Cody

# Problem 42639. Find the Final State of an Abelian Sandpile

Solution 1944627

Submitted on 21 Sep 2019 by Augusto Mazzei
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### Test Suite

Test Status Code Input and Output
1   Pass
A = 1; B_correct = 1; assert(isequal(sandpile(A),B_correct))

2   Pass
A = [0 0 0;0 4 1;1 0 0]; B_correct = [0 1 0;1 0 2;1 1 0]; assert(isequal(sandpile(A),B_correct))

p = 2 q = 2 A = 0 1 0 1 0 2 1 1 0

3   Pass
A = [0 0 0 0;0 4 4 0;0 0 0 0]; B_correct = [0 1 1 0;1 1 1 1;0 1 1 0]; assert(isequal(sandpile(A),B_correct))

p = 2 q = 2 A = 0 1 0 0 1 0 5 0 0 1 0 0 p = 2 q = 3 A = 0 1 1 0 1 1 1 1 0 1 1 0

4   Pass
A = [0 0 0 0 0;0 0 0 0 0;0 0 17 0 0;0 0 0 7 0;0 0 0 0 0]; B_correct = [0 0 1 0 0;0 2 1 2 0;1 1 1 3 1;0 2 3 1 2;0 0 1 2 0]; assert(isequal(sandpile(A),B_correct))

p = 3 q = 3 A = 0 0 0 0 0 0 0 1 0 0 0 1 13 1 0 0 0 1 7 0 0 0 0 0 0 p = 3 q = 3 A = 0 0 0 0 0 0 0 2 0 0 0 2 9 2 0 0 0 2 7 0 0 0 0 0 0 p = 3 q = 3 A = 0 0 0 0 0 0 0 3 0 0 0 3 5 3 0 0 0 3 7 0 0 0 0 0 0 p = 3 q = 3 A = 0 0 0 0 0 0 0 4 0 0 0 4 1 4 0 0 0 4 7 0 0 0 0 0 0 p = 3 q = 2 A = 0 0 0 0 0 0 1 4 0 0 1 0 2 4 0 0 1 4 7 0 0 0 0 0 0 p = 2 q = 3 A = 0 0 1 0 0 0 2 0 1 0 1 0 3 4 0 0 1 4 7 0 0 0 0 0 0 p = 4 q = 3 A = 0 0 1 0 0 0 2 0 1 0 1 0 4 4 0 0 2 0 8 0 0 0 1 0 0 p = 3 q = 3 A = 0 0 1 0 0 0 2 1 1 0 1 1 0 5 0 0 2 1 8 0 0 0 1 0 0 p = 3 q = 4 A = 0 0 1 0 0 0 2 1 2 0 1 1 1 1 1 0 2 1 9 0 0 0 1 0 0 p = 4 q = 4 A = 0 0 1 0 0 0 2 1 2 0 1 1 1 2 1 0 2 2 5 1 0 0 1 1 0 p = 4 q = 4 A = 0 0 1 0 0 0 2 1 2 0 1 1 1 3 1 0 2 3 1 2 0 0 1 2 0

5   Pass
A = [0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0;0 0 0 16 2 3 13 0 0 0 0;0 0 0 5 11 10 8 0 0 0 0;0 0 0 9 7 6 12 0 0 0 0;0 0 0 4 14 15 1 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0]; B_correct = [0 0 0 0 0 0 0 0 0 0 0;0 0 1 3 3 3 3 1 0 0 0;0 2 3 2 3 3 2 3 2 0 0;1 1 1 3 2 3 1 1 1 1 0;1 3 1 1 3 3 1 2 3 1 0;1 3 0 3 3 3 3 1 3 1 0;1 0 3 2 2 3 0 3 0 1 0;0 2 2 3 2 2 3 2 2 0 0;0 0 2 0 3 3 0 2 0 0 0;0 0 0 1 1 1 1 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0]; assert(isequal(sandpile(A),B_correct))

p = 4 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 12 3 3 13 0 0 0 0 0 0 0 6 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 4 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 8 4 3 13 0 0 0 0 0 0 0 7 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 4 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 4 5 3 13 0 0 0 0 0 0 0 8 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 4 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 6 3 13 0 0 0 0 0 0 0 9 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 4 q = 3 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 1 0 1 6 3 13 0 0 0 0 0 0 1 9 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 3 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 1 0 2 6 3 13 0 0 0 0 0 0 1 9 11 10 8 0 0 0 0 0 0 0 9 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 5 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 1 0 3 6 3 13 0 0 0 0 0 0 2 5 12 10 8 0 0 0 0 0 0 0 10 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 5 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 1 0 4 6 3 13 0 0 0 0 0 0 3 1 13 10 8 0 0 0 0 0 0 0 11 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 4 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 1 0 7 3 13 0 0 0 0 0 0 3 2 13 10 8 0 0 0 0 0 0 0 11 7 6 12 0 0 0 0 0 0 0 4 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 6 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 1 0 7 3 13 0 0 0 0 0 0 3 3 13 10 8 0 0 0 0 0 0 1 7 8 6 12 0 0 0 0 0 0 0 5 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 6 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 1 0 7 3 13 0 0 0 0 0 0 3 4 13 10 8 0 0 0 0 0 0 2 3 9 6 12 0 0 0 0 0 0 0 6 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 5 q = 4 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 1 1 7 3 13 0 0 0 0 0 0 4 0 14 10 8 0 0 0 0 0 0 2 4 9 6 12 0 0 0 0 0 0 0 6 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p = 5 q = 3 A = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 1 2 1 7 3 13 0 0 0 0 0 1 0 1 14 10 8 0 0 0 0 0 0 3 4 9 6 12 0 0 0 0 0 0 0 6 14 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...