Limits
2s, 512 MB

Mr. J wants to learn about combinatorics. He started reading a book on combinatorics and came across this problem:

A town, rectangular in shape, has a grid-like street network. It consists of x+1 parallel lines headed north-south and y+1 parallel lines headed east-west. You can think of Manhattan as an example. In how many ways can a car reach the north-east corner if it starts in the south-west comer and travels only in the east and north directions?"

So the problem is, you are at $A$ $(0, 0)$ position in a grid. You can only go to the right or towards the top. You have to determine, how many ways you can go to $B$ $(x, y)$.

Now Mr. J found the solution of the problem in the book, and he started to wonder what if he adds a third dimension to this problem.

Imagine there is a box with $x$ width, $y$ height and $z$ depth. You are standing in one corner $(0, 0, 0)$. In each move, you can only go front (+1 in X dimension), right (+1 in Y dimension) and towards the top (+1 in Z dimension). So from $(A, B, C)$ you can go to $(A+1, B, C)$, $(A, B+1, C)$, or $(A, B, C+1)$ in one move.

Now determine how many ways you can go to the corner $(x, y, z)$ from $(0, 0, 0)$. Two ways are considered different if after any one of the moves they are in a different position in the box.

The first line of the input is $T$ ($1 ≤ T ≤ 150$), the number of test cases. Then $T$ test cases follow.

Each test case has 3 integers $x$, $y$, $z$ ($1 ≤ x, y, z ≤ 5$) in a line. They represent the width, the height and the depth of the box respectively.

For each test case, print a line in "Case #K: R" format where K is the case number and R is the desired result.

Input | Output |
---|---|

3 1 1 1 1 1 2 2 1 1 | Case #1: 6 Case #2: 12 Case #3: 12 |

Login to submit.

79%
Solution Ratio

Sherlock221bEarliest,

Tarik.amtolyFastest, 0.0s

RobinHood3082Lightest, 0 B

aNkanpy.pritomShortest, 159B

Toph uses cookies. By continuing you agree to our Cookie Policy.