TopCoder Statistics - Problem Statement

Problem Statement

A single elimination tournament begins with teams numbered 1 through N, where N is a power of 2. In the first round, teams 1 and 2 compete against each other, teams 3 and 4 compete against each other, and so on up to teams N-1 and N. The N/2 losing teams are eliminated, and the N/2 winning teams advance to the second round.

In the second round, the winner of teams 1 and 2 compete against the winner of teams 3 and 4. The winner of teams 5 and 6 compete against the winner of teams 7 and 8. The winner of teams N-3 and N-2 compete against the winner of teams N-1 and N.

The tournament continues in this fashion, with half the remaining teams eliminated in each round, until there is only one team left. This team is the winner of the tournament. Obviously, the numeration of the teams is very important for determining the winner. You want your favorite team to win the tournament, so you want to find the order which gives your team the best chances to become the winner.

You will be given a String[] chances that contains exactly N elements, each containing exactly N space-separated probabilities. The j-th number in the i-th element of chances represents the probability (in percents) that team i will win a game against team j. The 1-based index of your favorite team in chances is team. You are to order the teams in such a way that your team will have the highest probability to win the tourney and return this probability as a double. See examples for further clarification.

Definition

Class:: SingleElimination
Method:: bestChance
Parameters:: String[], int
Returns:: double
Method signature:: double bestChance(String[] chances, int team)
(be sure your method is public)

Notes

Your return value must have an absolute or relative error less than 1e-9.

Constraints

The number of elements in chances will be a power of 2 between 1 and 8, inclusive.
Each element of chances will be a single-space-separated list of integers, with no additional whitespace and no leading zeros.
Each element of chances will contain a number of integers equal to the number of elements in chances.
Each integer in chances will be between 0 and 100, inclusive.
The i-th integer in the j-th element of chances and the j-th integer in the i-th element of chances will sum to 100, if i != j.
The i-th integer if the i-th element of chances will be 0.
team will be between 1 and the number of elements in chances, inclusive.

Examples

{"0 90 0 100", "10 0 50 100", "100 50 0 100", "0 0 0 0"}

1

Returns: 0.45

It's optimal for team 1 to play against team 4 in the first round. Team 1 always beats team 4, and to have any chances to win the tourney, needs team 2 to beat team 3 (with a 50%). Team 1 would then have a 90% chance of beating team 2 in the final game. Therefore, the correct answer is 0.5 * 0.9 = 0.45.
{"0 90 0 100", "10 0 50 100", "100 50 0 100", "0 0 0 0"}

2

Returns: 0.5
{"0 90 0 100", "10 0 50 100", "100 50 0 100", "0 0 0 0"}

3

Returns: 0.9500000000000001

The third team has much better chances.
{"0 90 0 100", "10 0 50 100", "100 50 0 100", "0 0 0 0"}

4

Returns: 0.0
{"0 90 50 100", "10 0 50 100", "50 50 0 100", "0 0 0 0"}

1

Returns: 0.7
{ "0 93 51 65 84 41 12 74", "7 0 60 93 57 45 74 97", "49 40 0 14 82 7 29 69", "35 7 86 0 51 8 41 20", "16 43 18 49 0 54 76 2", "59 55 93 92 46 0 1 94", "88 26 71 59 24 99 0 53", "26 3 31 80 98 6 47 0"}

1

Returns: 0.37567091675904
{ "0 75 4 53 33 2 48 86", "25 0 92 69 13 25 61 80", "96 8 0 82 14 0 91 44", "47 31 18 0 55 60 45 45", "67 87 86 45 0 70 97 45", "98 75 100 40 30 0 70 8", "52 39 9 55 3 30 0 34", "14 20 56 55 55 92 66 0"}

3

Returns: 0.31017612080000007
{ "0 0 52 64 34 13 17 4", "100 0 52 83 28 74 56 54", "48 48 0 22 41 94 85 21", "36 17 78 0 73 83 32 40", "66 72 59 27 0 28 60 94", "87 26 6 17 72 0 13 74", "83 44 15 68 40 87 0 25", "96 46 79 60 6 26 75 0"}

2

Returns: 0.4445831919999999
{ "0 4 30 28 39 73 87 5", "96 0 55 3 57 18 48 16", "70 45 0 87 16 67 46 68", "72 97 13 0 62 12 79 23", "61 43 84 38 0 9 99 22", "27 82 33 88 91 0 24 43", "13 52 54 21 1 76 0 72", "95 84 32 77 78 57 28 0"}

1

Returns: 0.14675196579343996
{ "0 67 26 65 0 66 32 48", "33 0 58 36 33 76 98 46", "74 42 0 23 30 83 82 72", "35 64 77 0 59 12 57 20", "100 67 70 41 0 15 74 47", "34 24 17 88 85 0 30 92", "68 2 18 43 26 70 0 63", "52 54 28 80 53 8 37 0"}

5

Returns: 0.359421731672
{ "0 34 85 15 1 36 31 47", "66 0 56 13 27 27 44 45", "15 44 0 85 52 46 5 6", "85 87 15 0 74 68 91 70", "99 73 48 26 0 61 87 39", "64 73 54 32 39 0 40 80", "69 56 95 9 13 60 0 86", "53 55 94 30 61 20 14 0"}

