Problem Statement
{ n if m = 0
f(m,n) = { 0 if n = 0
{ n*f(m-1,n) - g(m-1,n-1) otherwise
{ 0 if y = 0
g(x,y) = {
{ f(x,y) + g(x,y-1) otherwise
Given m and n your function will return the value of f.Definition
- Class:
- BigFunc
- Method:
- value
- Parameters:
- int, int
- Returns:
- long
- Method signature:
- long value(int m, int n)
- (be sure your method is public)
Notes
- It should be clear from the above recurrences that the function will always converge to a value. i.e. it will not go into an infinite recurrence.
Constraints
- m will be between 0 and 100 inclusive
- n will be between 0 and 100 inclusive
- The return value will be between 0 and 2^63-1 inclusive.
Examples
10
1
Returns: 1
1
4
Returns: 10
10
10
Returns: 14914341925
20
8
Returns: 1236466399775623332
50
2
Returns: 1125899906842625
100
0
Returns: 0
0
100
Returns: 100
100
1
Returns: 1
15
15
Returns: 665478473553144000
25
5
Returns: 299149971105959625
2
100
Returns: 338350
3
100
Returns: 25502500
23
3
Returns: 94151567436
7
14
Returns: 241561425
6
79
Returns: 2866497743240
84
1
Returns: 1
5
14
Returns: 1539825
6
85
Returns: 4770465871755
15
1
Returns: 1
11
1
Returns: 1
2
50
Returns: 42925
5
20
Returns: 12333300
9
49
Returns: 8818348440624625
1
91
Returns: 4186
17
8
Returns: 2502137235710736
7
76
Returns: 146564344279276
5
39
Returns: 632533200
9
61
Returns: 77325108640113601
11
3
Returns: 179196
20
3
Returns: 3487832978
4
25
Returns: 2153645
1
33
Returns: 561
19
5
Returns: 19349527020825
1
48
Returns: 1176
8
96
Returns: 80605262346859312
7
8
Returns: 3297456
13
25
Returns: 3470324885123487625
8
94
Returns: 66757162244130351
3
99
Returns: 24502500
2
52
Returns: 48230
15
4
Returns: 1088123500
1
6
Returns: 21
7
54
Returns: 9721668990825
3
97
Returns: 22591009
5
6
Returns: 12201
4
31
Returns: 6197520
10
63
Returns: 6146453785375960224
1
7
Returns: 28
10
3
Returns: 60074
9
52
Returns: 15885544497350788
11
6
Returns: 415998681
6
91
Returns: 7669354937686
4
77
Returns: 559085527
3
24
Returns: 90000
1
69
Returns: 2415
2
71
Returns: 121836
12
1
Returns: 1
7
2
Returns: 129
3
100
Returns: 25502500
8
55
Returns: 554589089159644
8
33
Returns: 5888429949457
2
100
Returns: 338350
1
29
Returns: 435
15
6
Returns: 501790686201
1
46
Returns: 1081
1
1
Returns: 1
4
13
Returns: 89271
1
40
Returns: 820
7
83
Returns: 295295255888556
27
2
Returns: 134217729
5
52
Returns: 3488249908
12
12
Returns: 13421957361110
2
65
Returns: 93665
12
15
Returns: 223160292749512
8
13
Returns: 1627802631
1
84
Returns: 3570
7
65
Returns: 42325704703425
17
9
Returns: 19179318935377305
4
20
Returns: 722666
22
1
Returns: 1
12
14
Returns: 93413954858887
20
7
Returns: 83544895168776356
14
10
Returns: 128037802953445
5
75
Returns: 30862792500
8
50
Returns: 237065826416665
3
81
Returns: 11029041
9
63
Returns: 106496009343230976
10
59
Returns: 3004219455962946550
6
43
Returns: 42065402654
8
59
Returns: 1037629077167998
22
1
Returns: 1
2
94
Returns: 281295
21
7
Returns: 580964060390826448
3
74
Returns: 7700625
8
38
Returns: 20607480744851
9
59
Returns: 55553266547279460
6
51
Returns: 137172159826
4
78
Returns: 596100583
8
72
Returns: 6145421331081828
29
3
Returns: 68630914235796
9
51
Returns: 13105638613715076
3
53
Returns: 2047761
7
33
Returns: 197863309281
44
2
Returns: 17592186044417
3
90
Returns: 16769025
15
17
Returns: 4680823029669806769
7
44
Returns: 1919898614700
8
68
Returns: 3687185189098690
1
11
Returns: 66
11
1
Returns: 1
13
19
Returns: 80481629714694580
7
24
Returns: 16164030000
15
15
Returns: 665478473553144000
8
100
Returns: 116177773111333330
10
50
Returns: 494346993683649625
6
99
Returns: 13790714119050
8
40
Returns: 32513090005332
9
98
Returns: 8593982052566357601
11
45
Returns: 6543372751114856625
10
40
Returns: 43591205959337700
16
14
Returns: 3086374641883169287
9
80
Returns: 1142108795719679040