Lua solves the problem of going up the ladder (output specific steps, iterations, and Recursion according to the specified format)

Problem description

The stairs have n steps. You can go upstairs to level 1 or Level 2. Compile a program to list each step.

Thought comments are all in the Code for the first time. Lua is very good at script language source code.

-- [[Replicate table: Deep copy --] -------------------------------------------------------------------------- function table. copy (t) Local T2 ={}; for K, V in pairs (t) doif type (v) = "table" thent2 [k] = table. copy (V); elset2 [k] = V; endendreturn T2; end -- [[-------------------------------------------------------------------- format: Convert the table into a string for formatting output --]] -------------------------------------------------------------------------- Function table. formatout (T, h) Local out = ""; for K, V in pairs (t) doif type (V) = "table" thenif K = 1 thenfor I = 1, h do out = string. format ("% S % s", out, ""); endout = string. format ("% S % s", out, "{\ n"); endout = string. format ("% S % s", out, table. formatout (v, H + 1); If K = table. getn (t) thenfor I = 1, h do out = string. form At ("% S % s", out, ""); endout = string. format ("% S % s", out, "}, \ n"); endelseif K = 1 thenfor I = 1, h do out = string. format ("% S % s", out, ""); endout = string. format ("% S % s", out, "{"); endout = string. format ("% S % d,", out, V); If (k = table. getn (t) thenout = string. format ("% S % s", out, "}, \ n"); endendendreturn out; end -- [[------------------------------------------------------------------------ format output --]-] ------------------------------------------------------------------------- Function table. print (t) Local out = table. formatout (T, 0); -- remove the last ", \ n" two characters print (string. sub (Out, 1, String. len (out)-2); end -- [Response @ paramsolution_new @ format {1, 2} {2, 1} {1} {1, 1, solution @ format {} {, 1 }}@ meaning under a specific n value, all solutions, each element It is a value to be inserted to solve the value @ format integer @ meaning, such as the input status of 1 2 @ exmple: solution_new ={} solution ={{ 1} {2, 1} {1, 1, 1} value = 1 after running the function: solution_new = {1, 1} {2, 1} {1, 1} {1, 1} --] processing function update_solution (solution_new, solution, value) Local STR = string. format ("% d", value) -- convert the value into a character table. foreach (solution, function (idx, ELE) table. insert (Ele, STR) Table. insert (solution_new, ELE) End) end -- [[solution: All feasible solutions of level n step {{},{}}]] -- function f_digui (N) local Solution = {} if n = 1 thensolution = {1} elseif n = 2 thensolution = {1, 1 }, {2} elsesolution ={} update_solution (solution, f_digui (n-2), 2); update_solution (solution, f_digui (n-1), 1); endreturn solutionend -- [[solution: all feasible solutions of steps 1 to n are {{},{},{}},{},{},{}}} solution [I]: all feasible solutions of level I step {{},{ }, {}} From here, we can see that iteration requires more space to save data] -- function f_diedai (n) Local Solution ={} for I _n = 1, N doif I _n = 1 thensolution [I _n] = {1} elseif I _n = 2 thensolution [I _n] = {1, 1 }, {2} elsesolution [I _n] = {} update_solution (solution [I _n], table. copy (solution [I _n-2]), 2); update_solution (solution [I _n], table. copy (solution [I _n-1]), 1); endendreturn solution [N] end -- [n returns the combination of each n value from starti to endi] -- function test (s Tarti, endi, FUC) for I = starti, endi, 1 dolocal array = {} print () print ("N value:", I) if FUC = "digui" thentable. print (f_digui (I) elsetable. print (f_diedai (I) endendend vertex test (3, 4, "digui"); -- Test (1, 4, "diedai"); -- table. print ({1, 2}, {3, 4}, {1, 2}, {3, 4}); out = "Hello Lua! \ N this is the first Lua code to solve the problem of going up the stairs \ n there are several good places: \ N1, recursive and iterative conversions \ N2, table replication and table output \ N3, use of some basic syntax "; print (out); test (4, 4, "diedai"); dimensions [[all variables are local variables by default, and local variables must be used] ---- [the function parameter in Lua is "Reference", that is: changing the value of this parameter in a function will change the variable] ---- [[(Code normalization -- as a reference) generally, all functions in programming languages should not return meaningful values. expected results should be saved through parameters. For example, in the update_solution function, we need to obtain solution_new as a parameter, instead of returning in the form of return solution_new, it is generally an error code used for Error Control, indicating whether the function is normally executed. If you need to return a meaningful value, the function name should be named get _ *** or, if no meaningful value is returned, the function is hard to understand, or the value can be returned, for example, in the f_digui of the recursive function] --