4

Returns: 0.5470337662104
{ "0 83 7 43 33 56 44 22", "17 0 19 78 84 14 60 44", "93 81 0 5 11 100 49 40", "57 22 95 0 21 40 58 86", "67 16 89 79 0 53 70 10", "44 86 0 60 47 0 47 11", "56 40 51 42 30 53 0 75", "78 56 60 14 90 89 25 0"}

5

Returns: 0.41433929782
{ "0 16 22 38 11 90 54 62", "84 0 27 95 77 66 60 23", "78 73 0 86 69 54 58 66", "62 5 14 0 88 70 4 23", "89 23 31 12 0 8 23 30", "10 34 46 30 92 0 33 76", "46 40 42 96 77 67 0 21", "38 77 34 77 70 24 79 0"}

1

Returns: 0.17544219598080002
{ "0 88 47 10 30 16 78 62", "12 0 100 58 30 54 79 80", "53 0 0 41 35 32 100 17", "90 42 59 0 9 72 14 37", "70 70 65 91 0 6 7 94", "84 46 68 28 94 0 50 70", "22 21 0 86 93 50 0 76", "38 20 83 63 6 30 24 0"}

6

Returns: 0.46440981887999994
{ "0 66 72 33 72 48 63 26", "34 0 75 66 32 4 23 79", "28 25 0 91 8 99 92 6", "67 34 9 0 58 1 10 87", "28 68 92 42 0 74 94 29", "52 96 1 99 26 0 60 9", "37 77 8 90 6 40 0 86", "74 21 94 13 71 91 14 0"}

7

Returns: 0.35961519312000007
{ "0 77 31 45 73 12 1 65", "23 0 12 1 20 5 76 24", "69 88 0 25 39 61 68 84", "55 99 75 0 84 21 14 82", "27 80 61 16 0 45 90 4", "88 95 39 79 55 0 0 85", "99 24 32 86 10 100 0 51", "35 76 16 18 96 15 49 0"}

7

Returns: 0.6675944704407
{ "0 59 23 59 13 63 26 71", "41 0 68 33 88 7 48 72", "77 32 0 99 34 67 82 36", "41 67 1 0 22 21 49 98", "87 12 66 78 0 92 52 50", "37 93 33 79 8 0 47 20", "74 52 18 51 48 53 0 53", "29 28 64 2 50 80 47 0"}

4

Returns: 0.20426807127551996
{ "0 58 29 1 96 47 10 44", "42 0 86 48 0 80 72 16", "71 14 0 29 61 37 21 100", "99 52 71 0 55 47 57 73", "4 100 39 45 0 21 41 79", "53 20 63 53 79 0 17 8", "90 28 79 43 59 83 0 6", "56 84 0 27 21 92 94 0"}

5

Returns: 0.32122253649200005
{ "0 37 49 37 85 39 69 74", "63 0 68 11 7 94 100 12", "51 32 0 99 4 36 48 94", "63 89 1 0 39 17 99 65", "15 93 96 61 0 68 46 12", "61 6 64 83 32 0 79 4", "31 0 52 1 54 21 0 77", "26 88 6 35 88 96 23 0"}

4

Returns: 0.49144859463743995
{ "0 27 59 35 4 79 16 12", "73 0 17 23 70 66 69 88", "41 83 0 0 37 99 82 92", "65 77 100 0 24 57 97 62", "96 30 63 76 0 12 45 37", "21 34 1 43 88 0 14 1", "84 31 18 3 55 86 0 39", "88 12 8 38 63 99 61 0"}

1

Returns: 0.13229890016
{ "0 36 53 82 87 19 30 66", "64 0 56 58 36 56 18 63", "47 44 0 37 2 88 74 60", "18 42 63 0 14 13 18 28", "13 64 98 86 0 4 46 49", "81 44 12 87 96 0 20 10", "70 82 26 82 54 80 0 13", "34 37 40 72 51 90 87 0"}

8

Returns: 0.4370994014399999
{ "0 71 34 96 62 82 67 73", "29 0 15 90 9 65 92 3", "66 85 0 34 83 80 90 11", "4 10 66 0 100 56 60 51", "38 91 17 0 0 64 85 88", "18 35 20 44 36 0 2 24", "33 8 10 40 15 98 0 38", "27 97 89 49 12 76 62 0"}

1

Returns: 0.5438704657919998
{ "0 71 40 54 5 44 96 11", "29 0 61 34 72 98 93 22", "60 39 0 65 55 50 62 61", "46 66 35 0 7 7 36 77", "95 28 45 93 0 47 24 33", "56 2 50 93 53 0 69 11", "4 7 38 64 76 31 0 72", "89 78 39 23 67 89 28 0"}

7

Returns: 0.23677526410240002
{ "0 42 64 50 47 53 16 74", "58 0 8 65 18 84 92 15", "36 92 0 97 74 62 39 54", "50 35 3 0 61 29 64 30", "53 82 26 39 0 41 89 67", "47 16 38 71 59 0 29 2", "84 8 61 36 11 71 0 69", "26 85 46 70 33 98 31 0"}

