Rosrun can not find an executable file.

edit

it contains a cpp program in the src folder called algorithm_1.cpp which I need to run.

this would appear to be the cause of your problem: .cpp files are not programs. They are source files which must be compiled into binaries first before they can be executed.

Specifying a .cpp file as the type of a node element in a .launch file will not work.

project(dijkstra)    
...
add_executable(${PROJECT_NAME} src/algorithm_1.cpp)

dijkstra.cpp is the source file, not the name of the binary (ie: the compiled program). That would be dijkstra.

If you remove the .cpp from the type attribute of the node element in your .launch file, things will probably start working (assuming the rest of the .launch file is correct).

Change name of your main source code file algorithm_1.cpp to dijkstra.cpp. Use the same name for both executable and source file which is a convention used by many people. Although they don't have to be same as you can see here. So try this:

...
add_executable(dijkstra src/dijkstra.cpp)

target_link_libraries(dijkstra
${catkin_LIBRARIES}
)
...

Compile your workspace, source your .bashrc and you're good to go.

Also check the CMakeLists.txt given here for other mistakes if you're still unable to run your node.