| # | Problem | Pass Rate (passed user / total user) |
|---|---|---|
| 9124 | Power |
|
| 9128 | Alphabetically order |
|
| 9132 | Connected Component |
|
| 9136 | Empty Circumcircle Problem |
|
| 9140 | Minimum Product Spanning Tree |
|
Description
Compute ab for the given integers a and b.
Input
The first line of input contains a positive integer t (t <= 100), which indicates the number of test cases. For each case, there are two positive integers a, b in a line (a ,b < 250).
Output
For each test case, output 
in a single line.
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Description
Given two strings, output them in alphabetical order.
Note: the order is AaBbCcDd ... YyZz.
Input
The first line of input contains a positive integer t (t <= 10000), which indicates the number of test cases. For each case a line, there are two strings separated by a single space. The lengths of the strings are no more than 10000.
Output
For each case a line, output the two strings in alphabetical order, separated by a single space.
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Description
Given an undirected graph with several connected components, find the one with the largest number of nodes. A connected component is a subset of nodes in which any two nodes are connected to each other by paths, and which is connected to no additional nodes.
Input
There will be several test cases. In each test case, the first line will be an integer N ( 0 < N <= 100000 ) representing the number of nodes. The second line contains an integer K(0<=K<=1000000) which is the number of edges. In the next K lines, each line contains two integers, A and B ( 0 <= A, B < N ), which are two end nodes of an undirected edge. If N = 0, the input ends.
Output
For each graph, print the number of nodes for the largest connected component.
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Given a triangle and a point p, check whether the interior of the circumcircle of the triangle is empty or it contains the point p. If the interior of the circumcircle of the triangle is empty, then output “yes”; otherwise, output “no”. A circumcircle center of a triangle is a point whose distances to the three points of the triangle are the same. The coordinates of all input points are integers. However, the center of the circumcircle can be general real numbers.
Notice: If point p is on the boundary of the circumcircle, it should be consider inside the circumcircle.
Input
The input contains several test cases. In each test case, there are eight integers representing the three coordinates of a triangle and the point p on a 2D plane. All the input integers are ranged from -10000 to 10000. You can assume that the area of the triangle is greater than 0.
Output
For each test case, print whether the corresponding circumcircle is empty. If it is empty, then print “yes”; otherwise, print “no”.
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Description
A spanning tree of a graph G = (V, E) is a subset of edges from E that forms a tree connecting all vertices of V. Suppose that G is edge-weighted and all edge weights are positive. Then a minimum product spanning tree of G is defined to be a spanning tree of G that minimizes the product of tree edge weights. Given an edge-weighted graph as shown in Figure 1, for example, the tree shown in Figure 2 is a minimum product spanning tree of this graph. Please write a program to show a minimum product spanning tree of a given edge-weighted graph. In order to make the answer fits in reasonable space, we ask only the natural logarithm of the weight of the spanning tree.
Figure 1: An edge-weighted graph whose weights are positive.
Figure 2: A minimum product spanning tree of the edge-weighted graph as shown in Figure 1.
Input
The input file contains multiple test cases. Each case begins with a line of two integers n (2 ≤ n ≤ 100) and m (1 ≤ m ≤ 4950), where n is the number of vertices and m is the number of edges in the graph. After that, there are m lines each containing three integers u, v and w (1 ≤ u, v ≤ n, u ≠ v, 0 < w ≤ 214) describing an edge of weight w connecting vertices u and v. You may assume that no two vertices are directly connected by more than one edge, and the given graph is connected. There is a blank line between two successive cases, and the input is terminated by end-of-file.
Output
For each case, print “Case i: d” in a line, where i is the test case number starting from 1, and d is the natural logarithm of the product of edge weights in a minimum product spanning tree, rounded to 2 digits after the decimal point. You may assume that the accumulated floating point error would not cause difference to the printed answer. Note that there is a single space character before i and d.
Hint
To calculate the natural logarithm of a number, you may use the “log” function by including
| double | log ( | double x ); |
| float | log ( | float x ); |
| long double | log ( | long double x ); |
This function receives a floating point number x as parameter, and return the natural logarithm of x. Note that in C, only the double version of this function exists with this name.