refactor: enhance minCostAssignment function with sentinel column for improved indexing

- Introduced a sentinel column to replace 0-indexing from the Rust version, simplifying potential assignments.
- Updated array initializations to accommodate the new indexing scheme, enhancing clarity and consistency in the algorithm.
- Adjusted logic for potential updates and augmenting paths to align with the new structure.
This commit is contained in:
Joe 2026-03-07 18:01:35 -06:00
parent d26f82b4f2
commit 3f469d615b

View file

@ -337,6 +337,8 @@ local function minCostAssignment(cost: { { number } }, rows: number, cols: numbe
local n = math.max(rows, cols)
local big = UNMATCHED_PENALTY * 2
local S = n + 1 -- sentinel column (replaces 0-index from the Rust version)
local INF = math.huge
local c: { { number } } = table.create(n)
for i = 1, n do
@ -349,24 +351,26 @@ local function minCostAssignment(cost: { { number } }, rows: number, cols: numbe
c[i] = row
end
local u = table.create(n + 1, 0)
local v = table.create(n + 1, 0)
local p = table.create(n + 1, 0)
local way = table.create(n + 1, 0)
local INF = math.huge
-- u[1..n] = row potentials, u[S] unused but allocated for uniform indexing
local u = table.create(S, 0)
-- v[1..n] = col potentials, v[S] = sentinel potential
local v = table.create(S, 0)
-- p[j] = row assigned to column j (0 = unassigned), p[S] = sentinel
local p = table.create(S, 0)
-- way[j] = previous column in augmenting path
local way = table.create(S, 0)
for i = 1, n do
p[0] = i
local j0 = 0
local minV = table.create(n + 1, INF)
local used = table.create(n + 1, false)
p[S] = i
local j0 = S
local minV = table.create(S, INF)
local used = table.create(S, false)
while true do
used[j0] = true
local i0 = p[j0]
local delta = INF
local j1 = 0
local j1 = S
for j = 1, n do
if used[j] then
@ -383,7 +387,10 @@ local function minCostAssignment(cost: { { number } }, rows: number, cols: numbe
end
end
for j = 0, n do
-- Update potentials: sentinel + real columns
u[p[S]] += delta
v[S] -= delta
for j = 1, n do
if used[j] then
u[p[j]] += delta
v[j] -= delta
@ -402,7 +409,7 @@ local function minCostAssignment(cost: { { number } }, rows: number, cols: numbe
local j1 = way[j0]
p[j0] = p[j1]
j0 = j1
if j0 == 0 then
if j0 == S then
break
end
end