implement Minimum Steps to One Using Bottom-Up Approach in C#

MinimumStepstoOneBottomdownApproachtakes integer n as input. Parameter n contains the total number of elements. Initial condition checks whether n is equal to 1. If n is equal to 1 then return 0. Initialize op1, op2 and op3 to max value. If n mod 3 is equal to 0 then call MinimumStepstoOneBottomdownApproach recursively and assign it to op1, if n mod 3 is equal to 0 then call MinimumStepstoOneBottomdownApproach recursively and assign it to op2 else subtract n by 1 and call MinimumStepstoOneBottomdownApproach. Finally return the value from the dp array

Time complexity − O(N)

Space complexity − O(N)

Example

public class DynamicProgramming{
   public int MinimumStepstoOneBottomdownApproach(int n){
      int[] dp = new int[100];
      dp[1] = 0;
      for (int i = 2; i < n; i++){
         int op1 = int.MaxValue, op2 = int.MaxValue, op3 = int.MaxValue;
         if (n % 3 == 0){
            op1 = dp[i / 3];
         }
         if (n % 2 == 0){
            op2 = dp[i / 2];
         }
         op3= dp[i -1];
         dp[i]= Math.Min(Math.Min(op1, op2), op3) + 1;
      }
      return dp[n-1];
   }
}

static void Main(string[] args){
   DynamicProgramming dp = new DynamicProgramming();
   Console.WriteLine(dp.MinimumStepstoOneBottomdownApproach(10))
}

Output

3