##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
(C++ code)
Here is the solution:
for i from 1 to numSCCs:
dp[i] = compCoins[i]
for v in reverse(topoOrder):
for u in compAdj[v]:
dp[v] = max(dp[v], compCoins[v] + dp[u])
print max(dp[1..numSCCs])
Process in reverse topological order so that dp[u] for each successor u is computed before dp[v].
This runs in time and uses space.