add fork choice rule

cryptarchia/cryptarchia.py

@@ -124,8 +124,8 @@ class Follower:
         # in that case, just ignore the block
 
     # Evaluate the fork choice rule and return the block header of the block that should be the head of the chain
-    def fork_choice(local_chain: Chain, forks: List[Chain]) -> BlockHeader:
-        pass
+    def fork_choice(local_chain: Chain, forks: List[Chain]) -> Chain:
+        return maxvalid_bg(local_chain, forks)
 
     def tip(self) -> BlockHeader:
         return self.fork_choice()
@@ -218,5 +218,35 @@ class Leader:
         return BlockHeader(parent=parent.id(), slot=slot)
 
 
+def common_prefix_len(a: Chain, b: Chain) -> int:
+    for i, (x, y) in enumerate(zip(a.blocks, b.blocks)):
+        if x.id() != y.id():
+            return i
+    return min(len(a.blocks), len(b.blocks))
+
+
+def chain_density(chain: Chain, slot: Slot) -> int:
+    return count(block for block in chain.blocks if block.slot < slot)
+
+def maxvalid_bg(local_chain: Chain, forks: List[Chain], k: int, s: int) -> Chain:
+    cmax = local_chain
+    for chain in forks:
+        lowest_common_ancestor = common_prefix_len(cmax, chain)
+        m = cmax.length() - lowest_common_ancestor
+        if m <= k:
+            # Classic longest chain rule with parameter k
+            if cmax.length() < chain.length():
+                cmax = chain
+        else:
+            # The chain is forking too much, we need to pay a bit more attention
+            # In particular, select the chain that is the densest after the fork
+            forking_slot = cmax.blocks[lowest_common_ancestor].slot
+            cmax_density = chain_density(cmax, forking_slot + s)
+            chain_density = chain_density(chain, forking_slot + s)
+            if cmax_density < chain_density:
+                cmax = chain
+
+    return cmax
+
 if __name__ == "__main__":
     pass