Problem Statement
There are k slots numbered 1 through k, and you must assign a distinct integer between 1 and n, inclusive, to each slot. The resulting configuration is called an arrangement of k from n. An example of an arrangement of 3 from 5 is (2, 4, 3).
An arrangement is called unfixed if no integer is equal to the number of its slot. For example, the arrangement (2, 4, 3) is not unfixed because the integer 3 is in slot number 3. The arrangement (2, 4, 5), on the other hand, is unfixed.
Given
Definition
- Class:
- UnfixedArrangements
- Method:
- count
- Parameters:
- int, int
- Returns:
- long
- Method signature:
- long count(int n, int k)
- (be sure your method is public)
Constraints
- n will be betwen 1 and 20, inclusive.
- k will be between 1 and n, inclusive.
Examples
3
2
Returns: 3
The unfixed arrangements of 2 from 3 are (2,1), (2,3) and (3,1).
1
1
Returns: 0
The only arrangement of 1 from 1 is not unfixed.
2
2
Returns: 1
The arrangement (2,1) is unfixed.
5
3
Returns: 32
1
1
Returns: 0
2
1
Returns: 1
2
2
Returns: 1
3
1
Returns: 2
3
2
Returns: 3
3
3
Returns: 2
4
1
Returns: 3
4
2
Returns: 7
4
3
Returns: 11
4
4
Returns: 9
5
1
Returns: 4
5
2
Returns: 13
5
3
Returns: 32
5
4
Returns: 53
5
5
Returns: 44
6
1
Returns: 5
6
2
Returns: 21
6
3
Returns: 71
6
4
Returns: 181
6
5
Returns: 309
6
6
Returns: 265
7
1
Returns: 6
7
2
Returns: 31
7
3
Returns: 134
7
4
Returns: 465
7
5
Returns: 1214
7
6
Returns: 2119
7
7
Returns: 1854
8
1
Returns: 7
8
2
Returns: 43
8
3
Returns: 227
8
4
Returns: 1001
8
5
Returns: 3539
8
6
Returns: 9403
8
7
Returns: 16687
8
8
Returns: 14833
9
1
Returns: 8
9
2
Returns: 57
9
3
Returns: 356
9
4
Returns: 1909
9
5
Returns: 8544
9
6
Returns: 30637
9
7
Returns: 82508
9
8
Returns: 148329
9
9
Returns: 133496
10
1
Returns: 9
10
2
Returns: 73
10
3
Returns: 527
10
4
Returns: 3333
10
5
Returns: 18089
10
6
Returns: 81901
10
7
Returns: 296967
10
8
Returns: 808393
10
9
Returns: 1468457
10
10
Returns: 1334961
11
1
Returns: 10
11
2
Returns: 91
11
3
Returns: 746
11
4
Returns: 5441
11
5
Returns: 34754
11
6
Returns: 190435
11
7
Returns: 870274
11
8
Returns: 3184129
11
9
Returns: 8743994
11
10
Returns: 16019531
11
11
Returns: 14684570
12
1
Returns: 11
12
2
Returns: 111
12
3
Returns: 1019
12
4
Returns: 8425
12
5
Returns: 61959
12
6
Returns: 398959
12
7
Returns: 2203319
12
8
Returns: 10146321
12
9
Returns: 37401155
12
10
Returns: 103459471
12
11
Returns: 190899411
12
12
Returns: 176214841
13
1
Returns: 12
13
2
Returns: 133
13
3
Returns: 1352
13
4
Returns: 12501
13
5
Returns: 104084
13
6
Returns: 770713
13
7
Returns: 4996032
13
8
Returns: 27772873
13
9
Returns: 128718044
13
10
Returns: 477471021
13
11
Returns: 1328953592
13
12
Returns: 2467007773
13
13
Returns: 2290792932
14
1
Returns: 13
14
2
Returns: 157
14
3
Returns: 1751
14
4
Returns: 17909
14
5
Returns: 166589
14
6
Returns: 1395217
14
7
Returns: 10391023