7

Returns: 0.30289878659712
{ "0 86 81 74 11 59 18 91", "14 0 71 100 14 33 49 90", "19 29 0 14 42 16 35 14", "26 0 86 0 46 67 14 9", "89 86 58 54 0 32 66 18", "41 67 84 33 68 0 64 81", "82 51 65 86 34 36 0 14", "9 10 86 91 82 19 86 0"}

4

Returns: 0.16996750065792005
{ "0 30", "70 0" }

1

Returns: 0.3
{ "0 30", "70 0" }

2

Returns: 0.7
{ "0" }

1

Returns: 1.0
{ "0 50 50 50 50 50 50 50", "50 0 50 50 50 50 50 50", "50 50 0 50 50 50 50 50", "50 50 50 0 50 50 50 50", "50 50 50 50 0 50 50 50", "50 50 50 50 50 0 50 50", "50 50 50 50 50 50 0 50", "50 50 50 50 50 50 50 0" }

6

Returns: 0.125
{ "0 51 50 50 50 50 50 50", "49 0 50 50 50 50 50 50", "50 50 0 50 50 50 50 50", "50 50 50 0 50 50 50 50", "50 50 50 50 0 50 50 50", "50 50 50 50 50 0 50 50", "50 50 50 50 50 50 0 50", "50 50 50 50 50 50 50 0" }

2

Returns: 0.124375
{"0 66 40 19 51 15 94 8 54 39 58 62 5 80 18 39", "34 0 90 72 36 18 24 15 7 66 72 93 78 5 91 99", "60 10 0 98 41 23 63 5 62 47 65 54 50 1 44 97", "81 28 2 0 39 86 14 22 65 13 76 70 91 17 21 27", "49 64 59 61 0 19 1 87 78 43 86 90 35 56 31 69", "85 82 77 14 81 0 89 43 32 11 61 74 20 69 86 7", "6 76 37 86 99 11 0 41 8 68 79 75 54 74 57 82", "92 85 95 78 13 57 59 0 83 26 43 25 5 18 73 54", "46 93 38 35 22 68 92 17 0 30 11 14 70 2 56 40", "61 34 53 87 57 89 32 74 70 0 71 29 74 10 1 11", "42 28 35 24 14 39 21 57 89 29 0 13 97 8 54 53", "38 7 46 30 10 26 25 75 86 71 87 0 7 29 4 52", "95 22 50 9 65 80 46 95 30 26 3 93 0 20 21 64", "20 95 99 83 44 31 26 82 98 90 92 71 80 0 7 23", "82 9 56 79 69 14 43 27 44 99 46 96 79 93 0 67", "61 1 3 73 31 93 18 46 60 89 47 48 36 77 33 0"}

1

Returns: 0.25622148877034123
{"0 14 34 94 54 72 84 7 21 25 48 60 51 41 51 14", "86 0 77 45 24 16 62 22 33 47 76 92 86 10 60 62", "66 23 0 88 51 1 66 64 21 80 66 46 30 66 70 41", "6 55 12 0 18 14 76 61 56 7 7 92 52 44 89 50", "46 76 49 82 0 12 18 87 45 38 22 98 99 45 55 12", "28 84 99 86 88 0 53 99 34 66 32 35 78 43 17 65", "16 38 34 24 82 47 0 53 86 89 92 78 60 26 16 24", "93 78 36 39 13 1 47 0 66 39 34 78 51 88 23 98", "79 67 79 44 55 66 14 34 0 5 1 53 100 63 73 30", "75 53 20 93 62 34 11 61 95 0 15 79 81 84 16 36", "52 24 34 93 78 68 8 66 99 85 0 62 21 24 20 93", "40 8 54 8 2 65 22 22 47 21 38 0 47 69 36 54", "49 14 70 48 1 22 40 49 0 19 79 53 0 86 71 11", "59 90 34 56 55 57 74 12 37 16 76 31 14 0 29 23", "49 40 30 11 45 83 84 77 27 84 80 64 29 71 0 46", "86 38 59 50 88 35 76 2 70 64 7 46 89 77 54 0"}

1

Returns: 0.2729489412311658
{"0 49 35 18 14 3 60 86 13 89 50 94 45 51 80 67", "51 0 7 8 100 28 5 18 51 77 16 89 65 76 61 25", "65 93 0 10 75 20 84 92 93 38 17 9 89 33 28 95", "82 92 90 0 29 2 59 13 1 14 64 18 76 28 31 8", "86 0 25 71 0 57 72 57 79 97 83 9 7 56 35 75", "97 72 80 98 43 0 19 100 10 89 2 63 100 59 33 12", "40 95 16 41 28 81 0 84 10 19 6 87 83 90 48 55", "14 82 8 87 43 0 16 0 97 6 12 31 96 2 65 14", "87 49 7 99 21 90 90 3 0 97 45 22 42 79 25 87", "11 23 62 86 3 11 81 94 3 0 67 65 40 67 16 37", "50 84 83 36 17 98 94 88 55 33 0 85 48 39 18 30", "6 11 91 82 91 37 13 69 78 35 15 0 5 46 26 8", "55 35 11 24 93 0 17 4 58 60 52 95 0 73 62 73", "49 24 67 72 44 41 10 98 21 33 61 54 27 0 68 84", "20 39 72 69 65 67 52 35 75 84 82 74 38 32 0 78", "33 75 5 92 25 88 45 86 13 63 70 92 27 16 22 0"}

