## Sunday, July 31, 2016

### TCS Code Vita Season-5 Round-1 set-2 Program-8

3D Maze problem

Suppose, an ant is trapped in a maze, with only one way in and one way out.

The maze is a cubic-lattice like structure of dimension NxNxN (Length=Breadth=Height=N). The way in is the left-bottom most point, and the way out is the right top-most point (along the principal diagonal). The below picture shows the maze for N=2.

Figure 1.
Assuming the ant only moves right, forward or upwards along the grids of the maze, calculate the total number of ways in which the ant can escape. Mathematically right, forward and upwards are defined at positive changes in co-ordinates on x, y and z axes respectively.

Example:
For, N=1, the grid structure and solution is shown below:

Figure 2.

Thus, for N=1, we have a net of 6 ways.

Input Format:

Single integer N
Output Format:

Output also consists of a single number corresponding to the number of ways the ant can escape the maze.
Constraints:
• 0<N<=8

Example
 Example Number Sample Input Sample Output 1 1 6 2 2 90

### TCS Code Vita Season-5 Round-1 set-2 Program-7

Problem : Pivot Table
According to Wikipedia, a Pivot Table is a useful summarization tool in data processing. Your task is to implement a Pivot tableaccording to given requirements

Requirements
1.    Must work against a data table of arbitrary sizes
2.    Data types to be supported are String and Numbers
3.    Must support the following aggregation functions - Sum, Count, Average, Invert (transpose)
4.    Must take inputs on which column to use as a Pivot and which column to use an aggregation function on
5.    The aggregated Pivot table must be sorted in ascending order
a.     For string data type, sorting function must sort rows, alphabetically
b.    For numeric data type, sorting function must sort rows from smallest to largest

We explain the aggregation functions using example for better understanding of the specifications Lets' say, the data is as follows

 A B C D Match1 Sachin 2 12.678 Match4 Rahul 23 14 Match5 Sonal 13 35.333 Match6 Rajiv 6 56.33 Match2 Manish 87 37 Match6 Nakul 34 45 Match2 Mukul 48 12.87 Match7 Srinath 24 29.625 Match1 Dora 83 51.667 Match8 James 79 59 Match4 Munna 45 53.333 Match6 Sachin 53 52.5 Match3 Sonal 21 58.93 Match2 Rajiv 69 61.5 Match7 Nakul 36 63.75 Match9 Mukul 96 56.222 Match5 Dora 43 51.714 Match3 Munna 80 49.417

Sum Function

• Can only be applied to Numeric columns i.e. C and D in this case
• Let's say we are grouping on column B and applying Sum function on column C then, the output will look as follows :

Dora 126
James 79
Manish 87
Mukul 144
Munna 125
Nakul 70
Rahul 23
Rajiv 75
Sachin 55
Sonal 34
Srinath 24

Count Function

• Let's say we are grouping on column A and applying Count function on column A then, the output will look as follows :

Match1 2
Match2 3
Match3 2
Match4 2
Match5 2
Match6 3
Match7 2
Match8 1
Match9 1

Average Function

• Can only be applied to Numeric columns i.e. C and D in this case
• Let's say we are grouping on column B and applying Average function on column D then, the output will look as follows :

Dora 52
James 59
Manish 37
Mukul 35
Munna 52
Nakul 55
Rahul 14
Rajiv 59
Sachin 33
Sonal 48
Srinath 30

Invert Function

• Let's say we are grouping on column B and applying Invert function on column D then, the output will look as follows :

Dora 51.667 # # # 51.714 # # # #
James # # # # # # # 59 #
Manish # 37 # # # # # # #
Mukul # 12.87 # # # # # # 56.222
Munna # # 49.417 53.333 # # # # #
Nakul # # # # # 45 63.75 # #
Rahul # # # 14 # # # # #
Rajiv # 61.5 # # # 56.33 # # #
Sachin 12.678 # # # # 52.5 # # #
Sonal # # 58.93 # 35.333 # # # #
Srinath # # # # # # 29.625 # #

The first column of output is column B in ascending order. The column A in the data table becomes column headers in the output (which is not printed in output). The non-hash values are values of column D for a combination of column A and column B in the original data table. Column A and column B combination in test cases for Invert function are unique. '#' character is a place holder for null values.

