2020 day 16

2020/16/day16.lua

@@ -0,0 +1,144 @@
+local rules, my_ticket, tickets = {}, {}, {}
+
+local parsing_mode = 0
+for line in io.lines() do
+    if line == '' then
+        -- who cares!
+    elseif line == 'your ticket:' then
+        parsing_mode = 1
+    elseif line == 'nearby tickets:' then
+        parsing_mode = 2
+    elseif parsing_mode == 0 then
+        -- Parse the rule into a validation function
+        local name, low1, high1, low2, high2 = line:match('(.+): (%d+)-(%d+) or (%d+)-(%d+)')
+        low1, high1, low2, high2 = tonumber(low1), tonumber(high1), tonumber(low2), tonumber(high2)
+        local function validator(value)
+            return (value >= low1 and value <= high1) or (value >= low2 and value <= high2)
+        end
+        rules[name] = validator
+    elseif parsing_mode == 1 then
+        -- Parse my ticket
+        for n in line:gmatch('%d+') do
+            table.insert(my_ticket, tonumber(n))
+        end
+    else
+        -- Parse another ticket
+        local ticket = {}
+        for n in line:gmatch('%d+') do
+            table.insert(ticket, tonumber(n))
+        end
+        table.insert(tickets, ticket)
+    end
+end
+
+local function is_valid(field)
+    for _, validator in pairs(rules) do
+        if validator(field) then
+            return true
+        end
+    end
+    return false
+end
+
+local invalid = {}
+
+local function part1()
+    local total = 0
+    for i, ticket in ipairs(tickets) do
+        for _, field in ipairs(ticket) do
+            if not is_valid(field) then
+                total = total + field
+                -- Help part 2 by storing the index of fully invalid tickets
+                table.insert(invalid, i)
+                break
+            end
+        end
+    end
+    return total
+end
+
+--[[
+    Build a table that maps, for each rule, all the columns it can apply on.
+    Then work by elimination to assemble the ticket order, and return the
+    product of all departure fields.
+--]]
+local function part2()
+    -- Remove invalid tickets found in part 1
+    table.sort(invalid, function (a, b) return a > b end)
+    for _, i in ipairs(invalid) do
+        table.remove(tickets, i)
+    end
+
+    -- For each rule, maps all the columns that fully match the rule.
+    local columns = {}
+    for name, _ in pairs(rules) do
+        columns[name] = {}
+    end
+
+    -- For each rule…
+    for name, validator in pairs(rules) do
+        -- For each column…
+        for i = 1, #tickets[1] do
+            local success = true
+            -- Check all tickets. If any ticket does not match, abort mission
+            for _, ticket in ipairs(tickets) do
+                if not validator(ticket[i]) then
+                    success = false
+                    break
+                end
+            end
+            if success then
+                -- This column matches!
+                table.insert(columns[name], i)
+            end
+        end
+    end
+
+    -- Field resolution
+    local ordering = {}
+    local function ordering_completed()
+        for i = 1, #tickets[1] do
+            if not ordering[i] then
+                return false
+            end
+        end
+        return true
+    end
+
+    while not ordering_completed() do
+        --[[
+            Loop over every rule until we find one where only a single column
+            has not been matched yet; this is the column of that rule.
+        --]]
+        for name, applicable_columns in pairs(columns) do
+            local matched, unique = nil, true
+            for _, column in ipairs(applicable_columns) do
+                if not ordering[column] then
+                    if matched then
+                        -- A column was already found before, so we cannot dedupe yet
+                        unique = false
+                        break
+                    else
+                        -- Keep this column and keep going to check for unicity
+                        matched = column
+                    end
+                end
+            end
+            if matched and unique then
+                ordering[matched] = name
+            end
+        end
+    end
+
+    -- Output the product
+    local total = 1
+    for i, name in ipairs(ordering) do
+        if name:match('^departure') then
+            total = total * my_ticket[i]
+        end
+    end
+    return total
+end
+
+print(part1())
+print(part2())

README.md

@@ -26,7 +26,7 @@ is acceptable; anything goes as long as I solve it myself!
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