2.3 Designing algorithms

2.3.1 The divide-and-conquer approach

merge sort

MERGE(A, p, q, r)
 1  n1 ← q - p + 1
 2  n2 ← r - q
 3  create arrays L[1 ‥ n1 + 1] and R[1 ‥ n2 + 1]
 4  for i ← 1 to n1
 5       do L[i] ← A[p + i - 1]
 6  for j ← 1 to n2
 7       do R[j] ← A[q + j]
 8  L[n1 + 1] ← ∞
 9  R[n2 + 1] ← ∞
10  i ← 1
11  j ← 1
12  for k ← p to r
13       do if L[i] ≤ R[j]
14             then A[k] ← L[i]
15                  i ← i + 1
16             else A[k] ← R[j]
17                  j ← j + 1

MERGE-SORT(A, p, r)

1 if p < r

2 then q ← ⌊(p + r)/2⌋

3 MERGE-SORT(A, p, q)

4 MERGE-SORT(A, q + 1, r)

5 MERGE(A, p, q, r)

var n,i:integer;
a:array[1..100] of integer;
procedure mergesort(p,q,r:integer);
var n1,n2,i,j,k:integer;
al,ar:array[1..100] of integer;
begin
    n1:=q-p+1;
    n2:=r-q;
    for i:=1 to n1 do al[i]:=a[p+i-1];
    al[n1+1]:=maxint;
    for i:=1 to n2 do ar[i]:=a[q+i];
    ar[n2+1]:=maxint;
    i:=1;j:=1;
    for k:=p to r do
        if al[i]<ar[j] then begin a[k]:=al[i];inc(i);end
        else begin a[k]:=ar[j];inc(j);end;        
        
end;
procedure merge(l,r:integer);
var i,q:integer;
begin
    if r>l then 
    begin
        q:=(r-l) div 2;
        merge(l,l+q);
        merge(l+q+1,r);
        mergesort(l,l+q,r);
    end;
end;
begin
    readln(n);
    for i:=1 to n do read(a[i]);
    merge(1,n);
    for i:=1 to n do write(a[i],' ');
end.