Codeforces Beta Round 53

Solutions for Codeforces Beta Round 53 (contest 57). 5/5 problems verified against sample I/O. Difficulty range: 1300-3000.

5 items

Codeforces Beta Round 53

Type: Beta | Problems: 5 | Verified: 5/5 | Rating range: 1300-3000 | Time: 8m 25s

Problem	Name	Rating	Tags	Solve Time	Verified
A	Square Earth?	1300	dfs-and-similar, greedy, implementation	1m 22s	✓
B	Martian Architecture	1600	implementation	1m 37s	✓
C	Array	1900	combinatorics, math	1m 21s	✓
D	Journey	2500	dp, math	2m 2s	✓
E	Chess	3000	math, shortest-paths	2m 3s	✓

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CF 57A - Square Earth?

We are asked to find the shortest distance between two points lying on the perimeter of a square of side length n. The square is aligned with the axes, so its corners are at (0,0), (n,0), (0,n), and (n,n). The two points are guaranteed to lie on the edges, not in the interior.

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CF 57B - Martian Architecture

Each construction describes a staircase placed on a one-dimensional line of cells. A staircase starts at cell l, ends at cell r, and adds heights in an arithmetic progression.

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CF 57C - Array

We are asked to count the number of arrays of length n containing integers from 1 to n such that the array is either entirely non-decreasing or entirely non-increasing.

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CF 57D - Journey

We are asked to compute the expected lifespan of a dynamic particle moving on a 2D grid with static obstacles. The grid has n rows and m columns. Static particles occupy certain cells, never sharing a row, column, or diagonally adjacent cell.

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CF 57E - Chess

We start on an infinite chessboard at square (0, 0). A knight moves using the usual chess move, two cells in one direction and one in the perpendicular direction. Some squares are removed from the board, and the knight is never allowed to stand on them.