How to make a datagridview cell as a datetime picker?

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Diagnostics;
using System.Drawing;
using System.Windows.Forms;

namespace TestForm1
{
	/// <summary>
    /// Helper class for datagridview items.
    /// </summary>

	public class dgvClass1 : ICloneable
    {
        /// <summary>
        /// priority is not a propery, so it is not visible in datagrid by default.
        /// </summary>
        public string priority;

        /// <summary>
        /// date is not a propery, so it is not visible in datagrid by default.
        /// </summary>
        public DateTime date;

        public int Number { get; set; }
        public string Name { get; set; }

        public dgvClass1()
        {
            this.date = DateTime.Now;
            this.priority = "Medium";
        }

        /// <summary>
        /// https://msdn.microsoft.com/en-us/library/system.object.memberwiseclone(v=vs.100).aspx
        /// </summary>
        public object Clone()
        {
            return (dgvClass1)this.MemberwiseClone();
        }
    }

    /// <summary>
    /// Test data grid with BindingList.
    /// Replace column with ComboBox.
    /// Replace date column with class CalendarColumn.
    /// </summary>
    public partial class Form5 : Form
    {
        public BindingList<dgvClass1> bindingList;

        public Form5()
        {
            InitializeComponent();

            // Allow user to resize column widths.
            this.dataGridView1.AutoSizeColumnsMode = DataGridViewAutoSizeColumnsMode.None;
            this.dataGridView1.AllowUserToAddRows = false;

            this.dataGridView1.DataBindingComplete += (s, ev) => Debug.WriteLine("BindingComplete");
            //this.dataGridView1.CurrentCellDirtyStateChanged += new DataGridViewRowEventHandler(this.DataGridChanged);
            this.dataGridView1.CellValueChanged += new DataGridViewCellEventHandler(this.dataGridView1_CellValueChanged);
            this.dataGridView1.RowValidated += new DataGridViewCellEventHandler(this.RowValidatedEvent);
        }

        /// <summary>
        /// Fill the BindingList and set the dataGridView1.DataSource.
        /// See:
        /// http://stackoverflow.com/questions/21333320/converting-column-in-datagridview-into-a-combobox
        /// http://www.codeproject.com/Articles/24656/A-Detailed-Data-Binding-Tutorial
        /// </summary>
        private void button1_Click(object sender, EventArgs e)
        {
            bindingList = new BindingList<dgvClass1>();
            bindingList.AllowNew = true;
            bindingList.AllowRemove = true;

            if (this.dataGridView1.DataSource != null)
            {
                this.dataGridView1.DataSource = null;
                this.dataGridView1.Columns.Remove("Priority");
            }

            this.AddTestData();
            this.AddComboBox();
            this.AddCalendarColumn();

            bindingList.AddingNew += (s, ev) => Debug.WriteLine("AddingNew");
            bindingList.ListChanged += (s, ev) => Debug.WriteLine("ListChanged");
        }

        /// <summary>
        /// http://www.codeproject.com/Articles/38972/Nullable-datetime-column-in-NET-DataGrid-with-Date
        /// </summary>
        private void AddTestData()
        {
            // Add row with test data.
            var item = new dgvClass1();
            item.Number = 1;
            item.Name = "Test data1";
            item.priority = "Low";          // Not visible field will be used in ComboBox later.
            bindingList.Add(item);

            // Add row with test data.
            item = new dgvClass1();
            item.Number = 2;
            item.Name = "Test data2";
            item.date = item.date.AddMonths(1);
            bindingList.Add(item);

            // Add row with test data.
            item = new dgvClass1();
            item.Number = 3;
            item.Name = "Test data3";
            item.date = item.date.AddMonths(2);
            bindingList.Add(item);

            var clone = (dgvClass1)item.Clone();
            clone.Number++;
            bindingList.Add(clone);

            clone = (dgvClass1)clone.Clone();
            clone.Number++;
            bindingList.Add(clone);

            this.dataGridView1.DataSource = bindingList;
            this.dataGridView1.Columns[0].Frozen = true;

            //this.dataGridView1.Columns[1].ValueType = typeof(int); 
        }

        /// <summary>
        /// Add ComboBox column at position 2.
        /// </summary>
        private void AddComboBox()
        {
            DataGridViewComboBoxColumn dgvCombo = new DataGridViewComboBoxColumn();
            dgvCombo.Name = "Priority";
            dgvCombo.Width = 100;
            dgvCombo.DataSource = new string[] { "Low", "Medium", "High" };
            dgvCombo.DisplayIndex = 2;
            this.dataGridView1.Columns.Add(dgvCombo);

            for (int rowNr = 0; rowNr < bindingList.Count; rowNr++)
            {
                var row = this.dataGridView1.Rows[rowNr];
                DataGridViewComboBoxCell dgvComboCell = (DataGridViewComboBoxCell)row.Cells["Priority"];
                dgvComboCell.Value = bindingList[row.Index].priority;
            }
        }

