We have to make the knight cover all the cells of the board and it can move to a cell only once.

There can be two ways of finishing the knight move - the first in which the knight is one knight''s move away from the cell from where it began, so it can go to the position from where it started and form a loop, this is called closed tour, the second in which the knight finishes anywhere else, this is called open tour. A move is valid if it is inside the chessboard and if the cell is not already

using System;
using System.Collections.Generic;
using System.Text;
using System.Linq;
namespace  CsharpCode_ConsoleApplication{
   public class KnightWalkProblem{
      public class cell{
         public int x, y;
         public int dis;
         public cell(int x, int y, int dis){
            this.x = x;
            this.y = y;
            this.dis = dis;
         }
      }
      static bool isInside(int x, int y, int N){
         if (x >= 1 && x <= N && y >= 1 && y <= N)
            return true;
            return false;
      }
      public int minStepToReachTarget(int[] knightPos, int[] targetPos, int N){
         int[] dx = { -2, -1, 1, 2, -2, -1, 1, 2 };
         int[] dy = { -1, -2, -2, -1, 1, 2, 2, 1 };
         Queue<cell> q = new Queue<cell>();
         q.Enqueue(new cell(knightPos[0], knightPos[1], 0));
         cell t;
         int x, y;
         bool[,] visit = new bool[N + 1, N + 1];
         for (int i = 1; i <= N; i++)
         for (int j = 1; j <= N; j++)
            visit[i, j] = false;
         visit[knightPos[0], knightPos[1]] = true;
         while (q.Count != 0){
            t = q.Peek();
            q.Dequeue();
            if (t.x == targetPos[0] && t.y == targetPos[1])
               return t.dis;
            for (int i = 0; i < 8; i++){
               x = t.x + dx[i];
               y = t.y + dy[i];
               if (isInside(x, y, N) && !visit[x, y]){
                  visit[x, y] = true;
                  q.Enqueue(new cell(x, y, t.dis + 1));
               }
            }
         }
         return int.MaxValue;
      }
   }
   class CsharpCode_Program{
      static void Main(string[] args){
         KnightWalkProblem kn = new KnightWalkProblem();
         int N = 30;
         int[] knightPos = { 1, 1 };
         int[] targetPos = { 30, 30 };
         Console.WriteLine(
            kn.minStepToReachTarget(
               knightPos,
               targetPos, N));
      }
   }
}