TopCoder Statistics - Problem Statement

Problem Statement

We have two fractions: a smaller fraction N1 / D1 and a bigger fraction N2 / D2.

Your task is to find three more fractions: A/B, C/D, and E/F.

These three fractions must have three distinct values, and they must all lie strictly between N1 / D1 and N2 / D2.

All values A, B, C, D, E, F must be integers between 1 and 10^9, inclusive.

Return the int[] {A, B, C, D, E, F}. All valid solutions will be accepted.

Definition

Class:: ThreeFractions
Method:: find
Parameters:: int, int, int, int
Returns:: int[]
Method signature:: int[] find(int N1, int D1, int N2, int D2)
(be sure your method is public)

Constraints

Each number in the input will be between 1 and 5000, inclusive.
The value of N1 / D1 will be strictly smaller than the value of N2 / D2.

Examples

1

3

2

3

Returns: {1, 2, 3, 5, 147, 233 }

We are looking for three fractions between 1/3 and 2/3. The three returned fractions are 1/2 = 0.5, 3/5 = 0.6, and 147/233 = approximately 0.631.
1

7

7

1

Returns: {2, 1, 5, 1, 3, 1 }

We are looking for three fractions between 1/7 and 7/1. The three returned fractions are 2/1, 5/1, and 3/1.
2

