Computer Science Club
The best thing about a boolean is even if
you are wrong, you are only off by a bit.
USACO
• It’s over!
• You can find analysis and test data at
ace.delos.com/OCT10B.htm (or 10S, 10G)
• If you “missed” it, go take it next weekend
• Nov.5-8
• You can still qualify for the next division by
getting ~85%
• Note that Gold #1 was almost the same as
the problem of the week… (the knapsack
one)
USACO Silver #2
• Count the number of lakes
• Recursive flood-fill (also known
as dfs or depth first search)
• Begin the recursion at each
unvisited point
• Mark points visited as you visit
them
• At each step, continue the
recursion to each unvisited
neighbor
• Each time you restart the
recursion, you have found a new
lake
W........WW.
.WWW.....WWW
....WW...WW.
.........WW.
.........W..
..W......W..
.W.W.....WW.
W.W.W.....W.
.W.W......W.
..W.......W.
Code for Flood Fill
int countlakes()
{
int groupc=0;
for(int x=0;x<numX;x++)
for(int y=0;y<numY;y++)
if(!vis[x][y]) // not visited yet
{
dfs(x,y); // start recursion
groupc++; // increment count
}
return groupc;
}
Code for Flood Fill (cont.)
int[] mx={-1,-1,-1,0,0,1,1,1}; // movement arrays
int[] my={-1,0,1,-1,1,-1,0,1}; // save a lot of typing!
void dfs(int x,int y)
{
if(x<0 || x>=numX || y<0 || y>=numY || vis[x][y])
return; // out of bounds or already visited
vis[x][y]=true; // mark as visited
for(int m=0;m<8;m++) // go through movement array
dfs(x+mx[m],y+my[m]); // recurse
}
Dijkstra’s Algorithm
Used to find the shortest path
between a starting position and
destination.
Given a graph with specified distances
of the directional paths between
nodes:
Task: Find the shortest path from
Node a (initial node) to Node f
(destination).
For example, A-C-D-F has a distance
of
3 + 10 + 2 = 15.
The path A-C-E-F has a distance of
3 + 3 + 5 = 11.
Is there a path even SHORTER than
that? Can you be sure your path is the
shortest possible?
Dijkstra’s cont… The Steps
Step 1: Each node has a
distance value. (a = 0, others =
∞)
3
Step 2: Two node sets: visited
and unvisited (init: none visited)
Step 3: a = curNode
Step 4: (recursive step!)
- Update unvisited neighbors of
curNode with new shortest dist
- move curNode to visited set
- new curNode = smallest
unvisited node
2
Dijkstra’s cont…Finishing Up
When curNode = destination,
shortest path = value of final
node.
Try to trace the algorithm and
find the shortest path and
minimal distance.
Consider…
Why don’t we need to recheck visited nodes? Why
can’t there be a shorter path
to a visited node?
3
2
REMEMBER…
 The first real USACO round will be this
weekend!
Practice with the free USACO Training lessons:
http://ace.delos.com/usacogate
 Sign in!
 Have fun coding 