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Can We Build This One?
Description ¡°Highways
are built, then life is rich.¡± Now people of Big Town want to become
rich, so they are planning to build highways to connect their villages. Big
Town is really big and has many villages. Its people plan to build some
highways between some pairs of villages so that every pair of villages
is connected by the highways either directly or indirectly. After
surveying the geographical surroundings, they find that there are some
paths along with highways can be built. Every path is denoted by a
triplet (a, b, c) which means a highway can built between the a-th village and the b-th village with a cost of c.
In order to save money, they will select only part of the paths to
build highways along so that the total cost to build highways along the
selected paths is minimal under the condition that every pair of
villages is connected. It is possible that multiple such
selections exist. People from every village want to have those highways
of good interest to them built. But some highways can never appear in
the selection since they are much too costly. So people ask whether a
certain highway can be selected if they agree to cut the cost. Your
task is to design a program to answer their queries. Input The first line of input contains three integers N, M and Q (1 < N ¡Ü 1,000, N − 1 ¡Ü M ¡Ü 100,000, 0 < Q ¡Ü 100,000), where N is the number of villages, M is the number of paths, and Q is the number of queries. Each of the next M lines contains three integers a, b, and c (1 ¡Ü a, b ¡Ü N, a ¡Ù b, 0 ¡Ü c ¡Ü 1,000,000). The triplet (a, b, c) describes a path. Each of following Q lines contains two integer i and x (1 ¡Ü i ¡Ü M, 0 ¡Ü x) describing a query, ¡°Can a highway be built along the i-th path if the cost of is reduced to x?¡± x is strictly lower than the original cost of building a highway along the i-th
path. It is assumed that every pair of village will be connected either
directly or indirectly if all possible highways are built. And there
may be more than one highway that can be built between a pair of
villages. Output Output one line for each query. Output either ¡°Yes¡± or ¡°No¡± as the answer to the the query. Sample Input Sample Output Source |
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