Add Job Sequencing in M4 (#5255)

Author: rzuckerm

archive/m/m4/job-sequencing.m4

@@ -0,0 +1,216 @@
+divert(-1)
+define(`show_usage',
+`Usage: please provide a list of profits and a list of deadlines
+m4exit(`1')')
+
+dnl Reference: https://www.gnu.org/software/m4/manual/m4.html#index-array
+dnl array_get(var_name, idx)
+define(`array_get', `defn(format(``%s[%s]'', `$1', `$2'))')
+
+dnl array_set(var_name, idx, value)
+define(`array_set', `define(format(``%s[%s]'', `$1', `$2'), `$3')')
+
+dnl 2D versions of "array_get" and "array_set"
+dnl array2_get(varname, idx1, idx2)
+define(`array2_get', `defn(format(``%s[%s][%s]'', `$1', `$2', `$3'))')
+
+dnl array2_set(varname, idx1, idx2, value)
+define(`array2_set', `define(format(``%s[%s][%s]'', `$1', `$2', `$3'), `$4')')
+
+dnl array2_swap(varname, idx1, idx2, common_idx):
+dnl   t = varname[idx1][common_idx]
+dnl   varname[idx1][common_idx] = varname[idx2][common_idx]
+dnl   varname[idx2][common_idx] = t
+define(`array2_swap',
+`pushdef(`t', array2_get(`$1', `$2', `$4'))dnl
+array2_set(`$1', `$2', `$4', array2_get(`$1', `$3', `$4'))dnl
+array2_set(`$1', `$3', `$4', t)dnl
+popdef(`t')'dnl
+)
+
+dnl is_valid(n)
+define(`is_valid', `eval(regexp(`$1', `^\s*-?[0-9]+\s*$') >= 0)')
+
+dnl parse_int_list(varname, args):
+dnl   varname[length] = 0
+dnl   foreach arg in args:
+dnl     if not is_valid(arg):
+dnl       Return 0
+dnl     varname[varname[length]] = arg
+dnl     varname[length] = varname[length] + 1
+dnl   Return 1
+define(`parse_int_list',
+`array_set(`$1', `length', 0)dnl
+_parse_int_list(`$1', $2)'dnl
+)
+define(`_parse_int_list',
+`ifelse(is_valid(`$2'), 0, `0',
+`array_set(`$1', array_get(`$1', `length'), `$2')dnl
+array_set(`$1', `length', incr(array_get(`$1', `length')))dnl
+ifelse(eval($# > 2), 1, `_parse_int_list(`$1', shift(shift($@)))', `1')'dnl
+)'dnl
+)
+
+dnl Reference: https://www.techiedelight.com/job-sequencing-problem-deadlines/
+dnl job_sequencing(profits_varname, deadlines_varname, jobs_varname, slots_varname):
+dnl   // Set up job details and longest deadline
+dnl   longest_deadline = 0
+dnl   jobs_varname["length"] = profits_varname["length"]
+dnl   for i = 0 to profits_varname["length"] - 1:
+dnl     jobs_varname[i]["profit"] = profits_varname[i]
+dnl     jobs_varname[i]["deadline"] = deadlines_varname[i]
+dnl     if deadlines_varname[i] > longest_deadline:
+dnl       longest_deadline = deadlines_varname[i]
+dnl
+dnl   // Initialize job slots
+dnl   slots_varname["length"] = longest_deadline + 1
+dnl   for i = 0 to longest_deadline:
+dnl     slots_varname[i] = -1
+dnl
+dnl   // Sort jobs by profit then deadline
+dnl   bubble_sort(jobs_varname)
+dnl
+dnl   // For each job, see if there is available slot at or before the deadline
+dnl   // if so, store this job in that slot
+dnl   for i = 0 to jobs_varname["length"] - 1:
+dnl     for j = jobs_varname[i]["deadline"] down to 1:
+dnl       if slots_varname[j] < 0:
+dnl         slots_varname[j] = i
+dnl         break
+define(`job_sequencing',
+`pushdef(`longest_deadline', 0)dnl
+_set_jobs(`$1', `$2', `$3')dnl
+_init_slots(`$4')dnl
+bubble_sort(`$3')dnl
+_set_slots(`$3', `$4', 0)dnl
+popdef(`longest_deadline')dnl
+'dnl
+)
+
+dnl profits_varname=$1, deadlines_varname=$2, jobs_varname=$3
+define(`_set_jobs',
+`array_set(`$3', `length', array_get(`$1', `length'))dnl
+_set_jobs_inner(`$1', `$2', `$3', 0)dnl
+'dnl
+)
+
+dnl profits_varname=$1, deadlines_varname=$2, jobs_varname=$3, i=$4
+define(`_set_jobs_inner',
+`ifelse(eval($4 < array_get(`$1', `length')), 1,
+`array2_set(`$3', `$4', `profit', array_get(`$1', `$4'))dnl
+array2_set(`$3', `$4', `deadline', array_get(`$2', `$4'))dnl
+ifelse(eval(array_get(`$2', `$4') > longest_deadline), 1,
