TopCoder Statistics - Problem Statement

Problem Statement

A very famous algorithms text presents its readers with a seemingly simple math problem in its opening chapter:
Find the smallest positive integer value of n such that a*(n^k) < k^n, where a and k are given integral values and ^ denotes exponentiation.
Solving this problem algebraically involves using the overly complicated Lambert W function. Instead you are to solve the problem by creating a class HardIneq with a method biggestVal which, given a and k, returns the smallest positive integer value of n such that a*(n^k) < k^n.

Definition

Class:: HardIneq
Method:: biggestVal
Parameters:: int, int
Returns:: int
Method signature:: int biggestVal(int a, int k)
(be sure your method is public)

Notes

Remember that log(x^y) = y * log(x) and that log(x*y) = log(x) + log(y)

Constraints

a will be between 1 and 10000, inclusive
k will be between 2 and 1000, inclusive

Examples

10

5

Returns: 8

if n = 1, we have a*(n^k) = 10*(1^5) = 10, and k^n = 5^1 = 5. 10 is not less than 5. n=2: 10*2^5 is not less than 5^2 n=2: 10*3^5 is not less than 5^3 and so on. Not until we get to n = 8, and have 10*8^5 = 327680, and 5^8 = 390625 is the inequality satisfied.
1

2

Returns: 1

1*(1^2) is less than 2^1, so we return 1.
2

20

Returns: 1
2000

200

Returns: 202
1000

100

Returns: 102
503

33

Returns: 36
31

23

Returns: 25
100

99

Returns: 101
657

12

Returns: 17
99

100

Returns: 1
861

2

Returns: 19
1634

242

Returns: 244
3147

434

Returns: 436
463

777

Returns: 1
4210

191

Returns: 193
1387

7

Returns: 13
2740

73

Returns: 76
6248

797

Returns: 799
4913

95

Returns: 98
4046

448

Returns: 450
265

651

Returns: 1
6103

582

Returns: 584
2208

649

Returns: 651
6063

918

Returns: 920
6661

714

Returns: 716
8667

459

Returns: 461
5040

509

Returns: 511
1562

541

Returns: 543
828

999

Returns: 1
2541

112

Returns: 115
4765

807

Returns: 809
561

517

Returns: 519
2245

613

Returns: 615
2626

84

Returns: 87
7991

962

Returns: 964
230

791

Returns: 1
7248

708

Returns: 710
8402

344

Returns: 346
9813

755

Returns: 757
7625

58

Returns: 61
3061

752

Returns: 754
3877

52

Returns: 55
2789

851

Returns: 853
4907

379

Returns: 381
6184

678

Returns: 680
1439

904

Returns: 906
9515

234

Returns: 237
505

912

Returns: 1
4238

506

Returns: 508
4320

680

Returns: 682
9142

214

Returns: 217
2200

492

Returns: 494
2866

237

Returns: 239
4924

866

Returns: 868
688

975

Returns: 1
613

91

Returns: 93
1801

94

Returns: 97
8722

508

Returns: 510
8507

841

Returns: 843
4072

390

Returns: 392
6690

424

Returns: 426
27

3

Returns: 10

Note that 27*9^3 is equal to 3^9.
729

6

Returns: 13
10000

1000

Returns: 1002
2000

200

Returns: 202
27

3

Returns: 10
9999

1000

Returns: 1002

Statistics

Problem Statement for "HardIneq"

Problem Statement

Definition

Notes

Constraints

Examples