The　problem　of　maximizing　the　sum　of　a　constrained　submodular　and　a　supermodular　function　has　many　applications　such　as　social　networks,　machine　learning,　and　artificial　intelligence.　In　this　article,　we　study　the　monotone　submodular　+　supermodular　maximization　problem　under　a　cardinality　constraint　and　a　p-system　constraint,　respectively.　For　each　problem,　we　provide　a　stochastic　algorithm　and　prove　the　approximation　ratio　of　each　algorithm　theoretically.　Since　the　algorithm　of　the　latter　problem　can　also　solve　the　former　problem,　we　do　some　numerical　experiments　of　the　two　algorithms　to　compare　the　time　as　well　as　the　quality　of　the　two　algorithms　in　solving　the　former　problem.