| # | Problem | Pass Rate (passed user / total user) |
|---|---|---|
| 11131 | Transition probability |
|
| 11160 | GCD and LCM |
|
| 12443 | Permutations |
|
Description
Bob is a businessman. He always stays at city A or city B.
Assume Bob stays at city A today , and we can use a transition matrix P to infer the probability of at which city will Bob stays tomorrow.
e.g.
Let VnT = [ va , vb ]Vn is a 2 by 1 column vector.
va denotes the probability that Bob stays at city A on n-th day,
vb denotes the probability that Bob stay at city B on n-th day.
After 1 day, the probability should be represented as Vn+1 , where Vn+1 = P * Vn.
P is a 2 by 2 square matrix, representing the transition probability:
P = ┌ p1 p2 ┐
└ p3 p4 ┘
As time passes, the probability of Bob staying at city A will decrease.
After n days, the probability of Bob staying at city A will smaller than or equal to a target value T.
The question is :
Suppose that Bob stays at city A today ( va = 1 , vb = 0)
How many days do we need to make va smaller than or equal to the target value T ?
Namely , n = ?
Note :
The test case will make va monotonically decrease .
助教出的測資一定會讓 va 隨著時間增加而逐漸遞減
Input
There are multiple testcases in the input.
The first line contains a integer N, indicating the number of testcases.
You can use this format in your code:
int i , N;
scanf("%d",&N);
for(i=0;i<N;i++){
// your code to deal with each testcase
}
The following lines are testcases.
For each testcase, there are 5 floating points in a line.
The 1st ~ 4th floating points (p1, p2, p3, p4) are the elements in trasition matrix P.
The 5th floating point is the target value T.
Output
For each testcase.
Output integer n that tell us how many days should we take to reach the target probability.
And add a '\n' at the end of each output.
Sample Input Download
Sample Output Download
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Description
Given three positive integers x, y, and z, compute their greatest common divisor (GCD) and least common multiple (LCM).
Input
The first line contains a positive integer N, which indicates the number of test cases in each input.
In the next N lines, each line contains three positive integer x, y, z.
Level 1: x, y, z < 10
Level 2: x, y, z < 10^2
Level 3: x, y, z < 10^3
Level 4: x, y, z < 10^4
Output
For each test case, output the GCD and LCM of x, y, and z in a line.
Note that you have to add '\n' at the end of output.
Sample Input Download
Sample Output Download
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Description
A permutation, also called an “arrangement number” or “order,” is a rearrangement of the elements of an ordered list into a one-to-one correspondence S_i. A string of length N has N! permutation. You need to show all results.
ORDER is important !! You should display it in lexicographic order.
ex. N=3,
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Input
N
1<=N<=6
Output
S_i is a sequence each element followed by a space.
S_1
S_2
.
.
.
S_N!
You still need to change line in the last line.