This paper proposes a method that speeds up a classifier trained with many conjunctive features: combinations of (primitive) features. The key idea is to precompute as partial results the weights of primitive feature vectors that represent fundamental classification problems and appear frequently in the target task. A prefix tree (trie) compactly stores the primitive feature vectors with their weights, and it enables the classifier to find for a given feature vector its longest prefix feature vector whose weight has already been computed. Experimental results on base phrase chunking and dependency parsing demonstrated that our method speeded up the SVM and LLM classifiers by a factor of 1.8 to 10.6.