0-1 knapsack problem is a classical Combinatorial optimization problem and NP complete problem.It has important application value and theoretical significance.In this paper

we formally derive the efficient dynamic programming algorithmic program for solving 0-1 knapsack problem by using PAR（Partition and Recurrence） method.Some of its variable algorithms can also be derived by analogy.The algorithm can be transformed into executive program and run normally using the automatic generation system in PAR platform.It guarantees the correctness and reliability of this kind of 0-1 knapsack problems algorithms.The main contribution of this paper is to extend PAR method to dealing with the combinatorial optimization problems with constraints

which greatly expand the scope of application of PAR method.The approach in this paper pioneers a new avenue to formally develop combination and optimization algorithms with high efficiency and trustworthiness.