Description
Problem 1: Dense! (1 pt.)
For this problem you are given two int arrays of the same length (let’s call them vectors). First compute
and print (in a newline) the elementwise multiplication of them. Then determine and print (in a newline)
if the given vectors are perpendicular to each other (i.e. if the inner product of them is zero, recall that
inner product of vectors is the sum of elementwise multiplication). Print “perpendicular” if they are
perpendicular and “not perpendicular” otherwise (all lowercase). First N is given as the length of each
array. Second, N numbers follow corresponding to first vector and then another N numbers are given for
the second vector. N is at most 10000.
Sample input:
7
5 0 20 10 -30 5 0
8 2 -1 2 0 1 20
Sample output:
40 0 -20 20 0 5 0
not perpendicular
Problem 2: Check mate! (7 pts.)
In this problem you are given a chess board with pieces on (all formatted as characters), you have to
detect whether black is on check, or not threatened at all.
Input is given as 8 lines of 8 characters (8 characters following by ‘\n’ for the first 7 lines, 8 characters for
the 8th line). Upper case letters stand for white and lower-case letters stand for black pieces. Don’t assume
the input is a proper/complete chess game (e.g. there might be all queens) but there always will be only
one king of each color. A hyphen “-“ stands for an empty cell. The output must be the number of
opponent (white) pieces that can capture the black king.
You can read the piece moves on Wikipedia (https://en.wikipedia.org/wiki/Chess). In short, all pieces
move and capture the same except for Pawn. Rook moves horizontally or vertically, Bishop moves
diagonally, Knight has L shaped jumps, Queen moves like both Rook and Bishop, and King can move to its
adjacent 8 cells only (a king cannot move to a cell where an opponent can capture it there). Pawn moves
straight toward the opponent but can capture the piece on its immediate right or left diagonal cell
towards the enemy (that is what matters for checking the king).
The king is in check, if it is threatened by an enemy piece (the piece can capture the king). Find and print
the number of white pieces that can capture the black king (if no piece threaten the king, then print 0
which means it is not a check situation).
White: K=king, Q=queen, R= rook, B=bishop, N=knight, P=pawn
Black: k=king, q=queen, r=rook, b=bishop, n=knight, p=pawn
Sample input (the text is the input of your program; the picture corresponds to the board it is representing
and is only here for demonstration):
—r—k
pp—-Qn
–p—–
——–
——–
P—–RP
-PP—PK
——–
Output:
1
• Explanation: the white queen is attacking the black king.
P3: CHECKMATE! EXTRA CREDIT (3 pts.):
If the king is in check and the player doesn’t have any move to get the king out of the check, it is checkmate
and the player loses the match. A king may get out of the check by either moving out of the threatened
cell (into a non-threatened one) or if another piece blocks the way of the opponent’s piece that can
capture the king (or knocks out the opponent’s piece that is threatening the king). Note that the king
might be threatened by two opponent pieces (more than one piece in general). In that case the only valid
move is for the king to move to a non-threatened cell (and if it doesn’t have such a move, then it is
checkmate).
Implement checkmate functionality. Input is the same as before. Output is same as before, except when
it is a checkmate, print 100. i.e. the example (with the picture above) is a case of checkmate. In this case
you print 100 instead of 1. It is a checkmate because the attacking queen is being supported by a rook
which means the king cannot capture the attacking queen (a king cannot move to a cell where it can be
captured, in this case by the supporting rook).
• Note: this extra credit problem is substantially harder than problem 2 as you need to implement
all the possible moves/captures for black player and all the captures for white player.
• In all cases if the king can move to a non-threatened cell, it is not a checkmate.
• You need to check if it is a single check (only one white piece can capture the king), if any black
piece can block the attacking piece or capture it (if it can, it is not a checkmate). If the king cannot
move to a non-threatened cell and if no other black piece can help, it is a checkmate and black
loses the game.
• If it is a multi-check (more than one piece can capture the black king), the only possible way to
get out of check is for the king to move to a cell where no other piece can capture it.