If the police entered someone's house without a warrant which amendment would they most likely be violating?

The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.

this is your 4th amendment right stand up for it

Another View: While the above answer is textbook correct, there ARE certain specified instances in which law enforcement may enter and search your residence in the absence of a warrant (e.g.: when in 'fresh pursuit' - when an offense is bieing committed in plain sight - emergency circumstances - etc).