Problem Statement | | |
You are given an undirected graph with n nodes and m edges.
The nodes are numbered 0 through n-1.
The edges are given in the int[]s a and b: for each valid index i, there is an edge between a[i] and b[i].
This graph may have self-loops or multiple edges.
Let f(k) denote the number of ways to choose a subset of exactly k edges so the graph consisting of all n nodes and the edges you selected is connected.
Let g(k) = f(k) modulo (10^9 + 7).
Return a int[] with exactly m-n+2 elements.
For each i starting from 0, element i of the return value should be g(i+n-1).
| | | Definition | | | | Class: | SpanningSubgraphs | | Method: | count | | Parameters: | int, int[], int[] | | Returns: | int[] | | Method signature: | int[] count(int n, int[] a, int[] b) | | (be sure your method is public) |
| | | | | | Constraints | | - | n will be between 1 and 15, inclusive. | | - | m will be between n-1 and 200, inclusive. | | - | a and b will contain exactly m elements each. | | - | Each element of a and b will be between 0 and n-1, inclusive. | | | Examples | | 0) | | | | | Returns: {3, 1 } | | This case is a triangle graph. For k=2, we can choose any subset of 2 edges, for a total of 3 choices. For k=3, we only have one way (choosing all edges). |
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| | 1) | | | | | Returns: {0 } | | Even though m is at least n-1, the graph you are given is not necessarily connected. |
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| | 2) | | | | 6 | {0,1,1,2,2,2,3,3,4} | {1,2,3,3,4,5,4,5,5} |
| Returns: {40, 48, 27, 8, 1 } | |
| | 3) | | | | 15 | {7,3,8,2,5,8,5,11,8,3,10,8,6,6,8,8,3,9,4,6,4,6,1,1,5,4,
0,9,4,7,6,0,6,2,2,6,11,4,6,10,9,2,6,0,4,7,6,8,1,3,11,3,
4,8,1,0,12,9,5,14,0,13,7,14,7,9,6,7,8,8,8,4,14,1,13,5,
1,6,13,14,0,4,8,5,13,7,2,10,10,11,8,2,4,13,12,10,5,13,
5,9,6,4,1,11,4,13,6,4,8,8,11,1,14,10,3,1,2,0,10,5,9,5,
10,8,4,2,5,12,7,2,3,2,4,6,9,3,7,9,2,14,14,0,14,3,12,12,
0,11,7,8,6,6,0,10,7,2,0,7,8,10,3,11,11,7,0,0,11,8,6,11,
13,4,11,11,8,5,13,11,9,14,10,1,12,12,3,3,0,13,13,6,2,9,
1,4,2,7,14,5} | {12,8,1,11,1,6,12,3,7,5,1,1,11,11,9,0,7,9,12,8,13,13,11,
0,2,14,12,12,13,10,13,12,2,14,11,13,14,3,12,14,11,5,3,0,
9,0,1,10,5,11,6,6,1,4,0,12,13,1,4,10,9,8,3,4,13,3,10,7,
3,2,13,0,1,13,7,3,3,9,9,10,9,9,0,13,12,3,14,4,1,7,5,0,0,
11,13,0,0,14,13,5,5,0,10,0,3,8,13,4,6,7,4,0,6,7,8,10,7,
4,6,13,0,6,3,2,11,8,7,12,0,14,12,6,10,8,6,9,2,4,14,9,4,
6,3,11,12,8,7,12,14,0,10,11,9,7,4,6,12,13,7,4,13,9,7,13,
2,4,7,6,2,0,10,7,8,13,1,14,13,3,12,14,2,4,6,7,10,11,8,4,
10,13,14,9,0,5,3,0,7,11} |
| Returns:
{165676111, 472152904, 401323420, 92841577, 361806106, 251066093, 860026758, 204774808, 800204699, 78217142, 290847617, 377659363, 799299488, 639266686, 463155556, 542289798, 505455263, 931966095, 332452321, 157494446, 701362585, 4372546, 189983818, 137009880, 456907012, 699388046, 492757156, 402334178, 262521060, 683669243, 218329042, 912344074, 469164876, 951780423, 845657616, 358560958, 877409160, 936645440, 506542339, 711561307, 182417811, 411559656, 609363889, 410499565, 523968597, 808436626, 796861282, 799905851, 332114660, 28142829, 832046308, 515892527, 461122988, 459763203, 639481498, 760842951, 53778152, 531539556, 499281391, 756160187, 408189379, 536177501, 236162240, 932086574, 249801471, 691291871, 305954956, 944526707, 689056121, 509929491, 860012851, 270237338, 530915439, 636690481, 284974622, 213167754, 791793494, 581854637, 515718421, 142304792, 170068497, 175763828, 669814256, 87330307, 657451539, 902803718, 994244944, 710593682, 158314930, 728217704, 428356628, 680806591, 426349961, 578797504, 448716917, 937968991, 727251530, 565010419, 762565871, 373908747, 569188731, 954967822, 83820159, 869337563, 549355611, 927598978, 992408503, 670497964, 348959921, 892858049, 328944072, 946559373, 830835081, 805632932, 389521576, 995252131, 717245242, 882920285, 127735960, 774020953, 299323686, 248711270, 707972648, 824068405, 929290955, 262377161, 603969848, 20319782, 655428762, 772441022, 315946694, 773490199, 63054183, 280718941, 320481045, 714052434, 119312921, 334810041, 844617606, 239955633, 647743078, 159621066, 358764917, 571545322, 29056136, 300270686, 822798951, 841318305, 809733973, 849084831, 542304340, 360014205, 268267900, 461637720, 441483501, 500466014, 722102413, 274028790, 889071123, 456597703, 989359978, 781914152, 339994675, 176509460, 71482668, 940949411, 727100238, 343026545, 279293690, 51741525, 759652847, 198027784, 293410546, 430593193, 339024072, 605239373, 602353448, 433606430, 526225238, 410141720, 62117055, 1274196, 19503, 198, 1 } | |
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