add assert for par of centroid tree

Author: lrvideckis

tests/library_checker_aizu_tests/cd_asserts.hpp

@@ -2,25 +2,28 @@
 #include "../../library/trees/centroid_decomp.hpp"
 void cd_asserts(const vector<vector<int>>& adj) {
   vector<int> decomp_size(sz(adj), -1);
+  vector<int> naive_par_decomp(sz(adj), -1);
   centroid(adj,
-    [&](const vector<vector<int>>& cd_adj, int cent,
-      int par_cent) -> void {
-      assert(decomp_size[cent] == -1);
-      auto dfs = [&](auto&& self, int u, int p) -> int {
-        int sub_size = 1;
-        for (int v : cd_adj[u])
-          if (v != p) sub_size += self(self, v, u);
-        return sub_size;
-      };
-      decomp_size[cent] = dfs(dfs, cent, -1);
-      if (par_cent != -1)
-        assert(1 <= decomp_size[cent] &&
-          2 * decomp_size[cent] <= decomp_size[par_cent]);
-      for (int u : cd_adj[cent]) {
-        int sz_subtree = dfs(dfs, u, cent);
-        assert(1 <= sz_subtree &&
-          2 * sz_subtree <= decomp_size[cent]);
-      }
-    });
+           [&](const vector<vector<int>>& cd_adj, int cent,
+               int par_cent) -> void {
+             assert(naive_par_decomp[cent] == par_cent);
+             assert(decomp_size[cent] == -1);
+             auto dfs = [&](auto&& self, int u, int p) -> int {
+               naive_par_decomp[u] = cent;
+               int sub_size = 1;
+               for (int v : cd_adj[u])
+                 if (v != p) sub_size += self(self, v, u);
+               return sub_size;
+             };
+             decomp_size[cent] = dfs(dfs, cent, -1);
+             if (par_cent != -1)
+               assert(1 <= decomp_size[cent] &&
+                      2 * decomp_size[cent] <= decomp_size[par_cent]);
+             for (int u : cd_adj[cent]) {
+               int sz_subtree = dfs(dfs, u, cent);
+               assert(1 <= sz_subtree &&
+                      2 * sz_subtree <= decomp_size[cent]);
+             }
+           });
   rep(i, 0, sz(adj)) assert(decomp_size[i] >= 1);
 }