1

Returns: 0.4207610465184181
{"0 79 45 44 7 73 25 11 35 34 29 98 81 69 61 90", "21 0 86 22 86 6 54 10 80 67 75 67 38 91 52 30", "55 14 0 77 97 93 76 85 25 74 20 20 50 80 49 70", "56 78 23 0 78 24 59 37 83 70 11 61 69 71 96 45", "93 14 3 22 0 84 48 49 61 98 48 69 56 3 4 74", "27 94 7 76 16 0 33 76 84 45 25 49 12 43 46 61", "75 46 24 41 52 67 0 44 17 38 26 94 12 95 89 98", "89 90 15 63 51 24 56 0 42 96 80 35 52 2 23 81", "65 20 75 17 39 16 83 58 0 24 69 46 68 9 100 89", "66 33 26 30 2 55 62 4 76 0 81 97 71 50 69 24", "71 25 80 89 52 75 74 20 31 19 0 80 41 64 40 52", "2 33 80 39 31 51 6 65 54 3 20 0 90 97 85 1", "19 62 50 31 44 88 88 48 32 29 59 10 0 94 98 97", "31 9 20 29 97 57 5 98 91 50 36 3 6 0 27 54", "39 48 51 4 96 54 11 77 0 31 60 15 2 73 0 90", "10 70 30 55 26 39 2 19 11 76 48 99 3 46 10 0"}

1

Returns: 0.40738716984695944
{"0 68 96 83 81 66 46 97 79 96 50 29 34 39 81 2", "32 0 69 48 32 27 95 86 63 39 77 94 63 85 28 82", "4 31 0 93 97 12 81 97 65 74 19 26 36 29 58 95", "17 52 7 0 55 35 44 34 89 2 67 29 58 86 16 91", "19 68 3 45 0 10 94 90 74 71 12 61 68 55 44 71", "34 73 88 65 90 0 11 40 45 10 80 15 62 93 84 57", "54 5 19 56 6 89 0 65 30 63 11 27 94 42 53 60", "3 14 3 66 10 60 35 0 12 32 43 56 41 35 1 79", "21 37 35 11 26 55 70 88 0 21 77 19 34 48 98 57", "4 61 26 98 29 90 37 68 79 0 58 40 55 65 76 56", "50 23 81 33 88 20 89 57 23 42 0 28 70 19 51 47", "71 6 74 71 39 85 73 44 81 60 72 0 42 1 90 23", "66 37 64 42 32 38 6 59 66 45 30 58 0 61 84 5", "61 15 71 14 45 7 58 65 52 35 81 99 39 0 23 77", "19 72 42 84 56 16 47 99 2 24 49 10 16 77 0 13", "98 18 5 9 29 43 40 21 43 44 53 77 95 23 87 0"}

1

Returns: 0.592765461224721
{"0 23 14 53 46 18 93 24 55 3 85 51 62 31 82 25", "77 0 20 71 65 3 21 77 74 31 93 62 99 13 73 25", "86 80 0 43 3 53 24 65 27 40 16 25 44 44 32 35", "47 29 57 0 72 17 16 66 1 68 38 11 45 47 58 74", "54 35 97 28 0 75 5 15 35 49 99 81 4 76 18 76", "82 97 47 83 25 0 99 45 83 17 59 29 87 43 55 81", "7 79 76 84 95 1 0 34 67 90 81 27 14 8 50 24", "76 23 35 34 85 55 66 0 4 19 54 19 92 63 44 68", "45 26 73 99 65 17 33 96 0 6 69 61 24 40 34 8", "97 69 60 32 51 83 10 81 94 0 97 91 5 46 11 79", "15 7 84 62 1 41 19 46 31 3 0 71 40 38 2 18", "49 38 75 89 19 71 73 81 39 9 29 0 90 60 1 2", "38 1 56 55 96 13 86 8 76 95 60 10 0 81 61 73", "69 87 56 53 24 57 92 37 60 54 62 40 19 0 77 58", "18 27 68 42 82 45 50 56 66 89 98 99 39 23 0 14", "75 75 65 26 24 19 76 32 92 21 82 98 27 42 86 0"}

