Implement Minimum Steps to One Using Top-Down Approach in C#

MinimumStepstoOneTopdownApproach takes integer n and an integer array 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 MinimumStepstoOneTopdownApproach recursively and assign it to op1 , If n mod 3 is equal to 0 then call MinimumStepstoOneTopdownApproach recursively and assign it to op2 else subtract n by 1 and call MinimumStepstoOneTopdownApproach . Finally call the Math.Min to calculate the minimum of three elements and return the value from the dp array

Time complexity − O(N)

Space complexity − O(N)

Example

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

static void Main(string[] args){
   DynamicProgramming dp = new DynamicProgramming();
   int[] dpArr = new int[150];
   Console.WriteLine(dp.MinimumStepstoOneTopdownApproach(10, dpArr));
}

Output

3