+`define(`longest_deadline', array_get(`$2', `$4'))')dnl
+_set_jobs_inner(`$1', `$2', `$3', incr($4))'dnl
+)'dnl
+)
+
+dnl slots_varname=$1
+define(`_init_slots',
+`array_set(`$1', `length', incr(longest_deadline))dnl
+_init_slots_inner(`$1', 0)dnl
+'dnl
+)
+
+dnl slots_varname=$1, i=$2
+define(`_init_slots_inner',
+`ifelse(eval($2 <= longest_deadline), 1,
+`array_set(`$1', `$2', -1)dnl
+_init_slots_inner(`$1', incr($2))'dnl
+)'dnl
+)
+
+dnl jobs_varname=$1, slots_varname=$2, i=$3
+define(`_set_slots',
+`ifelse(eval($3 < array_get(`$1', `length')), 1,
+`_set_slots_inner(`$2', `$3', array2_get(`$1', `$3', `deadline'))dnl
+_set_slots(`$1', `$2', incr($3))'dnl
+)'dnl
+)
+
+dnl slots_varname=$1, i=$2, j=$3
+define(`_set_slots_inner',
+`ifelse(eval($3 >= 1), 1,
+`ifelse(eval(array_get(`$1', `$3') < 0), 1,
+`array_set(`$1', `$3', `$2')',
+`_set_slots_inner(`$1', `$2', decr($3))'dnl
+)'dnl
+)'dnl
+)
+
+dnl Reference: https://en.wikipedia.org/wiki/Bubble_sort#Pseudocode_implementation
+dnl bubble_sort(varname):
+dnl   n = varname[length]
+dnl   do:
+dnl     swapped = false
+dnl     for i from 1 to n-1:
+dnl       if compare_jobs(varname, i-1, i):
+dnl         swap_jobs(varname, i-1, i)
+dnl         swapped = true
+dnl   while swapped
+define(`bubble_sort', `ifelse(_bubble_sort_outer(`$1', 1, 0), 1, `bubble_sort(`$1')')')
+define(`_bubble_sort_outer',
+`ifelse(eval($2 < array_get(`$1', `length')), 0,
+`$3',
+`ifelse(_bubble_sort_inner(`$1', $2), 1,
+`_bubble_sort_outer(`$1', incr($2), 1)', `_bubble_sort_outer(`$1', incr($2), $3)'dnl
+)'dnl
+)'dnl
+)
+define(`_bubble_sort_inner',
+`ifelse(eval(compare_jobs(`$1', decr($2), `$2')), 1,
+0, `swap_jobs(`$1', decr($2), $2)1'`'dnl
+)'dnl
+)
+
+dnl compare_jobs(job_varname, idx1, idx2):
+dnl   // Prioritize by profit, then deadline:
+dnl   // 0 means jobs need to be swapped, 1 otherwise
+dnl   return (job_varname[idx1]["profit"] > job_varname[idx2]["profit"]) or
+dnl     (job_varname[idx1]["profit"] == job_varname[idx2]["profit"] and
+dnl      job_varname[idx1]["deadline"] > job_varname[idx2]["deadline"])
+define(`compare_jobs',
+`eval(
+    array2_get(`$1', `$2', `profit') > array2_get(`$1', `$3', `profit') ||
+    (array2_get(`$1', `$2', `profit') == array2_get(`$1', `$3', `profit') &&
+    array2_get(`$1', `$2', `deadline') > array2_get(`$1', `$3', `deadline'))
+)'dnl
+)
+
+dnl swap_jobs(job_varname, idx1, idx2):
+dnl   swap(job_varname[idx1]["profit"], job_varname[idx2]["profit"])
+dnl   swap(job_varname[idx1]["deadline"], job_varname[idx2]["deadline"])
+define(`swap_jobs',
+`array2_swap(`$1', `$2', `$3', `profit')dnl
+array2_swap(`$1', `$2', `$3', `deadline')'dnl
+)
+
+dnl get_total_profit(jobs_varname, slots_varname):
+dnl   total = 0
+dnl   for i = 1 to slots_varname["length"] - 1:
+dnl     if slots_varname[i] >= 0:
+dnl       total = total + jobs_varname[slots_varname[i]]["profit"]
+dnl   return total
+define(`get_total_profit', `_get_total_profit(`$1', `$2', 0, 1)')
+
+dnl jobs_varname=$1, slots_varname=$2, total=$3, i=$4
+define(`_get_total_profit',
+`ifelse(eval($4 >= array_get(`$2', `length')), 1, `$3',
+`ifelse(eval(array_get(`$2', `$4') >= 0), 1,
+`_get_total_profit(`$1', `$2', eval($3 + array2_get(`$1', array_get(`$2', `$4'), `profit')), incr($4))',
+`_get_total_profit(`$1', `$2', `$3', incr($4))'dnl
+)'dnl
+)'dnl
+)
+
+divert(0)dnl
+ifelse(eval(
+    ARGC < 2 ||
+    !parse_int_list(`profits', ARGV1) ||
+    !parse_int_list(`deadlines', ARGV2)
+), 1, `show_usage()')dnl
+ifelse(eval(
+    array_get(`profits', `length') != array_get(`deadlines', `length')
+), 1, `show_usage()')dnl
+job_sequencing(`profits', `deadlines', `jobs', `slots')dnl
+get_total_profit(`jobs', `slots')