What kind of influence did Cārvāka had on Buddha's philosophy I have sometimes heard that Siddhartha Gautama's philosophy was influenced by Cārvāka system of philosophy. Is this true, and if true, to what extent has Cārvāka system influenced Buddhism?
The Buddha claims that what he is about to teach is previously unheard of. Hence I double that there were any material influences on the core of Buddhism though he did draw from existing customs and techniques which were appropriate. E.g. Sila, some of the Samatha meditation techniques, etc.

The core being the teaching like the Bodhipakkhiyādhammā, the 4 Nobel Truths, the Pratītyasamutpāda, Three marks of existence, Threefold Training, etc. which are original to Buddhism.

Buddha rejected 62 wrong view of his time. Ucchedavada proposed by Ajita Kesakambali, one of the earliest Cārvāka thinkers, was also rejected by Buddha among other. These views arise due to theorising and philosophising without going to the pinnacle of understanding or realisation of the ultimate truth. Hence there cannot be any perceivable influence from this doctrine.