diff --git a/Cargo.toml b/Cargo.toml
index 9b1e522..cb4e181 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,7 +6,7 @@ keywords = ["combinatorial", "optimization", "tree", "graph"]
 license-file = "LICENSE"
 readme = "README.md"
 categories = ["algorithms"]
-version = "0.1.1"
+version = "0.2.0"
 edition = "2021"
 authors = ["Du Shiqiao <lucidfrontier.45@gmail.com>"]
 
diff --git a/README.md b/README.md
index 33adfab..a34464f 100644
--- a/README.md
+++ b/README.md
@@ -84,10 +84,10 @@ fn main() {
     let lower_bound_fn = |n: &Node| {
         let current_profit = total_profit(n);
         let max_remained_profit: u32 = profits[n.len()..].into_iter().sum();
-        u32::MAX - (current_profit + max_remained_profit)
+        Some(u32::MAX - (current_profit + max_remained_profit))
     };
 
-    let cost_fn = |n: &Node| u32::MAX - total_profit(n);
+    let cost_fn = |n: &Node| Some(u32::MAX - total_profit(n));
 
     let leaf_check_fn = |n: &Node| n.len() == total_items;
 
diff --git a/examples/bbs_knapsack_problem.rs b/examples/bbs_knapsack_problem.rs
index db1afbb..97e4c24 100644
--- a/examples/bbs_knapsack_problem.rs
+++ b/examples/bbs_knapsack_problem.rs
@@ -60,10 +60,10 @@ fn main() {
     let lower_bound_fn = |n: &Node| {
         let current_profit = total_profit(n);
         let max_remained_profit: u32 = profits[n.len()..].into_iter().sum();
-        u32::MAX - (current_profit + max_remained_profit)
+        Some(u32::MAX - (current_profit + max_remained_profit))
     };
 
-    let cost_fn = |n: &Node| u32::MAX - total_profit(n);
+    let cost_fn = |n: &Node| Some(u32::MAX - total_profit(n));
 
     let leaf_check_fn = |n: &Node| n.len() == total_items;
 
diff --git a/src/bbs.rs b/src/bbs.rs
index cfcfdf3..5d6ef72 100644
--- a/src/bbs.rs
+++ b/src/bbs.rs
@@ -16,16 +16,19 @@ where
     N: Clone,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
 {
     type Item = N;
 
     fn next(&mut self) -> Option<Self::Item> {
         if let Some(n) = self.to_see.pop() {
-            if (self.lower_bound_fn)(&n) <= self.current_best_cost {
-                for s in (self.successor_fn)(&n) {
-                    self.to_see.push(s.clone());
+            // get lower bound
+            if let Some(lb) = (self.lower_bound_fn)(&n) {
+                if lb <= self.current_best_cost {
+                    for s in (self.successor_fn)(&n) {
+                        self.to_see.push(s.clone());
+                    }
                 }
             }
             Some(n)
@@ -40,7 +43,7 @@ where
     N: Clone,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
 {
 }
@@ -55,7 +58,7 @@ where
     N: Clone,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
 {
     BbsReachable {
@@ -86,8 +89,8 @@ where
     N: Clone,
     IN: IntoIterator<Item = N>,
     FN: FnMut(&N) -> IN,
-    FC1: Fn(&N) -> C,
-    FC2: Fn(&N) -> C,
+    FC1: Fn(&N) -> Option<C>,
+    FC2: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
     FR: Fn(&N) -> bool,
 {
@@ -100,10 +103,11 @@ where
         }
         let n = op_n.unwrap();
         if leaf_check_fn(&n) {
-            let cost = cost_fn(&n);
-            if res.current_best_cost > cost {
-                res.current_best_cost = cost;
-                best_leaf_node = Some(n)
+            if let Some(cost) = cost_fn(&n) {
+                if res.current_best_cost > cost {
+                    res.current_best_cost = cost;
+                    best_leaf_node = Some(n)
+                }
             }
         }
     }
@@ -175,10 +179,10 @@ mod test {
         let lower_bound_fn = |n: &Node| {
             let current_profit = total_profit(n);
             let max_remained_profit: u32 = profits[n.len()..].into_iter().sum();
-            u32::MAX - (current_profit + max_remained_profit)
+            Some(u32::MAX - (current_profit + max_remained_profit))
         };
 