3

3

4

Returns: {7, 10, 71, 100, 47, 69 }
2584

4181

1597

2584

Returns: {26708225, 43214816, 26708226, 43214816, 26708227, 43214816 }
7

9

4

1

Returns: {29, 36, 30, 36, 31, 36 }
15

19

11

9

Returns: {541, 684, 542, 684, 543, 684 }
13

20

17

13

Returns: {677, 1040, 678, 1040, 679, 1040 }
1

7

1

4

Returns: {17, 112, 18, 112, 19, 112 }
1

9

8

9

Returns: {37, 324, 38, 324, 39, 324 }
1

11

19

14

Returns: {57, 616, 58, 616, 59, 616 }
4

5

4

1

Returns: {17, 20, 18, 20, 19, 20 }
3

5

3

2

Returns: {25, 40, 26, 40, 27, 40 }
11

18

19

7

Returns: {309, 504, 310, 504, 311, 504 }
5

11

4

1

Returns: {21, 44, 22, 44, 23, 44 }
1

3

19

13

Returns: {53, 156, 54, 156, 55, 156 }
17

18

9

4

Returns: {273, 288, 274, 288, 275, 288 }
7

16

8

11

Returns: {309, 704, 310, 704, 311, 704 }
2

7

5

3

Returns: {25, 84, 26, 84, 27, 84 }
5

4

2

1

Returns: {21, 16, 22, 16, 23, 16 }
2

3

19

2

Returns: {17, 24, 18, 24, 19, 24 }
19

13

8

5

Returns: {381, 260, 382, 260, 383, 260 }
2

5

9

17

Returns: {137, 340, 138, 340, 139, 340 }
4

7

13

16

Returns: {257, 448, 258, 448, 259, 448 }
9

20

18

5

Returns: {181, 400, 182, 400, 183, 400 }
1

3

15

1

Returns: {5, 12, 6, 12, 7, 12 }
9

17

1

1

Returns: {37, 68, 38, 68, 39, 68 }
10

9

8

7

Returns: {281, 252, 282, 252, 283, 252 }
20

9

6

1

Returns: {81, 36, 82, 36, 83, 36 }
20

17

16

11

Returns: {881, 748, 882, 748, 883, 748 }
1

19

8

7

Returns: {29, 532, 30, 532, 31, 532 }
6

7

1

1

Returns: {25, 28, 26, 28, 27, 28 }
5

4

16

7

Returns: {141, 112, 142, 112, 143, 112 }
5

19

12

17

Returns: {341, 1292, 342, 1292, 343, 1292 }
3

5

13

4

Returns: {49, 80, 50, 80, 51, 80 }
1

4

14

3

Returns: {13, 48, 14, 48, 15, 48 }
9

2

12

1

Returns: {37, 8, 38, 8, 39, 8 }
5

6

17

16

Returns: {321, 384, 322, 384, 323, 384 }
7

16

17

15

Returns: {421, 960, 422, 960, 423, 960 }
1

3

1

1

Returns: {5, 12, 6, 12, 7, 12 }
6

5

18

11

Returns: {265, 220, 266, 220, 267, 220 }
1

10

4

1

Returns: {5, 40, 6, 40, 7, 40 }
1

3

13

4

Returns: {17, 48, 18, 48, 19, 48 }
9

5

5

1

Returns: {37, 20, 38, 20, 39, 20 }
2

5

18

5

Returns: {41, 100, 42, 100, 43, 100 }
3829

3215

4147

3482

Returns: {53330313, 44778520, 53330314, 44778520, 53330315, 44778520 }
1349

1313

3335

3246

Returns: {17515417, 17047992, 17515418, 17047992, 17515419, 17047992 }
451

1097

1996

4855

Returns: {8758421, 21303740, 8758422, 21303740, 8758423, 21303740 }
2187

2087

2378

2269

Returns: {19849213, 18941612, 19849214, 18941612, 19849215, 18941612 }
191

806

332

1401

Returns: {1070365, 4516824, 1070366, 4516824, 1070367, 4516824 }
4464

4957

3468

3851

Returns: {68763457, 76357628, 68763458, 76357628, 68763459, 76357628 }
2944

4259

737

569

Returns: {6700545, 9693484, 6700546, 9693484, 6700547, 9693484 }
3881

3121

1208

965

Returns: {14980661, 12047060, 14980662, 12047060, 14980663, 12047060 }
3535

4772

3573

4778

Returns: {67560921, 91202464, 67560922, 91202464, 67560923, 91202464 }
847

1556

1281

2327

Returns: {7883877, 14483248, 7883878, 14483248, 7883879, 14483248 }
1267

3477

1529

4196

Returns: {21265329, 58357968, 21265330, 58357968, 21265331, 58357968 }
1593

2494

1322

1197

Returns: {7627285, 11941272, 7627286, 11941272, 7627287, 11941272 }
601

1220

1971

4001

Returns: {9618405, 19524880, 9618406, 19524880, 9618407, 19524880 }
571

2021

1108

3921

Returns: {8955565, 31697364, 8955566, 31697364, 8955567, 31697364 }
366

1711

163

762

Returns: {1115569, 5215128, 1115570, 5215128, 1115571, 5215128 }
52

1211

43

1000

Returns: {208001, 4844000, 208002, 4844000, 208003, 4844000 }
4595

4646

901

895

Returns: {16450101, 16632680, 16450102, 16632680, 16450103, 16632680 }
1936

4325

2077

4630

Returns: {35854721, 80099000, 35854722, 80099000, 35854723, 80099000 }
23

434

283

5000

Returns: {460001, 8680000, 460002, 8680000, 460003, 8680000 }
606

3311

785

4289

Returns: {10396537, 56803516, 10396538, 56803516, 10396539, 56803516 }
1591

2094

2173

2860

Returns: {18201041, 23955360, 18201042, 23955360, 18201043, 23955360 }
