1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
|
/// <summary>
/// A static class providing useful methods for integer calculations
/// </summary>
public static class Integers
{
/// <summary>
/// Calculates the Greatest Common Dividor of two integer
/// </summary>
/// <param name="Number1">the first integer</param>
/// <param name="Number2">the second integer</param>
/// <returns>the Greatest Common Dividor</returns>
public static long GetGCD(long Number1, long Number2)
{
long remainder = 0;
do
{
remainder = Number1 % Number2;
Number1 = Number2;
Number2 = remainder;
} while (remainder != 0);
return Number1;
}
/// <summary>
/// Calculates the Smallest Common Multiple
/// </summary>
/// <param name="Number1">the first integer</param>
/// <param name="Number2">the first integer</param>
/// <returns>the Smallest Common Multiple</returns>
public static long GetSCM(long Number1, long Number2)
{
return (Number1 * Number2) / GetGCD(Number1, Number2);
}
/// <summary>
/// Checks if an integer divides another
/// </summary>
/// <param name="Number1">the Divident</param>
/// <param name="Number2">the Dividor</param>
/// <returns>true if Number2 ist dividor of Number1, else false</returns>
public static bool IsDivider(long Number1, long Number2)
{
return (Number1 % Number2) == 0;
}
/// <summary>
/// test if an integer is prime
/// </summary>
/// <param name="Number">the integer</param>
/// <returns>true if prime else false</returns>
public static bool IsPrime(long Number)
{
bool value;
PrimeNumberReader pnreader = new PrimeNumberReader();
pnreader.BeginGetNextPrime();
if (pnreader.GetNextPrime(Number - 1) == Number)
{
value = true;
}
else
{
value = false;
}
pnreader.EndGetNextPrime();
return value;
}
/// <summary>
/// Converts an integer to a string containing a roman number
/// </summary>
/// <param name="Number">The integer</param>
/// <returns>The string containing the roman</returns>
public static string ToRoman(long Number)
{
if (Number == 0)
{
return string.Empty;
}
if (Number >= 1000)
{
return "M" + ToRoman(Number - 1000);
}
if (Number >= 900)
{
return "CM" + ToRoman(Number - 900);
}
if (Number >= 500)
{
return "D" + ToRoman(Number - 500);
}
if (Number >= 400)
{
return "CD" + ToRoman(Number - 400);
}
if (Number >= 100)
{
return "C" + ToRoman(Number - 100);
}
if (Number >= 90)
{
return "XC" + ToRoman(Number - 90);
}
if (Number >= 50)
{
return "L" + ToRoman(Number - 50);
}
if (Number >= 40)
{
return "XL" + ToRoman(Number - 40);
}
if (Number >= 10)
{
return "X" + ToRoman(Number - 10);
}
if (Number >= 9)
{
return "IX" + ToRoman(Number - 9);
}
if (Number >= 5)
{
return "V" + ToRoman(Number - 5);
}
if (Number >= 4)
{
return "IV" + ToRoman(Number - 4);
}
if (Number >= 1)
{
return "I" + ToRoman(Number - 1);
}
return string.Empty;
}
/// <summary>
/// Converts a string containing a roman number to an integer
/// </summary>
/// <param name="Roman">The string containing a roman number</param>
/// <returns>The integer</returns>
public static long FromRoman(string Roman)
{
if (Roman.Length == 0)
{
return 0;
}
Roman = Roman.ToUpper();
long intern = 0;
for (int i = 0; i < Roman.Length; i++)
{
int value = 0;
switch (Roman[i])
{
case 'M':
value = +1000;
break;
case 'D':
value = +500;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("M").IndexOf(Roman[j]) != -1)
{
value = -500;
break;
}
}
break;
case 'C':
value = +100;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("MD").IndexOf(Roman[j]) != -1)
{
value = -100;
break;
}
}
break;
case 'L':
value = +50;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("MDC").IndexOf(Roman[j]) != -1)
{
value = -50;
break;
}
}
break;
case 'X':
value = +10;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("MDCL").IndexOf(Roman[j]) != -1)
{
value = -10;
break;
}
}
break;
case 'V':
value = +5;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("MDCLX").IndexOf(Roman[j]) != -1)
{
value = -5;
break;
}
}
break;
case 'I':
value = +1;
for (int j = i + 1; j < Roman.Length; j++)
{
if (("MDCLXV").IndexOf(Roman[j]) != -1)
{
value = -1;
break;
}
}
break;
default:
throw new ArgumentException("Roman number string contains an illegal character at index " + i.ToString());
}
intern += Convert.ToInt64(value);
}
return Convert.ToInt64( intern );
}
/// <summary>
/// Calculates the prime number factorization of a given integer
/// </summary>
/// <param name="Number">The integer to be factorized</param>
/// <returns>A SortedDictionary where the keys are the prime factors and the corresponding values their exponent</returns>
public static SortedDictionary<long,long> GetPrimeFactorization(long Number)
{
if (Number == 0)
{
throw new ArgumentOutOfRangeException("Number", "parameter must be greater than zero");
}
SortedDictionary<long, long> factors = new SortedDictionary<long, long>();
if (Number == 1)
{
factors.Add(1, 1);
return factors;
}
long MaxFactor = Convert.ToInt64(Math.Ceiling(Math.Sqrt(Number)));
long CurrentPrime;
PrimeNumberReader pnr = new PrimeNumberReader();
pnr.BeginGetNextPrime();
do
{
CurrentPrime = pnr.GetNextPrime();
while ((Number % CurrentPrime) == 0)
{
Number /= CurrentPrime;
if (factors.ContainsKey(CurrentPrime))
{
factors[CurrentPrime]++;
}
else
{
factors.Add(CurrentPrime, 1);
}
}
if (Number == 1)
{
break;
}
}
while (MaxFactor > CurrentPrime);
if (Number != 1)
{
if (factors.ContainsKey(Number))
{
factors[Number]++;
}
else
{
factors.Add(Number, 1);
}
}
pnr.EndGetNextPrime();
return factors;
}
/// <summary>
/// Generates a list containing all the dividers of a given integer
/// </summary>
/// <param name="Number">The integer</param>
/// <returns>A List containing the dividers</returns>
public static List<long> GetDividers(long Number)
{
return Integers.GetDividers(GetPrimeFactorization(Number));
}
/// <summary>
/// Generates a list containing all the dividers of an integer specified by its prime factorization
/// </summary>
/// <param name="PrimeFactorization">The prime factorization of the integer</param>
/// <returns>A List containing the dividers</returns>
public static List<long> GetDividers(SortedDictionary<long,long> PrimeFactorization)
{
SortedDictionary<long, long> DividerMask = new SortedDictionary<long, long>();
long DividerCount = 1;
foreach (KeyValuePair<long, long> pfactor in PrimeFactorization)
{
DividerCount *= pfactor.Value + 1;
long divMask = 1;
foreach (KeyValuePair<long, long> dmask in DividerMask)
{
divMask *= PrimeFactorization[dmask.Key] + 1;
}
DividerMask.Add(pfactor.Key, divMask);
}
List<long> Dividers = new List<long>(Convert.ToInt32(DividerCount));
for (long i = 0; i < DividerCount; i++)
{
long Divider = 1;
foreach (KeyValuePair<long, long> pfactor in PrimeFactorization)
{
long pow = (i / DividerMask[pfactor.Key]) % (pfactor.Value + 1);
for (long j = 1; j <= pow; j++)
{
Divider *= pfactor.Key;
}
}
Dividers.Add(Divider);
}
Dividers.Sort();
return Dividers;
}
}
|