fluidb/PLAN.md

Tarjan's algorithm for SCC detection

UNVISITED = -1
n = number of nodes in graph
g = adjacency list with directed edges

id = 0       # Used to give each node an id
sccCount = 0 # Used to count number of SCCs found
# Index i in these arrays represents node i 
ids = [0, 0, ... 0, 0] # Length n 
low = [0, 0, ... 0, 0] # Length n 
onStack = [false, false, ..., false] # Length n 
stack = an empty stack data structure

function findSccs():
    for(i = 0; i < n; i++): ids[i] = UNVISITED 
    for(i = 0; i < n; i++):
        if(ids[i] == UNVISITED): 
            dfs(i)
    return low

function dfs(at): 
    stack.push(at)
    onStack[at] = true 
    ids[at] = low[at] = id++
    
    # Visit all neighbours & min low-link on callback
    for(to : g[at]):
        if(ids[to] == UNVISITED): dfs(to)
        if(onStack[to]): low[at] = min(low[at],low[to])
    # After having visited all the neighbours of ‘at’ # if we're at the start of a SCC empty the seen
    # stack until we’re back to the start of the SCC. 
    if(ids[at] == low[at]):
        for(node = stack.pop();;node = stack.pop()): onStack[node] = false
            low[node] = ids[at]
            if(node == at): break
        sccCount++