The Erythea Campaign
Time Limit: 2 Seconds
Memory Limit: 65536 KB
O' mighty warrior,
Thy mission is to slay the foul king of Erythea.
Thou shall find him in his realm in the south.
God bless you,
King of Isladia.
After reading the order, you know you have a long, dangerous way down to the
south, to find the king of Erythea in his realm and kill him. The Erythea realm
is a rectangular region, with a number of horrible strongholds in it. Impenetrable
walls enclose the region, so the only way for you to enter the realm is to fly
by your Pegasus (flying horse) and land in some point in the region. The hiding
place of the king is known so you just need to find your way to that location.
As the area is extensive and covered by different terrain types, you have to
travel on the grid-like roads in the region. The problem is, there are many
guards on the towers of strongholds who can see you, and once seen, you have
no chance to see your family again! The closer you travel to the strongholds,
the greater the chances to be seen by the guards. The problem is to find the
safest way from the point your Pegasus lands to the point where the king is.
More abstractly, you have an m X n grid with squares of the same size, denoting
the realm and the roads in it. You can travel along the lines in the grid (roads),
and at each intersection (road crossing) you may turn into another road. Assume
each stronghold comprises a set of adjacent squares of the grid (Figure 1).
As you cannot enter a stronghold, your path never intersects the interior of
a stronghold, yet you can travel on a road which is on stronghold boundaries
(Figure 2). Suppose you can land your Pegasus exactly on a road crossing (the
source point - S in Figure 1) and the hiding place of the king is on another
road crossing (the destination point - D in Figure 1). Neither of these points
lie inside a stronghold but may be placed on a stronghold boundary (as D does
in Figure 1). Each road crossing is assigned a risk level which depends on the
shortest road distance from the crossing to a point of the grid which is on
the boundary of a stronghold. For a road crossing with the shortest road distance
d to a boundary of strongholds, the risk level equals to m + n - d (Figure 3).
It is assumed that there is at least one stronghold in the region, so that the
definition of risk level is well-defined. The problem is, given the region's
map and the source and destination points, find the path from the source to
the destination which lies on the grid lines, so that sum of the risk levels
of the points on the path (including source and destination) be minimum. As
stated before, the path cannot intersect the interior of a stronghold.
The input file consists of several test cases. The first line of the file contains
a single number M, which is the number of test cases in the file (1 <= M
<= 10). The rest of the file consists of the data of the test cases. Each
test case data begins with a line containing the number of rows and the number
of columns in the grid, which are in the range 1 to 80. The second line of a
test case contains two pairs of integers, which are y and x coordinates of the
source point (where the Pegasus landed) and the y and x coordinates of the destination
point (where you may find the king). The horizontal and vertical lines in the
grid are indexed from left to right and top to bottom from 0, so the coordinates
can be expressed using these indices.
Following the first two lines, there are lines that describe the map of the
region. Each line consists of a string of 0's and 1's, describing squares of
the corresponding row. A 1 in the string tells you that the corresponding square
in the grid belongs to a stronghold. The width of the region is the length of
all strings, and its height in the number of strings.
The output for each test case is the total risk of the minimum risk path from
the landing point to the destination. Recall that the total risk of a path is
sum of the risk levels of the points in the path (including source and destination).
If no path exists between source and destination, the output should be 'no solution'.
The output for each test case must be written on a separate line.
1 5 7 1
4 0 1 5
The above input file contains two test cases. The first test case is the one
shown in Figure 1.
Source: Asia 1999, Tehran (Iran)