1. A method for providing a test case for a modified program, comprising: obtaining a modification item that modifies a previous version of the program; finding a first instrument of a plurality of instruments inserted into the program that is before the modification item; finding a second instrument of the plurality of instruments inserted into the program that is after the modification item; obtaining an execution path of the modified program that is between the first instrument and the second instrument and associated with the modification as well as a constraint set corresponding to the execution path; obtaining an execution result, outputted by the first instrument, of executing the previous version of the program using an original test case; and determining a test case applicable for the execution path based on the execution result and the constraint set; wherein determining a test case applicable for the execution path comprises: further defining the constraint set using the execution result to form a combined constraint set; solving the combined constraint set; and judging whether the original test case is applicable for the execution path according to the solving result; and further wherein the judging comprises, in a case where the combined constraint set has no solution, determining the original test case not applicable for the execution path; modifying parameter settings related to local variables in the constraint set to make the combined constraint set have a solution; and generating a new test case based on the original test case and the modified parameter settings.