Now that the workings of the four functions have been explained, let us understand the input and output specifications.

Input Format:

First line of input contains total number of test cases, denoted by N
Each test case comprises of 5 parts-
• First line of a test case contains a function name (Sum , Average, Invert and Count)
• Second line contains the column no. on which grouping will be applied.(Column index starts from 1)
• Third line contains the column no. on which the aggregation function will be applied
• Next variable number of lines contain the actual data delimited by space
• A test case is terminated by -1

Output Format:

For each test case print the output of the appropriate function as explained above.
• Perform rounding up when printing output for Sum and Average functions.
• Do not perform rounding when printing output for Invert function.

Sample Input and Output
 SNo. Input Output 1 4 Sum23idx 49.865 30.071 blkqtywhw 17.909 96.138 nqngodb 69.900 34.593 hcf-1 Count3279.424 bwipx eqmz 15.80061.570 uhaci fifo 36.9339.881 alt cjven 63.37331.110 mpcq pdg 9.170-1 Average3276.114 69.394 nuvr 1.99280.233 5.676 kxf 2.7831.940 85.761 zlnv 5.53774.016 79.417 atp 89.162-1 Invert23cky foq 57.193 80.148mkf kjqs 15.449 43.623ohu turnf 95.211 57.271-1 17.909 9749.865 3169.9 35 cjven 1eqmz 1fifo 1pdg 1 atp 80kxf 6nuvr 70zlnv 86foq 57.193 # #kjqs # 15.449 #turnf # # 95.211

### TCS Code Vita Season-5 Round-1 set-2 Program-6

Problem : Clockwise Bricks Breaker

Clockwise Bricks Breaker is a game where there is a ball which is used to break the block of bricks. Brick's Blocks are always in a form of a square matrix( e.g 2X2, 4X4). The ball has some characteristics like for breaking each brick from the block. It consumes 1 unit of energy and the whole setup is in a manner that the ball will break bricks always - in clock wise direction, in a ring fashion and start from top-left. Take an example of 4X4 brick block.

Figure 1.

Figure 2.

Figure 3.
The numbers on the bricks are nothing but points gained by breaking that brick which is assigned row wise starting from 1 to NxN. The game gets over when energy of ball exhausts and once ball initiated with some energy it will only stop when all its energy exhaust.

Your Task is to calculate total points (points of a block should be the positional value of that block as mentioned in the picture: You have to add points of all the broken bricks) gained by a player, where the energy of ball and size of block will be given.

Input Format:

First line of input should be the number of test cases T

Next T lines contain two variables N and E delimited by a whitespace where,
• N =size of square block (i.e. block will be of NXN bricks)
• E =Energy of ball

Output Format:

Output will be T lines containing the integer which is total number points gained by that energy.
OR

Print "Invalid Input" if constraint fails
Constraints:
• 0< T<=10
• 0< N <=200
• 0<= E <=N*N

Example
 Example Number Sample Input Sample Output Explaination 1 24 51 50 36Invalid Input For first test case as with Energy 5, the ball will break 5 bricks having points 1,4,16,13,2 So 1+4+16+13+2=36.Second test case is Invalid Input because constraint E<=N*N not satisfied. 2 25 09 -3 0Invalid Input For first test case it is 0 as energy is zero. For second test case it is Invalid Input because constraint E >= 0 not satisfied.

### TCS Code Vita Season-5 Round-1 set-2 Program-5

Problem : Even Sum
A number is even if it is divisible by 2, but in this case a number is even if the active bits (1s in its binary representation) of a given number are 2. So your task is to find the sum of first N even numbers.
Input Format:

First line of the input contains an integer T denoting the number of test cases.

