top sort

test.lua

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+-- adjacency list: adj[u] = {v1, v2, ...}
+local adj = {}
+
+local function add_edge(u, v)
+    adj[u] = adj[u] or {}
+    table.insert(adj[u], v)
+end
+
+-- Example graph
+add_edge("A", "B")
+add_edge("B", "C")
+add_edge("C", "D")
+-- Uncomment next line to introduce a cycle:
+add_edge("A", "D")
+
+---------------------------------------------------------
+-- Topological sort (DFS-based, with cycle detection)
+---------------------------------------------------------
+local visited = {}  -- "perm" mark: node completely processed
+local in_stack = {} -- "temp" mark: node currently in recursion stack
+local order = {}    -- reverse topological order
+local cycle = nil   -- store cycle if found
+
+local function dfs(u, path)
+    visited[u] = true
+    in_stack[u] = true
+    table.insert(path, u)
+
+    for _, v in ipairs(adj[u] or {}) do
+        if not visited[v] then
+            dfs(v, path)
+            if cycle then return end
+        elseif in_stack[v] then
+            -- found a cycle
+            cycle = {}
+            -- extract the cycle part from path
+            for i = #path, 1, -1 do
+                table.insert(cycle, 1, path[i])
+                if path[i] == v then break end
+            end
+            table.insert(cycle, v) -- close the cycle
+            return
+        end
+    end
+
+    in_stack[u] = false
+    table.remove(path)
+    table.insert(order, 1, u)
+end
+
+local function topo_sort()
+    for u, _ in pairs(adj) do
+        if not visited[u] then
+            dfs(u, {})
+            if cycle then return nil, cycle end
+        end
+    end
+
+    -- build rank map
+    local rank = {}
+    for i, u in ipairs(order) do
+        rank[u] = i
+    end
+    return rank
+end
+
+---------------------------------------------------------
+-- Run it
+---------------------------------------------------------
+local rank, cycle = topo_sort()
+if cycle then
+    print("Cycle detected:")
+    print(table.concat(cycle, " -> "))
+else
+    print("Topological order ranks:")
+    for k, v in pairs(rank) do
+        print(k, v)
+    end
+end