-        let cost_fn = |n: &Node| u32::MAX - total_profit(n);
+        let cost_fn = |n: &Node| Some(u32::MAX - total_profit(n));
 
         let leaf_check_fn = |n: &Node| n.len() == total_items;
 
diff --git a/src/bfs.rs b/src/bfs.rs
index ab3152d..3ca9ab5 100644
--- a/src/bfs.rs
+++ b/src/bfs.rs
@@ -22,14 +22,14 @@ where
     N: Clone,
     IN: IntoIterator<Item = N>,
     FN: FnMut(&N) -> IN,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
     FR: Fn(&N) -> bool,
 {
     bms(
         start,
         successor_fn,
-        |_| C::min_value(),
+        |_| Some(C::min_value()),
         usize::MAX,
         usize::MAX,
         cost_fn,
@@ -95,7 +95,7 @@ mod test {
                     }
                 })
                 .sum();
-            u32::MAX - cost
+            Some(u32::MAX - cost)
         };
 
         let leaf_check_fn = |n: &Node| n.len() == total_items;
diff --git a/src/bms.rs b/src/bms.rs
index d0e46d2..d40452d 100644
--- a/src/bms.rs
+++ b/src/bms.rs
@@ -48,7 +48,7 @@ where
     N: Clone,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
 {
     type Item = N;
@@ -64,7 +64,10 @@ where
         if let Some(node) = self.to_see.pop_front() {
             let mut successors: Vec<_> = (self.successor_fn)(&node)
                 .into_iter()
-                .map(|n| ((self.eval_fn)(&n), n))
+                .filter_map(|n| {
+                    let cost = (self.eval_fn)(&n)?;
+                    Some((cost, n))
+                })
                 .collect();
             successors.sort_unstable_by_key(|x| x.0);
             successors
@@ -90,7 +93,7 @@ where
     N: Clone,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
 {
     BmsReachable {
@@ -127,8 +130,8 @@ where
     N: Clone,
     IN: IntoIterator<Item = N>,
     FN: FnMut(&N) -> IN,
-    FC1: Fn(&N) -> C,
-    FC2: Fn(&N) -> C,
+    FC1: Fn(&N) -> Option<C>,
+    FC2: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
     FR: Fn(&N) -> bool,
 {
@@ -142,10 +145,11 @@ where
         }
         let n = op_n.unwrap();
         if leaf_check_fn(&n) {
-            let cost = cost_fn(&n);
-            if current_best_cost > cost {
-                current_best_cost = cost;
-                best_leaf_node = Some(n)
+            if let Some(cost) = cost_fn(&n) {
+                if current_best_cost > cost {
+                    current_best_cost = cost;
+                    best_leaf_node = Some(n)
+                }
             }
         }
     }
@@ -310,12 +314,12 @@ mod test {
         let eval_fn = |n: &Node| {
             let (remained_duration, route) =
                 greedy_tsp_solver(n.city, n.children.clone(), &time_func);
-            n.t + remained_duration + time_func(*route.last().unwrap(), start)
+            Some(n.t + remained_duration + time_func(*route.last().unwrap(), start))
         };
 
         let branch_factor = 10;
         let beam_width = 5;
-        let cost_fn = |n: &Node| n.t + time_func(n.city, start);
+        let cost_fn = |n: &Node| Some(n.t + time_func(n.city, start));
         let leaf_check_fn = |n: &Node| n.is_leaf();
 
         let (cost, best_node) = bms(
diff --git a/src/dfs.rs b/src/dfs.rs
index b4af6fb..983a43d 100644
--- a/src/dfs.rs
+++ b/src/dfs.rs
@@ -22,14 +22,14 @@ where
     N: Clone,
     IN: IntoIterator<Item = N>,
     FN: FnMut(&N) -> IN,
-    FC: Fn(&N) -> C,
+    FC: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
     FR: Fn(&N) -> bool,
 {
     bbs(
         start,
         successor_fn,
-        |_| C::min_value(),
+        |_| Some(C::min_value()),
         cost_fn,
         leaf_check_fn,
     )
@@ -93,7 +93,7 @@ mod test {
                     }
                 })
                 .sum();
-            u32::MAX - cost
+            Some(u32::MAX - cost)
         };
 
         let leaf_check_fn = |n: &Node| n.len() == total_items;
diff --git a/src/gds.rs b/src/gds.rs
index d1c176f..3ba1de5 100644
--- a/src/gds.rs
+++ b/src/gds.rs
@@ -24,8 +24,8 @@ where
     N: Clone,
     IN: IntoIterator<Item = N>,
     FN: FnMut(&N) -> IN,
-    FC1: Fn(&N) -> C,
-    FC2: Fn(&N) -> C,
+    FC1: Fn(&N) -> Option<C>,
+    FC2: Fn(&N) -> Option<C>,
     C: Ord + Copy + Bounded,
     FR: Fn(&N) -> bool,
 {
@@ -168,9 +168,9 @@ mod test {
         let time_func = |p: CityId, c: CityId| distance_matrix[p][c];
 
         let successor_fn = |n: &Node| n.generate_child_nodes(&time_func);
-        let eval_fn = |n: &Node| n.t;
+        let eval_fn = |n: &Node| Some(n.t);
 
-        let cost_fn = |n: &Node| n.t + time_func(n.city, start);
+        let cost_fn = |n: &Node| Some(n.t + time_func(n.city, start));
         let leaf_check_fn = |n: &Node| n.is_leaf();
 
         let (cost, best_node) =