14
8
Returns: 67741129
14
9
Returns: 378673901
14
10
Returns: 1764651461
14
11
Returns: 6581134823
14
12
Returns: 18414450877
14
13
Returns: 34361893981
14
14
Returns: 32071101049
15
1
Returns: 14
15
2
Returns: 183
15
3
Returns: 2222
15
4
Returns: 24913
15
5
Returns: 256134
15
6
Returns: 2394751
15
7
Returns: 20157542
15
8
Returns: 150869313
15
9
Returns: 988344062
15
10
Returns: 5551390471
15
11
Returns: 25992300894
15
12
Returns: 97388068753
15
13
Returns: 273749755382
15
14
Returns: 513137616783
15
15
Returns: 481066515734
16
1
Returns: 15
16
2
Returns: 211
16
3
Returns: 2771
16
4
Returns: 33801
16
5
Returns: 380699
16
6
Returns: 3931555
16
7
Returns: 36920799
16
8
Returns: 312129649
16
9
Returns: 2346167879
16
10
Returns: 15434831091
16
11
Returns: 87057596075
16
12
Returns: 409295679481
16
13
Returns: 1539794649171
16
14
Returns: 4345634192131
16
15
Returns: 8178130767479
16
16
Returns: 7697064251745
17
1
Returns: 16
17
2
Returns: 241
17
3
Returns: 3404
17
4
Returns: 44885
17
5
Returns: 549704
17
6
Returns: 6215749
17
7
Returns: 64441684
17
8
Returns: 607496041
17
9
Returns: 5155334720
17
10
Returns: 38896509881
17
11
Returns: 256840738076
17
12
Returns: 1453986832381
17
13
Returns: 6860638482424
17
14
Returns: 25902759280525
17
15
Returns: 73362643649444
17
16
Returns: 138547156531409
17
17
Returns: 130850092279664
18
1
Returns: 17
18
2
Returns: 273
18
3
Returns: 4127
18
4
Returns: 58501
18
5
Returns: 774129
18
6
Returns: 9513973
18
7
Returns: 107951927
18
8
Returns: 1123029513
18
9
Returns: 10622799089
18
10
Returns: 90449857081
18
11
Returns: 684702346767
18
12
Returns: 4536075689293
18
13
Returns: 25762467303377
18
14
Returns: 121951698034461
18
15
Returns: 461904032857319
18
16
Returns: 1312349454922513
18
17
Returns: 2486151753313617
18
18
Returns: 2355301661033953
19
1
Returns: 18
19
2
Returns: 307
19
3
Returns: 4946
19
4
Returns: 75009
19
5
Returns: 1066634
19
6
Returns: 14158747
19
7
Returns: 174549738
19
8
Returns: 1986644929
19
9
Returns: 20730064706
19
10
Returns: 196677847971
19
11
Returns: 1679650774658
19
12
Returns: 12752503850497
19
13
Returns: 84731451264186
19
14
Returns: 482626240281739
19
15
Returns: 2291179503374234
19
16
Returns: 8702813980639617
19
17
Returns: 24796092486996338
19
18
Returns: 47106033220679059
19
19
Returns: 44750731559645106
20
1
Returns: 19
20
2
Returns: 343
20
3
Returns: 5867
20
4
Returns: 94793
20
5
Returns: 1441679
20
6
Returns: 20558551
20
7
Returns: 273660967
20
8
Returns: 3383042833
20
9
Returns: 38609869067
20
10
Returns: 403978495031
20
11
Returns: 3843107102339
20
12
Returns: 32908313146393
20
13
Returns: 250514001320647
20
14
Returns: 1668866557980343
20
15
Returns: 9530573107600319
20
16
Returns: 45361686034627361
20
17
Returns: 172743930157869827
20
18
Returns: 493435697986613143
20
19
Returns: 939765362752547227
20
20
Returns: 895014631192902121