uva 10917

Problem C: A Walk Through the Forest

Jimmy experiences a lot of stress at work these days, especially since
his accident made working difficult. To relax after a hard day, he likes to walk
home. To make things even nicer, his office is on one side of a forest, and his
house is on the other. A nice walk through the forest, seeing the birds and
chipmunks is quite enjoyable.

The forest is beautiful, and Jimmy wants to take a different route everyday.
He also wants to get home before dark, so he always takes a path to make
progress towards his house. He considers taking a path
from A to B to be progress if there exists
a route from B to his home that is shorter than any possible
route from A. Calculate how many different routes through the
forest Jimmy might take.

Input

Input contains several test cases followed by a line containing 0.
Jimmy has numbered each intersection or joining of paths starting with 1. His
office is numbered 1, and his house is numbered 2. The first line of each test
case gives the number of intersections N, 1
< N ≤ 1000, and the number of
paths M. The
followingM lines each contain a pair of
intersections a b and
an integer distance 1 ≤ d ≤ 1000000 indicating a
path of length d between
intersection a and a different
intersection b. Jimmy may walk a path any direction
he chooses. There is at most one path between any pair of
intersections.

Output

For each test case, output a single integer indicating the number of
different routes through the forest. You may assume that this number does not
exceed 2147483647.

Sample Input

5 6

1 3 2

1 4 2

3 4 3

1 5 12

4 2 34

5 2 24

7 8

1 3 1

1 4 1

3 7 1

7 4 1

7 5 1

6 7 1

5 2 1

6 2 1

0

Output for Sample Input

2

4

根据终点走最短路，然后根据题意建图，易知为DAG，记忆化搜索求路径长度即可。