UNITY (programming language)

Description

All statements are assignments, and are separated by #. A statement can consist of multiple assignments, of the form a,b,c := x,y,z, or a := x || b := y || c := z. You can also have a quantified statement list, <# x,y : expression :: statement>, where x and y are chosen randomly among the values that satisfy expression. A quantified assignment is similar. In <|| x,y : expression :: statement >, statement is executed simultaneously for all pairs of x and y that satisfy expression.

Bubble sort

Bubble sort the array by comparing adjacent numbers, and swapping them if they are in the wrong order. Using Θ ( n ) expected time, Θ ( n ) processors and Θ ( n 2 ) expected work. The reason you only have Θ ( n ) expected time, is that k is always chosen randomly from { 0 , 1 } . This can be fixed by flipping k manually.

Program bubblesortdeclare n: integer, A: array [0..n-1] of integerinitially n = 20 # <|| i : 0 <= i and i < n :: A[i] = rand() % 100 >assign <# k : 0 <= k < 2 :: <|| i : i % 2 = k and 0 <= i < n - 1 :: A[i], A[i+1] := A[i+1], A[i] if A[i] > A[i+1] > >end

Rank-sort

You can sort in Θ ( log ⁡ n ) time with rank-sort. You need Θ ( n 2 ) processors, and do Θ ( n 2 ) work.

Program ranksortdeclare n: integer, A,R: array [0..n-1] of integerinitially n = 15 # <|| i : 0 <= i < n :: A[i], R[i] = rand() % 100, i >assign <|| i : 0 <= i < n :: R[i] := <+ j : 0 <= j < n and (A[j] < A[i] or (A[j] = A[i] and j < i)) :: 1 > > # <|| i : 0 <= i < n :: A[R[i]] := A[i] >end

Floyd–Warshall algorithm

Using the Floyd–Warshall algorithm all pairs shortest path algorithm, we include intermediate nodes iteratively, and get Θ ( n ) time, using Θ ( n 2 ) processors and Θ ( n 3 ) work.

Program shortestpathdeclare n,k: integer, D: array [0..n-1, 0..n-1] of integerinitially n = 10 # k = 0 # <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] = rand() % 100 >assign <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] := min(D[i,j], D[i,k] + D[k,j]) > || k := k + 1 if k < n - 1end

We can do this even faster. The following programs computes all pairs shortest path in Θ ( log 2 ⁡ n ) time, using Θ ( n 3 ) processors and Θ ( n 3 log ⁡ n ) work.

Program shortestpath2declare n: integer, D: array [0..n-1, 0..n-1] of integerinitially n = 10 # <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] = rand() % 10 >assign <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] := min(D[i,j], <min k : 0 <= k < n :: D[i,k] + D[k,j] >) >end

After round r , D[i,j] contains the length of the shortest path from i to j of length 0 … r . In the next round, of length 0 … 2 r , and so on.