Number Grid Filling
Time limit1sMemory limit128 MB
Construct an N by M grid so that absolute differences of all adjacent cell pairs form exactly the set 1..2NM-N-M with each value used once.
- Level
Hard8 of 10
- Topics
- Math, Combinatorics, Matrix
- Solved
- No attempts yet
Problem
Fill an N x M grid with integers. Two cells are adjacent if they share an edge.
If you take the absolute differences between all adjacent pairs, the integers from 1 through 2NM - N - M must each appear exactly once.
Given N and M, output any grid that satisfies the condition.
Input
The first line contains two integers N and M. (1 <= N, M <= 1,000)
Output
Print the grid in N lines. Each line must contain M integers separated by spaces.
If there are multiple valid answers, print any one of them. Every cell value must be an integer from 1 through 2 x 10^9.