The Shloshim ends eight days after Simchas Torah, which in the year 5785 falls out on Shabbos the 1st of MarCheshvan. Hence, all the laws of Shloshim end Shabbos morning. 

Background:

The holiday of Sukkos nullifies Shiva or Shloshim. Thus, if one began Shiva before Sukkos, the Shiva is nullified by Sukkos and counts as seven days towards the Shloshim. The 7 days also count towards the Shloshim. Furthermore, Shemini Atzeres counts as a full seven days [however does not nullify the Shloshim[1]].[2] Furthermore, in the Diaspora, the second day of Shemini Atzeres counts as a further day of Shloshim. Thus, [in Eretz Yisrael] one counts after Shemini Atzeres 9 days of Shloshim and [in the Diaspora] one counts 8 days of Shloshim. If one ended the Shiva before Sukkos, then Sukkos nullifies the Shloshim.

[1] Michaber ibid and ibid; Taz 399:6 in name of Rosh

The reason it does not nullify the Shloshim: The Holiday of Shemini Atzeres does not nullify the Shloshim being that one did not keep any of the recognized laws of Shloshim post Shiva, prior to Shemini Atzeres. Now, although one does not launder during Chol Hamoed, this is due to the laws of Chol Hamoed and hence cannot be used to nullify the Shloshim. [Taz 399:6 in name of Rosh] Now, although there are added stringencies to this prohibition due to the Aveilus of Shloshim, as explained in Michaber 399:3 based on Ramban, nevertheless, there must be an act of mourning of Shloshim being practiced that is unique and recognizable to others in order for the Chag to nullify the Shloshim. [Taz ibid]

[2] Michaber ibid