Character X: Test Both Diagonal Strips¶
Problem setter's solutions: test each grid cell, or substitute into a fixed template supplied with the problem. Codex (GPT-6): standard C++17 implementations, explicit output dimensions and whitespace validation.
Algorithm and proof¶
Enumerate rows \(i=1,\ldots,8\) and columns \(j=1,\ldots,10\) . Print the requested character if \(j\in[i,i+2]\) or \(j\in[9-i,11-i]\) ; otherwise print a space. End each row with a newline.
These closed intervals are exactly the two required diagonal strips. Logical OR takes their union, printing overlapping cells once. Every other cell becomes a space. Increasing row and column order visits every position exactly once in the required order.
Complexity and implementation¶
Each pattern prints a fixed \(80\) cells and \(8\) newlines. Total time is \(O(T+1)\) and extra space is \(O(1)\) . Parenthesize each strip condition to make the AND/OR grouping clear.
Trailing spaces belong to the rectangle and must be preserved. Do not add blank lines between patterns. When \(T=0\) , the loop is skipped and output is empty.
std.cpp directly implements the geometric definition and is preferred. The setter's fixed-template solution and alternative.cpp avoid reconstructing the pattern cell by cell, but apply to this fixed shape and size. Both programs pass all formal inputs; local timings largely include startup and output.
See the test plan, generation instructions, and environment and measurements.