1

Returns: 0.25260635020900735
{"0 88 30 39 94 94 3 44 31 28 94 90 67 66 74 31", "12 0 88 79 11 81 12 39 36 11 46 94 55 47 28 57", "70 12 0 67 58 7 88 98 74 9 83 56 91 41 75 7", "61 21 33 0 51 45 29 42 39 12 45 29 42 67 22 75", "6 89 42 49 0 3 18 17 2 10 20 2 57 4 62 5", "6 19 93 55 97 0 96 83 69 20 75 60 62 79 26 75", "97 88 12 71 82 4 0 15 67 27 97 27 97 1 85 70", "56 61 2 58 83 17 85 0 45 55 54 71 56 65 20 28", "69 64 26 61 98 31 33 55 0 60 6 26 12 19 99 80", "72 89 91 88 90 80 73 45 40 0 53 74 78 88 5 52", "6 54 17 55 80 25 3 46 94 47 0 51 79 100 80 27", "10 6 44 71 98 40 73 29 74 26 49 0 70 40 40 68", "33 45 9 58 43 38 3 44 88 22 21 30 0 80 63 65", "34 53 59 33 96 21 99 35 81 12 0 60 20 0 45 6", "26 72 25 78 38 74 15 80 1 95 20 60 37 55 0 20", "69 43 93 25 95 25 30 72 20 48 73 32 35 94 80 0"}

1

Returns: 0.5698644476516238
{"0 28 20 72 44 77 1 98 48 89 99 70 40 1 71 6", "72 0 73 39 19 87 92 69 99 36 4 91 26 69 92 36", "80 27 0 79 19 97 84 28 56 29 99 15 31 81 96 51", "28 61 21 0 71 30 89 6 18 89 30 78 5 72 65 79", "56 81 81 29 0 85 29 15 61 9 17 71 74 84 30 23", "23 13 3 70 15 0 72 90 86 38 53 16 25 3 46 76", "99 8 16 11 71 28 0 18 39 95 50 31 59 67 8 48", "2 31 72 94 85 10 82 0 100 3 95 18 4 39 9 40", "52 1 44 82 39 14 61 0 0 67 9 79 29 69 49 59", "11 64 71 11 91 62 5 97 33 0 21 41 33 54 80 12", "1 96 1 70 83 47 50 5 91 79 0 32 84 87 83 16", "30 9 85 22 29 84 69 82 21 59 68 0 95 82 29 44", "60 74 69 95 26 75 41 96 71 67 16 5 0 33 78 51", "99 31 19 28 16 97 33 61 31 46 13 18 67 0 91 87", "29 8 4 35 70 54 92 91 51 20 17 71 22 9 0 26", "94 64 49 21 77 24 52 60 41 88 84 56 49 13 74 0"}

1

Returns: 0.4761268007868508
{"0 53 67 6 24 25 8 83 27 2 35 41 42 34 4 80", "47 0 23 9 87 2 87 69 30 18 41 36 77 15 57 12", "33 77 0 6 93 5 8 10 33 19 7 85 27 22 7 28", "94 91 94 0 96 77 52 50 21 18 96 96 39 40 38 87", "76 13 7 4 0 20 22 16 6 82 78 100 61 45 21 74", "75 98 95 23 80 0 92 86 25 78 40 95 7 2 25 70", "92 13 92 48 78 8 0 84 31 82 17 80 40 26 32 21", "17 31 90 50 84 14 16 0 32 49 52 49 16 9 100 25", "73 70 67 79 94 75 69 68 0 9 50 52 84 98 64 98", "98 82 81 82 18 22 18 51 91 0 89 46 34 68 89 62", "65 59 93 4 22 60 83 48 50 11 0 78 96 98 14 27", "59 64 15 4 0 5 20 51 48 54 22 0 66 88 88 54", "58 23 73 61 39 93 60 84 16 66 4 34 0 94 67 91", "66 85 78 60 55 98 74 91 2 32 2 12 6 0 89 34", "96 43 93 62 79 75 68 0 36 11 86 12 33 11 0 100", "20 88 72 13 26 30 79 75 2 38 73 46 9 66 0 0"}

1

Returns: 0.11593123158472919
{"0 76 43 80 28 32 89 82 76 92 60 32 13 54 66 34", "24 0 60 51 78 14 87 81 32 22 91 17 34 72 13 48", "57 40 0 10 3 35 84 52 67 75 73 50 61 65 21 3", "20 49 90 0 69 62 82 9 51 38 99 19 33 88 37 35", "72 22 97 31 0 28 12 40 38 88 25 27 7 98 7 40", "68 86 65 38 72 0 49 48 28 79 85 25 53 1 5 57", "11 13 16 18 88 51 0 4 40 95 29 5 47 78 92 60", "18 19 48 91 60 52 96 0 67 30 42 63 36 95 89 57", "24 68 33 49 62 72 60 33 0 33 18 43 100 76 5 71", "8 78 25 62 12 21 5 70 67 0 35 24 5 53 20 40", "40 9 27 1 75 15 71 58 82 65 0 80 4 15 79 70", "68 83 50 81 73 75 95 37 57 76 20 0 47 12 36 42", "87 66 39 67 93 47 53 64 0 95 96 53 0 14 92 97", "46 28 35 12 2 99 22 5 24 47 85 88 86 0 81 89", "34 87 79 63 93 95 8 11 95 80 21 64 8 19 0 12", "66 52 97 65 60 43 40 43 29 60 30 58 3 11 88 0"}