        /// <summary>
        /// Uses class CalendarColumn.
        /// https://msdn.microsoft.com/en-us/library/7tas5c80(v=vs.100).aspx
        /// </summary>
        private void AddCalendarColumn()
        {
            CalendarColumn col = new CalendarColumn();
            col.Name = "Datum";
            col.Width = 100;
            this.dataGridView1.Columns.Add(col);
            ////this.dataGridView1.Columns["Datum"].DefaultCellStyle.Format = "yyyy-MM-dd HH:mm";   // "dd/MM/yyyy";

            foreach (DataGridViewRow row in this.dataGridView1.Rows)
            {
                row.Cells["Datum"].Value = bindingList[row.Index].date;
            }
        }

        public void DataGridChanged(object sender, DataGridViewRowEventArgs e)
        {
            Debug.Print("CollectionChanged");
        }

        private void RowValidatedEvent(object sender, DataGridViewCellEventArgs e)
        {
            Debug.Print("RowValidatedEvent");
        }

        private void dataGridView1_CellValueChanged(object sender, DataGridViewCellEventArgs e)
        {
            if (this.dataGridView1.Columns[e.ColumnIndex].Name == "Priority")
            {
                string oldPriority = this.bindingList[e.RowIndex].priority;
                string newPriority = this.dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Value.ToString();
                this.bindingList[e.RowIndex].priority = newPriority;
                //this.dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Style.BackColor = Color.Yellow;
                Debug.Print("Priority changed from: " + oldPriority + " to: " + newPriority);
            }
            else if (this.dataGridView1.Columns[e.ColumnIndex].Name == "Datum")
            {
                ////DateTime oldDate = this.bindingList[e.RowIndex].date;
                DateTime newDate;
                DateTime.TryParse(this.dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Value.ToString(), out newDate);
                this.bindingList[e.RowIndex].date = newDate;
            }
        }

        /// <summary>
        /// Show changes in bindingList.
        /// </summary>
        private void button2_Click(object sender, EventArgs e)
        {
            string str = string.Empty;

            foreach (var item in this.bindingList)
            {
                str += item.Name + ", " + item.priority + ", " + item.date + "\n";
            }

            MessageBox.Show(str);
        }

        private void buttonDelete_Click(object sender, EventArgs e)
        {
            if (this.dataGridView1.CurrentRow != null)
            {
                this.bindingList.RemoveAt(this.dataGridView1.CurrentRow.Index);
            }
        }

        private void buttonAdd_Click(object sender, EventArgs e)
        {
            var item = new dgvClass1();
            bindingList.Add(item);
            this.dataGridView1.Rows[this.bindingList.Count - 1].Cells["Priority"].Value = item.priority;    // "Medium"
            this.dataGridView1.Rows[this.bindingList.Count - 1].Cells["Datum"].Value = item.date; 
        }
    }
}

<pre lang="C#">And the CalendarColumn class in a separate file:

namespace TestForm1
{
    using System;
    using System.Windows.Forms;

    /// <summary>
    /// How to: Host Controls in Windows Forms DataGridView Cells
    /// https://msdn.microsoft.com/en-us/library/7tas5c80(v=vs.100).aspx
    /// </summary>
    public class CalendarColumn : DataGridViewColumn
    {
        public CalendarColumn()
            : base(new CalendarCell())
        {
        }

        public override DataGridViewCell CellTemplate
        {
            get
            {
                return base.CellTemplate;
            }
            set
            {
                // Ensure that the cell used for the template is a CalendarCell.
                if (value != null &&
                    !value.GetType().IsAssignableFrom(typeof(CalendarCell)))
                {
                    throw new InvalidCastException("Must be a CalendarCell");
                }
                base.CellTemplate = value;
            }
        }
    }

    public class CalendarCell : DataGridViewTextBoxCell
    {

        public CalendarCell()
            : base()
        {
            // Use the short date format.
            this.Style.Format = "d";
        }

        public override void InitializeEditingControl(int rowIndex, object
            initialFormattedValue, DataGridViewCellStyle dataGridViewCellStyle)
        {
            // Set the value of the editing control to the current cell value.
            base.InitializeEditingControl(rowIndex, initialFormattedValue,
                dataGridViewCellStyle);
            CalendarEditingControl ctl =
                DataGridView.EditingControl as CalendarEditingControl;
            // Use the default row value when Value property is null.
            if (this.Value == null)
            {
                ctl.Value = (DateTime)this.DefaultNewRowValue;
            }
            else
            {
                ctl.Value = (DateTime)this.Value;
            }
        }

        public override Type EditType
        {
            get
            {
                // Return the type of the editing control that CalendarCell uses.
                return typeof(CalendarEditingControl);
            }
        }

        public override Type ValueType
        {
            get
            {
                // Return the type of the value that CalendarCell contains.