Each of the next T lines contains a single integer N.
Output Format:

For each test case, print a single integer denoting sum of first N even numbers mod 1000000007.
Constraints:
1.    0 < N <=10^5
Example:
 Example Number Sample Input Sample Output 1 12 8 2 21525 315666

### TCS Code Vita Season-5 Round-1 set-2 Program-4

Problem : Knight Moves

Background

A Chess board position is accurately captured by Forsyth-Edwards notation and is abbreviated as FEN. A FEN "record" defines a particular game position, all in one text line and using only the ASCII character set. A FEN record contains six fields. A complete description of the FEN format to represent Chess positions can be found at
here

For the purpose of this problem only consider first of the six fields of FEN. Before we describe the problem, let us look at how FEN maps to a board position. The following 5 images show board positions and its corresponding FEN representation.

Figure 1.

 This board position depicts initial position before any side has made a move. In FEN format this board position is represented as rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w

Let's say, White plays e4. Then the board position looks like shown below

Figure 2.

 This board position depicts the Chess board after White has played e4. In FEN format this board position is represented as rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b

Similarly, 3 more half-moves are depicted in following diagrams

Figure 3.                                                  Figure 4.                                                      Figure 5.

The FENs corresponding to Figure 3, 4 and 5 are represented as

3. rnbqkbnr/pppp1ppp/8/4P3/4P3/8/PPPP1PPP/RNBQKBNR w
4. rnbqkbnr/pppp1ppp/8/4p3/4PP2/8/PPPP2PP/RNBQKBNR b
5. rnbqkbnr/pppp1ppp/8/8/4Pp2/8/PPPP2PP/RNBQKBNR w

Wikipedia describes first field of FEN format as follows

Each rank is described, starting with rank 8 and ending with rank 1; within each rank, the contents of each square are described from file "a" through file "h". Following the
Standard Algebraic Notation (SAN), each piece is identified by a single letter taken from the standard English names (pawn = "P", knight = "N", bishop = "B", rook = "R", queen = "Q" and king = "K").[1] White pieces are designated using upper-case letters ("PNBRQK") while black pieces use lowercase ("pnbrqk"). Empty squares are noted using digits 1 through 8 (the number of empty squares), and "/" separates ranks.

The second field denotes whose move it is now. "w" depicts that it is White's turn to play and "b" indicates that it is Black's turn to play

CodeVita Problem Statement

Given a board position in FEN format, your task is to find out all the move(s) that Knight(s) of the playing side can make.

Input Format:
1.    First line contains single FEN record, which corresponds to a particular board position and also indicates whose turn it is.

Output Format:
1.    The output must be printed as follows
1.    All legal moves that Knight can make must be in the format "[<Move Format>]"
2.    Where <Move Format> is move represented in format "[fromSquare][toSquare]"
2.    See Example section for better understanding of output format
3.    Follow Output printing specification to print the output in required format

Sample Input and Output
 SNo. Input Board Depiction Output 1 3k4/8/8/8/8/1K4R1/5R2/7N w [] 2 3k4/8/8/8/8/6b1/5r2/K6N w [h1g3, h1f2] 3 2k1b3/6n1/n7/5R2/8/8/8/4K3 b [g7e6, g7f5, g7h5, a6b8, a6c7, a6c5, a6b4]

Print Specification:
2. If more than one move is possible, moves should be separated by a comma followed by whitespace
3. Moves of a single bishop should be printed in Move Format. Scan the board from 8th rank to 1st rank from a-file to h-file. Whichever square gets hit first, that move should be printed first.
4. If more than one bishop exists for side to move, then start scanning for bishop from 8th rank to 1st rank, left to right i.e. from a-file to h-file. Whichever bishop appears first, print all moves for that bishop first.
5. Verify your understanding of how printing should happen against examples shown above

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