add zfunction algorithm

strings/z_function.dart

@@ -0,0 +1,59 @@
+import 'package:test/test.dart';
+
+/*
+The z function of a string S with size n returns an array Z, where Z[i] is the largest size
+of a substring that starts at index i and matches the prefix of the string S.
+Obs: Z[0] is always 0.
+
+Example:
+
+  string S: "abcabcabc"
+  array Z: [0, 0, 0, 3, 0, 0, 6, 0, 0]
+
+  string S: "aaaa"
+  array Z: [0, 3, 2, 1]
+
+Complexity: linear in the length of the string - O(n)
+Source: https://cp-algorithms.com/string/z-function.html
+*/
+
+import 'dart:math';
+
+List<int> zFunction(String s) {
+  final z = List.filled(s.length, 0);
+  int l = 0;
+  int r = 0;
+
+  // The first element must be 0, so the loop starts at index 1.
+  for (int i = 1; i < s.length; i++) {
+    if (i < r) {
+      z[i] = min(r - i, z[i - l]);
+    }
+    // Calculate the quantity of chars in common from string and substring prefix
+    while (i + z[i] < s.length && s[z[i]] == s[i + z[i]]) {
+      z[i]++;
+    }
+    if (i + z[i] > r) {
+      l = i;
+      r = i + z[i];
+    }
+  }
+  return z;
+}
+
+void main() {
+  String string;
+  List<int> z;
+
+  test(('zFunction: '), () {
+    string = 'abcabcabc';
+    z = [0, 0, 0, 3, 0, 0, 6, 0, 0];
+    expect(zFunction(string), z);
+  });
+
+  test(('zFunction: '), () {
+    string = 'aaaa';
+    z = [0, 3, 2, 1];
+    expect(zFunction(string), z);
+  });
+}