usaco-guide/content/4_Silver/DFS.md

id	title	author	prerequisites	description
dfs	Depth First Search	Siyong Huang	Bronze - Introduction to Graphs	A way to traverse a graph using recursion.

Depth First Search

• CSES Building Roads

Tutorial

• Recommended:
  • CPH 12.1
  • CSAcademy DFS
• Additional:
  • CPC.7
  • cp-algo DFS
    • hard to parse if this is your first time learning about DFS
  • Topcoder Graphs Pt 2

Problems

• CSES Trees
  • Subordinates
  • Tree Distances I
  • Tree Distances II
• CF
  • PolandBall & Forest
  • Bear & Friendship
  • Journey
    • DFS on Tree
• Wizard's Tour
• USACO
  • Mootube, Silver (Easy)
  • Closing the Barn, Silver (Easy)
  • Moocast, Silver (Easy)
  • Pails (Normal)
  • Milk Visits (Normal)
  • Count Cross
  • Wormhole Sort (Normal)
    • also binary search on the answer
  • Fence Planning
  • Moo Particle
• Other
  • POI Hotels
  • Kattis Birthday Party (Easy)
    • DFS with each edge removed

Graph Two-Coloring

Graph two-coloring refers to assigning a boolean value to each node of the graph, dictated by the edge configuration The most common example of a two-colored graph is a bipartite graph, in which each edge connects two nodes of opposite colors.

• CSES Building Teams

Tutorial

The idea is that we can arbitrarily label a node and then run DFS. Every time we visit a new (unvisited) node, we set its color based on the edge rule. When we visit a previously visited node, check to see whether its color matches the edge rule. For example, an implementation of coloring a bipartite graph is shown below.

//UNTESTED

bool is_bipartite = true;
void dfs(int node)
{
  visited[node] = true;
  for(int u:adj_list[node])
    if(visited[u])
    {
      if(color[u] == color[node])
        is_bipartite = false;
    }
    else
    {
      color[u] = !color[node];
      dfs(u);
    }
}

• Additional:
  • Bipartite Graphs: cp-alg bipartite check
    • Note: CP-Algorithms uses BFS, but DFS accomplishes the same task

Problems

• CF Bipartiteness
• The Great Revegetation (Normal)