189 lines
5.4 KiB
C#
189 lines
5.4 KiB
C#
using System;
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using System.Text;
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namespace ZeckendorfArithmetic {
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class Zeckendorf : IComparable<Zeckendorf> {
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private static readonly string[] dig = { "00", "01", "10" };
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private static readonly string[] dig1 = { "", "1", "10" };
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private int dVal = 0;
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private int dLen = 0;
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public Zeckendorf() : this("0") {
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// empty
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}
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public Zeckendorf(string x) {
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int q = 1;
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int i = x.Length - 1;
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dLen = i / 2;
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while (i >= 0) {
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dVal += (x[i] - '0') * q;
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q *= 2;
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i--;
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}
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}
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private void A(int n) {
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int i = n;
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while (true) {
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if (dLen < i) dLen = i;
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int j = (dVal >> (i * 2)) & 3;
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switch (j) {
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case 0:
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case 1:
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return;
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case 2:
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if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
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dVal += 1 << (i * 2 + 1);
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return;
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case 3:
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int temp = 3 << (i * 2);
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temp ^= -1;
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dVal = dVal & temp;
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B((i + 1) * 2);
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break;
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}
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i++;
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}
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}
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private void B(int pos) {
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if (pos == 0) {
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Inc();
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return;
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}
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if (((dVal >> pos) & 1) == 0) {
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dVal += 1 << pos;
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A(pos / 2);
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if (pos > 1) A(pos / 2 - 1);
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}
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else {
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int temp = 1 << pos;
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temp ^= -1;
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dVal = dVal & temp;
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B(pos + 1);
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B(pos - (pos > 1 ? 2 : 1));
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}
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}
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private void C(int pos) {
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if (((dVal >> pos) & 1) == 1) {
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int temp = 1 << pos;
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temp ^= -1;
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dVal = dVal & temp;
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return;
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}
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C(pos + 1);
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if (pos > 0) {
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B(pos - 1);
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}
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else {
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Inc();
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}
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}
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public Zeckendorf Inc() {
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dVal++;
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A(0);
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return this;
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}
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public Zeckendorf Copy() {
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Zeckendorf z = new Zeckendorf {
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dVal = dVal,
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dLen = dLen
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};
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return z;
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}
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public void PlusAssign(Zeckendorf other) {
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for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
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if (((other.dVal >> gn) & 1) == 1) {
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B(gn);
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}
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}
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}
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public void MinusAssign(Zeckendorf other) {
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for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
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if (((other.dVal >> gn) & 1) == 1) {
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C(gn);
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}
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}
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while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
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dLen--;
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}
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}
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public void TimesAssign(Zeckendorf other) {
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Zeckendorf na = other.Copy();
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Zeckendorf nb = other.Copy();
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Zeckendorf nt;
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Zeckendorf nr = new Zeckendorf();
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for (int i = 0; i < (dLen + 1) * 2; i++) {
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if (((dVal >> i) & 1) > 0) {
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nr.PlusAssign(nb);
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}
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nt = nb.Copy();
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nb.PlusAssign(na);
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na = nt.Copy();
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}
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dVal = nr.dVal;
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dLen = nr.dLen;
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}
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public int CompareTo(Zeckendorf other) {
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return dVal.CompareTo(other.dVal);
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}
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public override string ToString() {
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if (dVal == 0) {
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return "0";
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}
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int idx = (dVal >> (dLen * 2)) & 3;
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StringBuilder sb = new StringBuilder(dig1[idx]);
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for (int i = dLen - 1; i >= 0; i--) {
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idx = (dVal >> (i * 2)) & 3;
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sb.Append(dig[idx]);
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}
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return sb.ToString();
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}
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}
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class Program {
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static void Main(string[] args) {
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Console.WriteLine("Addition:");
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Zeckendorf g = new Zeckendorf("10");
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g.PlusAssign(new Zeckendorf("10"));
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Console.WriteLine(g);
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g.PlusAssign(new Zeckendorf("10"));
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Console.WriteLine(g);
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g.PlusAssign(new Zeckendorf("1001"));
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Console.WriteLine(g);
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g.PlusAssign(new Zeckendorf("1000"));
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Console.WriteLine(g);
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g.PlusAssign(new Zeckendorf("10101"));
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Console.WriteLine(g);
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Console.WriteLine();
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Console.WriteLine("Subtraction:");
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g = new Zeckendorf("1000");
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g.MinusAssign(new Zeckendorf("101"));
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Console.WriteLine(g);
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g = new Zeckendorf("10101010");
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g.MinusAssign(new Zeckendorf("1010101"));
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Console.WriteLine(g);
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Console.WriteLine();
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Console.WriteLine("Multiplication:");
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g = new Zeckendorf("1001");
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g.TimesAssign(new Zeckendorf("101"));
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Console.WriteLine(g);
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g = new Zeckendorf("101010");
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g.PlusAssign(new Zeckendorf("101"));
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Console.WriteLine(g);
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}
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}
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}
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