1

Returns: 0.4295738247802675
{"0 69 22 82 81 69 73 82 78 74 34 72 31 71 71 86", "31 0 17 98 59 95 3 89 58 57 78 7 76 2 66 34", "78 83 0 49 71 52 47 43 84 63 10 5 9 53 55 65", "18 2 51 0 86 11 43 63 23 71 71 10 19 73 84 12", "19 41 29 14 0 87 88 67 44 72 37 77 51 44 99 14", "31 5 48 89 13 0 2 4 36 15 16 80 88 90 73 84", "27 97 53 57 12 98 0 25 98 48 100 9 37 6 16 93", "18 11 57 37 33 96 75 0 58 69 70 70 55 30 64 23", "22 42 16 77 56 64 2 42 0 61 81 100 91 36 38 76", "26 43 37 29 28 85 52 31 39 0 56 20 83 43 42 50", "66 22 90 29 63 84 0 30 19 44 0 22 80 84 62 11", "28 93 95 90 23 20 91 30 0 80 78 0 51 63 85 14", "69 24 91 81 49 12 63 45 9 17 20 49 0 1 5 53", "29 98 47 27 56 10 94 70 64 57 16 37 99 0 90 88", "29 34 45 16 1 27 84 36 62 58 38 15 95 10 0 69", "14 66 35 88 86 16 7 77 24 50 89 86 47 12 31 0"}

1

Returns: 0.41641654526434807
{"0 83 38 19 57 54 18 72 95 68 37 14 61 100 38 86", "17 0 34 36 82 29 6 3 93 94 4 67 76 49 53 84", "62 66 0 23 98 85 89 28 20 92 75 46 20 11 41 77", "81 64 77 0 65 91 4 40 76 3 23 54 55 2 8 68", "43 18 2 35 0 81 82 48 92 33 42 29 87 79 46 69", "46 71 15 9 19 0 42 71 22 27 46 16 64 12 4 55", "82 94 11 96 18 58 0 50 53 49 79 18 80 41 93 67", "28 97 72 60 52 29 50 0 49 8 37 79 65 72 18 67", "5 7 80 24 8 78 47 51 0 94 29 86 96 23 6 49", "32 6 8 97 67 73 51 92 6 0 71 19 12 51 36 32", "63 96 25 77 58 54 21 63 71 29 0 23 26 81 79 21", "86 33 54 46 71 84 82 21 14 81 77 0 29 78 53 46", "39 24 80 45 13 36 20 35 4 88 74 71 0 8 31 17", "0 51 89 98 21 88 59 28 77 49 19 22 92 0 64 5", "62 47 59 92 54 96 7 82 94 64 21 47 69 36 0 3", "14 16 23 32 31 45 33 33 51 68 79 54 83 95 97 0"}

1

Returns: 0.4829371453450644
{"0 98 53 98 100 46 28 53 29 89 78 83 22 65 64 71", "2 0 45 59 61 40 9 59 9 3 82 11 1 92 47 69", "47 55 0 22 3 23 44 1 76 28 89 40 56 42 40 11", "2 41 78 0 68 36 73 31 78 93 39 21 3 99 54 59", "0 39 97 32 0 86 15 91 58 55 66 81 48 24 30 27", "54 60 77 64 14 0 20 8 89 56 98 70 72 12 2 92", "72 91 56 27 85 80 0 69 68 6 13 43 74 8 43 52", "47 41 99 69 9 92 31 0 44 77 87 45 77 79 55 25", "71 91 24 22 42 11 32 56 0 97 32 29 25 43 21 97", "11 97 72 7 45 44 94 23 3 0 54 65 7 9 50 54", "22 18 11 61 34 2 87 13 68 46 0 43 26 15 32 20", "17 89 60 79 19 30 57 55 71 35 57 0 88 8 41 36", "78 99 44 97 52 28 26 23 75 93 74 12 0 68 5 77", "35 8 58 1 76 88 92 21 57 91 85 92 32 0 18 54", "36 53 60 46 70 98 57 45 79 50 68 59 95 82 0 36", "29 31 89 41 73 8 48 75 3 46 80 64 23 46 64 0"}

1

Returns: 0.6546562870622976
{"0 23 67 8 84 62 80 46 13 42 97 67 53 98 68 55", "77 0 16 2 56 56 44 77 42 29 66 95 81 93 76 99", "33 84 0 55 87 29 90 77 43 68 30 12 100 73 88 56", "92 98 45 0 29 18 82 25 10 56 40 76 13 47 47 93", "16 44 13 71 0 25 53 98 50 2 10 58 8 2 61 37", "38 44 71 82 75 0 35 65 21 17 46 22 47 14 97 83", "20 56 10 18 47 65 0 65 26 52 60 51 76 5 97 11", "54 23 23 75 2 35 35 0 67 13 90 6 3 9 71 41", "87 58 57 90 50 79 74 33 0 77 17 30 16 33 92 65", "58 71 32 44 98 83 48 87 23 0 2 45 21 47 87 85", "3 34 70 60 90 54 40 10 83 98 0 5 33 73 12 24", "33 5 88 24 42 78 49 94 70 55 95 0 83 1 18 31", "47 19 0 87 92 53 24 97 84 79 67 17 0 44 66 21", "2 7 27 53 98 86 95 91 67 53 27 99 56 0 81 36", "32 24 12 53 39 3 3 29 8 13 88 82 34 19 0 100", "45 1 44 7 63 17 89 59 35 15 76 69 79 64 0 0"}