                return typeof(DateTime);
            }
        }

        public override object DefaultNewRowValue
        {
            get
            {
                // Use the current date and time as the default value.
                return DateTime.Now;
            }
        }
    }

    class CalendarEditingControl : DateTimePicker, IDataGridViewEditingControl
    {
        DataGridView dataGridView;
        private bool valueChanged = false;
        int rowIndex;

        public CalendarEditingControl()
        {
            this.Format = DateTimePickerFormat.Short;
            //this.Format = DateTimePickerFormat.Custom;
            //this.CustomFormat = "yyyy-MM-dd HH:mm";
        }

        // Implements the IDataGridViewEditingControl.EditingControlFormattedValue 
        // property.
        public object EditingControlFormattedValue
        {
            get
            {
                return this.Value.ToShortDateString();
            }
            set
            {
                if (value is String)
                {
                    try
                    {
                        // This will throw an exception of the string is 
                        // null, empty, or not in the format of a date.
                        this.Value = DateTime.Parse((String)value);
                    }
                    catch
                    {
                        // In the case of an exception, just use the 
                        // default value so we're not left with a null
                        // value.
                        this.Value = DateTime.Now;
                    }
                }
            }
        }

        // Implements the 
        // IDataGridViewEditingControl.GetEditingControlFormattedValue method.
        public object GetEditingControlFormattedValue(
            DataGridViewDataErrorContexts context)
        {
            return EditingControlFormattedValue;
        }

        // Implements the 
        // IDataGridViewEditingControl.ApplyCellStyleToEditingControl method.
        public void ApplyCellStyleToEditingControl(
            DataGridViewCellStyle dataGridViewCellStyle)
        {
            this.Font = dataGridViewCellStyle.Font;
            this.CalendarForeColor = dataGridViewCellStyle.ForeColor;
            this.CalendarMonthBackground = dataGridViewCellStyle.BackColor;
        }

        // Implements the IDataGridViewEditingControl.EditingControlRowIndex 
        // property.
        public int EditingControlRowIndex
        {
            get
            {
                return rowIndex;
            }
            set
            {
                rowIndex = value;
            }
        }

        // Implements the IDataGridViewEditingControl.EditingControlWantsInputKey 
        // method.
        public bool EditingControlWantsInputKey(
            Keys key, bool dataGridViewWantsInputKey)
        {
            // Let the DateTimePicker handle the keys listed.
            switch (key & Keys.KeyCode)
            {
                case Keys.Left:
                case Keys.Up:
                case Keys.Down:
                case Keys.Right:
                case Keys.Home:
                case Keys.End:
                case Keys.PageDown:
                case Keys.PageUp:
                    return true;
                default:
                    return !dataGridViewWantsInputKey;
            }
        }

        // Implements the IDataGridViewEditingControl.PrepareEditingControlForEdit 
        // method.
        public void PrepareEditingControlForEdit(bool selectAll)
        {
            // No preparation needs to be done.
        }

        // Implements the IDataGridViewEditingControl
        // .RepositionEditingControlOnValueChange property.
        public bool RepositionEditingControlOnValueChange
        {
            get
            {
                return false;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingControlDataGridView property.
        public DataGridView EditingControlDataGridView
        {
            get
            {
                return dataGridView;
            }
            set
            {
                dataGridView = value;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingControlValueChanged property.
        public bool EditingControlValueChanged
        {
            get
            {
                return valueChanged;
            }
            set
            {
                valueChanged = value;
            }
        }

        // Implements the IDataGridViewEditingControl
        // .EditingPanelCursor property.
        public Cursor EditingPanelCursor
        {
            get
            {
                return base.Cursor;
            }
        }

        protected override void OnValueChanged(EventArgs eventargs)
        {
            // Notify the DataGridView that the contents of the cell
            // have changed.
            valueChanged = true;
            this.EditingControlDataGridView.NotifyCurrentCellDirty(true);
            base.OnValueChanged(eventargs);
        }
    }
}