ARC 089 D. Checker
https://beta.atcoder.jp/contests/arc089/tasks/arc089_b
この解説では、座標を(横,縦)で表している。
$(x,y)$ が黒であることと $(x \bmod 2K, y \bmod 2K)$ が黒であることは同値である。
$(x,y)$ が白であることと $(x+K,y)$ が黒であることは同値である。
#include <iostream> #include <algorithm> #include <vector> using namespace std; int main() { int n, k; cin >> n >> k; vector<vector<int>> s(4 * k + 1, vector<int>(4 * k + 1)); for (int i = 0; i < n; i++) { int x, y; char c; cin >> x >> y >> c; if (c == 'W') { x += k; } x %= 2 * k; y %= 2 * k; s[x + 1][y + 1]++; s[x + 2 * k + 1][y + 1]++; s[x + 1][y + 2 * k + 1]++; s[x + 2 * k + 1][y + 2 * k + 1]++; } for (int i = 0; i + 1 < s.size(); i++) { for (int j = 0; j + 1 < s.size(); j++) { s[i + 1][j + 1] += s[i + 1][j] + s[i][j + 1] - s[i][j]; } } auto sum = [&](int y, int x, int n) { return s[y + n][x + n] - s[y + n][x] - s[y][x + n] + s[y][x]; }; int ans = 0; for (int i = 0; i < 2 * k; i++) { for (int j = 0; j < 2 * k; j++) { int s1 = sum(i, j, k); int s2 = sum(i + k, j + k, k); ans = max(ans, s1 + s2); } } cout << ans << endl; }
図1のコード
\documentclass[dvipdfmx,margin=1cm]{standalone} \usepackage{newtxtext} \usepackage{newtxmath} \usepackage{tikz} \usetikzlibrary{calc} \usetikzlibrary{patterns} \begin{document} \begin{tikzpicture}[yscale=-1, foo/.style={circle,inner sep=0.07cm}, ] \foreach \x/\y in {2/0, 6/0, 0/2, 4/2, 2/4, 6/4, 0/6, 4/6} { \draw[fill=black!10] (\x,\y) rectangle ++(2,2); } \draw[help lines] (-0.5,-0.5) grid (8.5,8.5); \draw[step=2] (-0.5,-0.5) grid (8.5,8.5); \draw[ultra thick] (0,0) rectangle (4,4); \node[fill=black,foo] (a) at ($(0,3) +(.5,.5)$) {}; \node[fill=black,foo] (b) at ($(4,7) +(.5,.5)$) {}; \draw[-latex,very thick] (b) to node [auto,xshift=-0.4cm] {$\bmod 2K$} (a); \node[fill=white,draw=black,foo] (c) at ($(5,1) +(.5,.5)$) {}; \node[fill=black,foo] (d) at ($(7,1) +(.5,.5)$) {}; \node[fill=black,foo] (e) at ($(3,1) +(.5,.5)$) {}; \draw[-latex,very thick] (c) to node [auto] {$+K$} (d); \draw[-latex,very thick] (d) to [bend right=30] node [auto,xshift=-0.1cm] {$\bmod 2K$} (e); \draw (0,0) to [very thick,bend right=20] node [auto] {$2K$} (4,0); \draw (0,0) to [very thick,bend left=20] node [auto,swap] {$2K$} (0,4); \end{tikzpicture} \end{document}
図 2 のコード
% pgfmanual v3.0.1a \documentclass[dvipdfmx,margin=1cm]{standalone} \usepackage{newtxtext} \usepackage{newtxmath} \usepackage{tikz} \usetikzlibrary{calc} \usetikzlibrary{patterns} \begin{document} \begin{tikzpicture}[yscale=-1] \begin{scope}[shift={(0,2)},local bounding box=scope1] \draw [help lines] (-0.5,-0.5) grid (4.5,4.5); \draw [step=2] (-0.5,-0.5) grid (4.5,4.5); \draw [very thick] (0,0) rectangle (4,4); \foreach \dy/\dx in {0/0} { \foreach \x/\y in {1/0, 3/1, 2/3}{ \draw [fill=black,circle] ($(\x,\y) + (.5,.5) + (\dx,\dy)$) circle[radius=0.1cm]; } } % pattern=crosshatch dots -- See pgfmanual p.666 \draw [ultra thick,pattern=crosshatch dots] (1,2) rectangle (3,4); \draw [ultra thick,pattern=crosshatch dots] (0,0) rectangle (1,2); \draw [ultra thick,pattern=crosshatch dots] (3,0) rectangle (4,2); \draw [-latex,line width=0.1cm] (0.5,1.5) -- (1,2); \end{scope} \begin{scope}[shift={(10,0)},local bounding box=scope2] \draw [fill=black!20] (0,0) rectangle (4,4); \draw [fill=red!20] (4,0) rectangle (8,4); \draw [fill=blue!20] (0,4) rectangle (4,8); \draw [fill=green!20] (4,4) rectangle (8,8); \draw [help lines] (-0.5,-0.5) grid (8.5,8.5); \draw [step=2] (-0.5,-0.5) grid (8.5,8.5); \draw [very thick] (0,0) rectangle (4,4); \foreach \dy/\dx in {0/0, 0/4, 4/0, 4/4} { \foreach \x/\y in {1/0, 3/1, 2/3}{ \draw [fill=black,circle] ($(\x,\y) + (.5,.5) + (\dx,\dy)$) circle[radius=0.1cm]; } } \draw [-latex,ultra thick] (2,0) to [bend right=30] node [auto] {Copy} (6,0); \draw [-latex,ultra thick] (0,2) to [bend left=30] node [auto,swap] {Copy} (0,6); \draw [-latex,ultra thick] (2,8) to [bend left=30] node [auto,swap] {Copy} (6,8); \draw [ultra thick,pattern=crosshatch dots] (1,2) rectangle (3,4); \draw [ultra thick,pattern=crosshatch dots] (3,4) rectangle (5,6); \draw [-latex,line width=0.1cm] (0.5,1.5) -- (1,2); \end{scope} \draw [-latex,ultra thick] ($(scope1.east)+(0.5,0)$) -- node [auto] {Transform} ($(scope2.west)-(0.5,0)$); \end{tikzpicture} \end{document}