1

Returns: 0.4490825617251912
{"0 60 63 62 91 21 52 53 5 80 85 74 64 25 7 82", "40 0 17 29 64 66 33 56 6 3 48 25 30 85 18 51", "37 83 0 71 52 55 33 43 34 32 29 59 98 81 5 91", "38 71 29 0 92 29 8 70 46 44 12 94 70 42 14 48", "9 36 48 8 0 21 6 55 75 6 5 59 72 39 25 35", "79 34 45 71 79 0 17 69 96 98 72 57 96 61 93 87", "48 67 67 92 94 83 0 21 26 94 94 64 17 63 43 29", "47 44 57 30 45 31 79 0 66 24 78 66 47 6 2 74", "95 94 66 54 25 4 74 34 0 9 87 57 91 98 31 2", "20 97 68 56 94 2 6 76 91 0 89 44 54 70 45 80", "15 52 71 88 95 28 6 22 13 11 0 90 64 31 84 47", "26 75 41 6 41 43 36 34 43 56 10 0 51 40 25 41", "36 70 2 30 28 4 83 53 9 46 36 49 0 85 72 39", "75 15 19 58 61 39 37 94 2 30 69 60 15 0 68 63", "93 82 95 86 75 7 57 98 69 55 16 75 28 32 0 33", "18 49 9 52 65 13 71 26 98 20 53 59 61 37 67 0"}

1

Returns: 0.3251032548607492
{"0 5 29 5 89 21 68 46 75 76 99 30 28 3 88 92", "95 0 50 77 11 60 2 82 41 6 87 55 14 2 96 14", "71 50 0 64 67 56 41 32 4 4 9 44 2 46 85 89", "95 23 36 0 28 30 63 93 66 50 92 62 38 39 63 48", "11 89 33 72 0 81 4 48 70 43 79 50 77 78 94 20", "79 40 44 70 19 0 30 40 8 77 11 13 42 62 49 33", "32 98 59 37 96 70 0 67 92 57 49 52 31 57 96 51", "54 18 68 7 52 60 33 0 80 51 13 10 87 56 30 100", "25 59 96 34 30 92 8 20 0 28 60 65 41 96 93 63", "24 94 96 50 57 23 43 49 72 0 70 85 66 51 48 1", "1 13 91 8 21 89 51 87 40 30 0 8 19 60 25 42", "70 45 56 38 50 87 48 90 35 15 92 0 16 58 89 43", "72 86 98 62 23 58 69 13 59 34 81 84 0 95 91 70", "97 98 54 61 22 38 43 44 4 49 40 42 5 0 71 10", "12 4 15 37 6 51 4 70 7 52 75 11 9 29 0 63", "8 86 11 52 80 67 49 0 37 99 58 57 30 90 37 0"}

1

Returns: 0.4479836784710465
{"0 15 25 13 93 77 34 84 78 74 74 25 50 9 9 40", "85 0 11 91 78 13 9 97 51 71 47 75 10 59 16 52", "75 89 0 92 8 29 81 92 14 58 18 55 13 39 8 5", "87 9 8 0 94 61 39 70 67 60 11 21 57 95 36 15", "7 22 92 6 0 88 98 93 26 8 54 50 4 48 92 53", "23 87 71 39 12 0 52 75 23 64 21 14 64 29 95 45", "66 91 19 61 2 48 0 58 41 22 39 38 18 98 28 65", "16 3 8 30 7 25 42 0 48 40 58 2 92 33 53 23", "22 49 86 33 74 77 59 52 0 77 27 62 24 39 7 16", "26 29 42 40 92 36 78 60 23 0 47 27 44 27 93 67", "26 53 82 89 46 79 61 42 73 53 0 51 84 61 72 11", "75 25 45 79 50 86 62 98 38 73 49 0 99 11 14 49", "50 90 87 43 96 36 82 8 76 56 16 1 0 39 46 47", "91 41 61 5 52 71 2 67 61 73 39 89 61 0 30 29", "91 84 92 64 8 5 72 47 93 7 28 86 54 70 0 49", "60 48 95 85 47 55 35 77 84 33 89 51 53 71 51 0"}

