雅虎北京研究院hack大赛

Question 1 / 5 (Problem A)

Given a rational number expressed as A/B where A and B are integers, find the position of M^th occurrence of digit D (0-9) after decimal point. For example 3/7 = 0.4285714285... (A=3, B=7), so the 2nd (M=2) 4 (D=4) is the 7th digit after decimal point.

Limits:

• 0 < A, B, M < 2 x 10⁸

• 0 <= D <= 9

Input:

The first line of the input gives the number of test cases, N. N test cases follow. Each test case consists of one line containing 4 numbers, A, B, M and D separated by spaces.

Output:

Each line contains the position (starting from 1) of the specified digit D. Output “0” if it is impossible to find the digit.

Sample:

InputOutut

7
3 7 1 1
3 7 2 2
3 7 3 6
5 11 2 3
5 11 3 7
20 193 20 6
200000 19893 50 8

6
8
0
0
0
191
470

Test case: (Please write a program to read the test case input data below from STDIN and print the output to STDOUT in the format as described above)

30
3 7 1 1
3 7 2 2
3 7 3 6
5 11 2 3
5 11 3 7
20 193 20 6
200000 19893 50 8
2 18 999 1
121 10000 2 1
121 10000 3 1
121 10000 1 5
1 1 1 1
12 21 21 2
123 321 321 3
1234 4321 4321 4
12345 54321 54321 5
123456 654321 654321 6
1234567 7654321 7654321 7
12345678 87654321 87654321 8
21 12 21 2
321 123 321 3
4321 1234 4321 4
54321 12345 54321 5
654321 123456 654321 6
7654321 1234567 7654321 7
87654321 12345678 87654321 8
24691111 199998000 1 3
24691111 199998000 100 5
24691111 199998000 5 3
24691111 199998000 99999999 9 

 

Question 2 / 5

Given a N*N grid where N is an even number and 6 points A, B, C, D, E and F. The coordinates of each point are (x_a, y_a), (x_b, y_b), ..., (x_f, y_f). Define S to be the following.

S = 2 * (S_ABC + S_DEF) where S_ABC and S_DEF are the area of the triangle ABC and DEF.

Below is an example of 4*4 grid. In this case S = 2 * S_ABC + 2 * S_DEF= 6 + 8 = 14.

Now your task is, given an arbitrary S, find one possible solution of the 6 points that meets the above requirement.

Limits:

• x_a, y_a, x_b, y_b, ..., x_f, y_f are integers between 0 and N.
• N and S are natural numbers.
• 0 < N, S < 10¹⁰

Input:

The first line of the input gives the number of test cases, N. N test cases follow. Each test case consists of one line containing 2 numbers, N and S separated by one space.

Output:

The coordinates of A, B, C, D, E and F. If no possible solution can be found, output the word “impossible” (quotes for clarity).

Sample:

InputOutput

3
4 14
4 36
6 21

0 0 1 4 2 1 0 0 1 4 2 1
impossible
0 0 1 6 2 2 0 0 1 6 2 1

Test case: (Please write a program to read the test case input data below from STDIN and print the output to STDOUT in the format as described above)

13
4 14
4 36
100 9999
100 19999
100 20000
100 20001
12 21
123 321
1234 4321
12345 54321
123456 654321
1234567 7654321
12345678 87654321

 

Question 3 / 5 (Problem C)

You are given N line segments, with each line segment depicted by its starting and ending points, calculate the longest continuous line segment with the given line segments set.

Limits:

• 1 < N < 100
• ​The starting and ending point integer ranges from 0 to 10,000

Input:

The first line of the input is the number of line segments N, each following line has two integers depicting the starting and ending points, respectively.

Output:

Length of longest consecutive line segment.

Sample:

InputOutput

5
0  1
0  5
7  10
8  12
1  3

5

With the given input set, the longest continuous line segment starts at 0 and ends at 5 (or starts at 7 and ends at 12), gives the length 5.

Test case: (Please write a program to read the test case input data below from STDIN and print the output to STDOUT in the format as described above)

 

Question 4 / 5

Given a source M*N matrix A and a target M*N matrix B, elements in each matrix are integers of range 0 ~ (M*N-1), each integer only appears once in the same matrix. Please find the steps to change matrix A to B. The rules are:

• Only “0” can switch with neighbor element. A neighbor element is the one that is to the left/right/top/bottom of “0”.

• Certain values in matrix A cannot be changed, they are designated in array C.

Input:

First line is M, N separated by space, followed by M lines of elements in matrix A, then followed by M lines of elements in matrix B, then followed by a line of elements in array C. Values in each line are separated by spaces.

Output:

One line with X steps, separated by space. Each step is the value of element that would switch with “0”.

Sample:

 

For A= [0 1 2
3 4 5
6 7 8], B= [3 1 2 
6 4 5
0 7 8], C=[1]InputOutput

3 3
0 1 2
3 4 5
6 7 8
3 1 2
6 4 5
0 7 8
1

3 6

Test case: (Please write a program to read the test case input data below from STDIN and print the output to STDOUT in the format as described above)

3 3
0 1 2
3 4 5
6 7 8
3 1 2
6 4 5
0 7 8
1

Scoring: The sample test-case is not worth any points. Your code should be able to clear the hidden test-cases which we'll run after the contest. Depending on how many test-cases your code passes, you'll get a score.

 

Question 5 / 5

A palindrome is a word, phrase, number, or sentence, whose meaning may be interpreted the same way in either forward or reverse direction.

Some well-known English palindromes are, "Able was I ere I saw Elba", "A man, a plan, a canal Panama!",  "Madam, I'm Adam" or "Madam in Eden, I'm Adam", "Doc, note: I dissent. A fast never prevents a fatness. I diet on cod" and "Never odd or even".

You are given a list of words, please use those words to find out the longest palindrome, with as many characters as you can.

Notes:

1. The sentence need not to be logically meaningful nor grammatically correct, it can be any combination of the words;

2. Palindrom's are case insensitive, e.g. letter 'E' is considered same as letter 'e';

3. You can only use the words in the given list;

4. Each word can be used at most once;

5. Word list may contain 1~100000 words.

Input:

First line is the number of the words in the list, then followed by the list of words, with one word in each line.

Output:

Just output any of the longest sentence you found. If the given list can’t construct a valid palindrome sentence, just output “impossible”.

Sample:

InputOutput5
ate
Lisa
Bonet
basil
no

Lisa Bonet ate no basil

 

Sample 2:

InputOutput8
cat
in
Oozy
zoo
park
a
sanitary
rat

oozy rat in a sanitary zoo

Sample 3:

InputOutput

5
too
hard
to
get
​one

impossible

 

Test cases: (Please write a program to read the test case data from STDIN and print the output to STDOUT in the format described above).