In general, cholecystectomy does not usually lead to constipation, and there is generally no correlation between having a cholecystectomy and how long it takes for constipation to return to normal.
Bile is involved in digestion and helps in the absorption and digestion of lipids. Clinically, after cholecystectomy, because the concentration and storage of bile is reduced, some patients may experience an increase in the number of bowel movements and a change in the character of the stool, but not constipation. Even patients with previous constipation may experience relief after cholecystectomy.
If constipation occurs after cholecystectomy and the symptoms are severe enough to interfere with your life, you should tell your doctor so that the cause can be identified and treated in a timely manner.