Data update

Task/Chinese-remainder-theorem/PascalABC.NET/chinese-remainder-theorem.pas

@@ -0,0 +1,41 @@
+function GCD(a, b: integer): integer;
+begin
+  while b > 0 do
+    (a, b) := (b, a mod b);
+  Result := a;
+end;
+
+function ModularMultiplicativeInverse(a, m: integer): integer;
+begin
+  var b := a Mod m;
+  for var x := 1 To m - 1 do
+    if (b * x) Mod m = 1 Then begin Result := x; exit end;
+  Result := 1;
+end;
+
+procedure Solve(n, a: array of integer);
+begin
+  var coprime := 1;
+  foreach var (i, j) in n.combinations(2) do coprime *= GCD(i, j);
+  if coprime <> 1 then
+  begin println('Not pairwise co-prime'); exit end;
+
+  var prod := n.Aggregate(1, (i, j)-> i * j);
+  var sm := 0;
+  for var i := 0 To n.Length - 1 do
+  begin
+    var p := prod div n[i];
+    sm += a[i] * ModularMultiplicativeInverse(p, n[i]) * p;
+  end;
+  var result := sm Mod prod;
+
+  for var counter := 0 to n.Length - 1 do
+    WriteLn($'{result} = {a[counter]} (mod {n[counter]})');
+end;
+
+begin
+  solve(|3, 5, 7|, |2, 3, 2|);
+  solve(|10, 4, 9|, |11, 22, 19|);
+  solve(|11, 12, 13|, |10, 4, 12|);
+  solve(|5, 7, 9, 11|, |1, 2, 3, 4|);
+end.