2729

4078

2905

4341

Returns: {47386357, 70810392, 47386358, 70810392, 47386359, 70810392 }
2448

3577

119

160

Returns: {1566721, 2289280, 1566722, 2289280, 1566723, 2289280 }
769

3822

100

497

Returns: {1528773, 7598136, 1528774, 7598136, 1528775, 7598136 }
1439

1187

4928

4065

Returns: {23398141, 19300620, 23398142, 19300620, 23398143, 19300620 }
529

4549

262

2253

Returns: {4767349, 40995588, 4767350, 40995588, 4767351, 40995588 }
1443

607

4337

1130

Returns: {6522361, 2743640, 6522362, 2743640, 6522363, 2743640 }
2062

3379

1323

2168

Returns: {17881665, 29302688, 17881666, 29302688, 17881667, 29302688 }
2156

4385

1861

3785

Returns: {32641841, 66388900, 32641842, 66388900, 32641843, 66388900 }
555

1307

1305

3073

Returns: {6822061, 16065644, 6822062, 16065644, 6822063, 16065644 }
2261

3013

1805

2404

Returns: {21741777, 28973008, 21741778, 28973008, 21741779, 28973008 }
1552

4067

1815

4756

Returns: {29525249, 77370608, 29525250, 77370608, 29525251, 77370608 }
611

3740

801

4903

Returns: {11982933, 73348880, 11982934, 73348880, 11982935, 73348880 }
2831

2418

2166

1799

Returns: {20371877, 17399928, 20371878, 17399928, 20371879, 17399928 }
2488

3083

1899

2351

Returns: {23397153, 28992532, 23397154, 28992532, 23397155, 28992532 }
3193

4819

1353

2042

Returns: {26080425, 39361592, 26080426, 39361592, 26080427, 39361592 }
103

419

545

2177

Returns: {896925, 3648652, 896926, 3648652, 896927, 3648652 }
275

84

395

99

Returns: {108901, 33264, 108902, 33264, 108903, 33264 }
43

787

182

3331

Returns: {572933, 10485988, 572934, 10485988, 572935, 10485988 }
1468

1711

3963

4619

Returns: {27122769, 31612436, 27122770, 31612436, 27122771, 31612436 }
221

584

1150

3029

Returns: {2677637, 7075744, 2677638, 7075744, 2677639, 7075744 }
521

1119

1435

3082

Returns: {6422889, 13795032, 6422890, 13795032, 6422891, 13795032 }
401

1068

187

498

Returns: {798793, 2127456, 798794, 2127456, 798795, 2127456 }
2662

3921

3309

4874

Returns: {51898353, 76443816, 51898354, 76443816, 51898355, 76443816 }
1726

4027

1384

3229

Returns: {22293017, 52012732, 22293018, 52012732, 22293019, 52012732 }
3554

3989

1969

2210

Returns: {31417361, 35262760, 31417362, 35262760, 31417363, 35262760 }
536

4833

179

1614

Returns: {3460417, 31201848, 3460418, 31201848, 3460419, 31201848 }
3930

4403

1238

1387

Returns: {21803641, 24427844, 21803642, 24427844, 21803643, 24427844 }
351

628

2271

4063

Returns: {5704453, 10206256, 5704454, 10206256, 5704455, 10206256 }
391

403

1276

1315

Returns: {2056661, 2119780, 2056662, 2119780, 2056663, 2119780 }
239

2438

483

4927

Returns: {4710213, 48048104, 4710214, 48048104, 4710215, 48048104 }
1320

4039

569

1741

Returns: {9192481, 28127596, 9192482, 28127596, 9192483, 28127596 }
1733

3533

1011

2059

Returns: {14272989, 29097788, 14272990, 29097788, 14272991, 29097788 }
766

347

117

53

Returns: {162393, 73564, 162394, 73564, 162395, 73564 }
2275

4246

681

1271

Returns: {11566101, 21586664, 11566102, 21586664, 11566103, 21586664 }
42

169

1206

4639

Returns: {779353, 3135964, 779354, 3135964, 779355, 3135964 }
2491

4654

2210

4129

Returns: {41141357, 76865464, 41141358, 76865464, 41141359, 76865464 }
260

3503

119

1587

Returns: {1650481, 22237044, 1650482, 22237044, 1650483, 22237044 }
377

483

2977

3814

Returns: {5751513, 7368648, 5751514, 7368648, 5751515, 7368648 }
3753

2981

4735

3761

Returns: {56460133, 44846164, 56460134, 44846164, 56460135, 44846164 }
1

5000

2

5000

Returns: {20001, 100000000, 20002, 100000000, 20003, 100000000 }
1

2

1001

2000

Returns: {8001, 16000, 8002, 16000, 8003, 16000 }
4991

4993

4997

4999

Returns: {99800037, 99840028, 99800038, 99840028, 99800039, 99840028 }
1

1

2

1

Returns: {5, 4, 6, 4, 7, 4 }
4999

5000

5000

5000

Returns: {99980001, 100000000, 99980002, 100000000, 99980003, 100000000 }
2

3

2001

3000

Returns: {24001, 36000, 24002, 36000, 24003, 36000 }

Statistics

Problem Statement for "ThreeFractions"

Problem Statement

Definition

Constraints

Examples