1

Returns: 0.3335643072387244
{"0 70 75 88 59 35 99 47 6 92 94 49 97 12 47 22", "30 0 24 15 81 82 87 9 45 91 78 46 70 62 87 89", "25 76 0 68 11 30 22 32 26 86 9 11 73 96 58 85", "12 85 32 0 4 48 81 24 15 38 3 43 28 76 5 89", "41 19 89 96 0 24 53 86 39 37 68 15 47 77 68 38", "65 18 70 52 76 0 33 3 81 61 89 89 2 69 9 74", "1 13 78 19 47 67 0 91 81 16 98 50 93 96 7 98", "53 91 68 76 14 97 9 0 3 44 31 28 13 24 5 3", "94 55 74 85 61 19 19 97 0 26 61 45 99 78 64 16", "8 9 14 62 63 39 84 56 74 0 84 96 49 27 16 88", "6 22 91 97 32 11 2 69 39 16 0 55 43 44 68 2", "51 54 89 57 85 11 50 72 55 4 45 0 73 16 49 56", "3 30 27 72 53 98 7 87 1 51 57 27 0 24 17 28", "88 38 4 24 23 31 4 76 22 73 56 84 76 0 13 83", "53 13 42 95 32 91 93 95 36 84 32 51 83 87 0 54", "78 11 15 11 62 26 2 97 84 12 98 44 72 17 46 0"}

1

Returns: 0.6324916867882954
{"0 44 29 73 76 65 31 80 28 21 47 67 75 42 14 70", "56 0 38 63 79 82 31 100 56 30 9 83 22 25 69 93", "71 62 0 46 97 13 14 11 59 80 84 96 78 81 29 54", "27 37 54 0 82 90 77 32 54 66 17 77 16 83 45 54", "24 21 3 18 0 92 75 49 40 18 75 48 31 33 99 72", "35 18 87 10 8 0 62 23 37 53 4 31 5 76 96 20", "69 69 86 23 25 38 0 56 80 24 52 20 66 67 55 5", "20 0 89 68 51 77 44 0 3 12 4 46 34 52 38 68", "72 44 41 46 60 63 20 97 0 67 27 76 59 97 1 32", "79 70 20 34 82 47 76 88 33 0 10 94 73 36 37 54", "53 91 16 83 25 96 48 96 73 90 0 94 6 56 43 6", "33 17 4 23 52 69 80 54 24 6 6 0 38 43 80 53", "25 78 22 84 69 95 34 66 41 27 94 62 0 36 4 87", "58 75 19 17 67 24 33 48 3 64 44 57 64 0 30 71", "86 31 71 55 1 4 45 62 99 63 57 20 96 70 0 24", "30 7 46 46 28 80 95 32 68 46 94 47 13 29 76 0"}

1

Returns: 0.2520203408179665
{"0 27 47 89 22 26 20 32 28 100 86 22 91 96 70 74", "73 0 93 75 47 2 90 4 55 100 41 86 98 92 63 65", "53 7 0 22 59 26 37 12 14 47 36 76 100 98 55 63", "11 25 78 0 76 37 35 54 51 36 46 18 62 33 48 68", "78 53 41 24 0 100 11 75 15 6 55 79 90 70 18 83", "74 98 74 63 0 0 52 56 92 69 5 100 30 84 41 89", "80 10 63 65 89 48 0 39 75 58 76 97 79 60 58 100", "68 96 88 46 25 44 61 0 15 55 27 89 26 91 32 61", "72 45 86 49 85 8 25 85 0 38 46 19 32 18 74 57", "0 0 53 64 94 31 42 45 62 0 24 69 89 99 56 91", "14 59 64 54 45 95 24 73 54 76 0 90 28 62 37 48", "78 14 24 82 21 0 3 11 81 31 10 0 31 32 61 62", "9 2 0 38 10 70 21 74 68 11 72 69 0 66 26 43", "4 8 2 67 30 16 40 9 82 1 38 68 34 0 68 33", "30 37 45 52 82 59 42 68 26 44 63 39 74 32 0 8", "26 35 37 32 17 11 0 39 43 9 52 38 57 67 92 0"}

1

Returns: 0.49356105896773816
{"0 70 0 50 50 50 50 50 50 50 50 50 50 50 50 50", "30 0 50 50 50 50 50 50 50 50 50 50 50 50 50 50", "100 50 0 40 50 50 50 50 50 50 50 50 50 50 50 50", "50 50 60 0 50 50 50 50 50 50 50 50 50 50 50 50", "50 50 50 50 0 50 50 50 50 50 50 50 50 50 50 50", "50 50 50 50 50 0 50 50 50 50 50 50 50 50 50 50", "50 50 50 50 50 50 0 50 50 50 50 50 50 50 50 50", "50 50 50 50 50 50 50 0 50 50 50 50 50 50 50 50", "50 50 50 50 50 50 50 50 0 50 50 50 50 50 50 50", "50 50 50 50 50 50 50 50 50 0 50 50 50 50 50 50", "50 50 50 50 50 50 50 50 50 50 0 50 50 50 50 30", "50 50 50 50 50 50 50 50 50 50 50 0 50 50 50 50", "50 50 50 50 50 50 50 50 50 50 50 50 0 50 50 50", "50 50 50 50 50 50 50 50 50 50 50 50 50 0 50 50", "50 50 50 50 50 50 50 50 50 50 50 50 50 50 0 50", "50 50 50 50 50 50 50 50 50 50 70 50 50 50 50 0"}

1

Returns: 0.07875

Statistics

Problem Statement for "SingleElimination"

Problem Statement

Definition

Notes

Constraints

Examples