TopCoder Statistics - Problem Statement

Problem Statement

You recently got a job at a company that designs various kinds of filters, and today, you've been given your first task. A client needs a filter that accepts some objects and rejects some other objects based on their size. The requirements are described in the int[] sizes and the String outcome. If character i in outcome is 'A', then all objects of size sizes[i] must be accepted, and if character i is 'R', then all objects of size sizes[i] must be rejected. If an object's size does not appear in sizes, then it doesn't matter if it is accepted or rejected.

Unfortunately, your knowledge of filters is very limited, and you can only design filters of one specific kind called (A, B)-filters. Each such filter is characterized by two integers A and B. It accepts an object if and only if its size is between A and B, inclusive. You have excellent (A, B)-filter construction skills, so you can construct any such filter where 1 <= A <= B.

If it is possible to construct an (A, B)-filter that fulfills all the requirements described in sizes and outcome, return a int[] containing the filter's parameters, where element 0 is A and element 1 is B. If there are several appropriate filters, choose the one that minimizes B - A. If there are no suitable filters, return an empty int[].

Definition

Class:: Filtering
Method:: designFilter
Parameters:: int[], String
Returns:: int[]
Method signature:: int[] designFilter(int[] sizes, String outcome)
(be sure your method is public)

Constraints

sizes will contain between 1 and 50 elements, inclusive.
Each element of sizes will be between 1 and 100, inclusive.
All elements of sizes will be distinct.
outcome will contain the same number of characters as the number of elements in sizes.
Each character in outcome will be 'A' or 'R'.
outcome will contain at least one 'A' character.

Examples

{3, 4, 5, 6, 7}

"AAAAA"

Returns: {3, 7 }

Any filter with A <= 3 and B >= 7 will work in this case. Among them, A = 3 and B = 7 gives the minimal difference of B - A.
{3, 4, 5, 6, 7}

"AARAA"

Returns: { }

This is similar to the previous example, but objects of size 5 need to be rejected. It's impossible to achieve this using a single (A, B)-filter.
{3, 4, 5, 6, 7}

"RAAAA"

Returns: {4, 7 }

However, it's possible to reject only objects of size 3.
{9}

"A"

Returns: {9, 9 }
{11,42}

"AR"

Returns: {11, 11 }
{35,15}

"AR"

Returns: {35, 35 }
{4,3}

"AA"

Returns: {3, 4 }
{10,32,65}

"AAA"

Returns: {10, 65 }
{4,73,40}

"ARA"

Returns: {4, 40 }
{38,48,23}

"RAA"

Returns: { }
{47,7,37}

"RAR"

Returns: {7, 7 }
{32,64,66}

"RAA"

Returns: {64, 66 }
{6,11,46}

"RAR"

Returns: {11, 11 }
{63,33,44}

"ARR"

Returns: {63, 63 }
{9,12,1,3}

"AAAA"

Returns: {1, 12 }
{5,2,10,19}

"AAAR"

Returns: {2, 10 }
{13,38,18,42}

"ARAA"

Returns: { }
{38,31,41,77}

"AARR"

Returns: {31, 38 }
{7,14,10,18}

"AARA"

Returns: { }
{30,20,37,34}

"RARA"

Returns: { }
{5,6,18,24}

"ARRA"

Returns: { }
{33,44,73,60}

"ARRR"

Returns: {33, 33 }
{14,8,13,11}

"ARAA"

Returns: {11, 14 }
{57,34,41,36}

"RRAA"

Returns: {36, 41 }
{8,9,34,64}

"RARA"

Returns: { }
{30,42,35,15}

"ARRR"

Returns: {30, 30 }
{43,27,37,47}

"ARRA"

Returns: {43, 47 }
{19,18,33,24}

"RRRA"

Returns: {24, 24 }
{8,6,5,2}

"ARRR"

Returns: {8, 8 }
{29,18,24,8,12,4,26,17,3,10,2,25,35,28}

"RRRRRRRRRRARRR"

Returns: {2, 2 }
{5,20,48,69,75,46,53,1,15,54,55,2,36,3,62,21,28,31,82,71,72,14,17,16,86,26,19,24,6,47,40,29,30,41,88,79,39,58,66,56,76,67}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRR"

Returns: {88, 88 }
{32,37,46,40,15,76,42,3,33,10,53,50,64,38,78,52,13,56,71,43,26,25,9,12,55,28,57,44,7,67,17,30,4,21,47,61,75,6,14,80,48,72,11,16,27,2,8,62,36,63}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRR"

Returns: {17, 17 }
{51,1,37,17,14,12,72,65,35,52,26,4,78,70,13,31,59,66,50,20,30,27,29,43,25}

"RARRRRRRRRRARRRRRRRRRRRRR"

Returns: {1, 4 }
{49,32,38,46,10,12,21,39,16,43,19,9,45,33,48,44,50,13,5,1,11,35,41,51,6,2,30,34,7,14,31,36,24,23,47,4,22,25,18,42,27,37,20}

"AAAAAAAAAAAAAAAAAARRAAAAARAAAAAAAAARAAAAAAA"

Returns: {6, 51 }
{34,44,9,45,16,6,5,42,4,27,18,12,24,25,3,31,28,15,33,7,37,35,30,29,17,36,40,41,38,26,14}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {3, 45 }
{68,57,7,41,76,53,43,77,84,52,34,48,27,75,36}

"RARRRARRRARARRR"

Returns: {48, 57 }
{40,37,14,10,25,2,38,12,11,5,30,32,34,46,33,43,39,31,24,19,16,7,13,4,3,44,18,35,28}

"RRRRRARRRRRRRRRRRRRRRRRRRRRRR"

Returns: {2, 2 }
{44,23,14,39,30,71,42,87,6,86,88,8,81,95,52,7,54,75,69,35,79,11,12,43,65,46,85,50,100,99,21,27,55,49,25,28,84,98,76,47}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRR"

Returns: {100, 100 }
{15,43,86,25,73,11,62,63,51,45,49,83,42,70,14}

"RRRRRRRRRRRRRRA"

Returns: {14, 14 }
{45,1,70,67,47}

"AARRA"

Returns: {1, 47 }
{48,22,47,35,67,15,41,26,4,66,27,61,20,54,69,10,9}

"ARAAARAARAAARAARR"

Returns: {26, 69 }
{24,17,5,62,52,66,39,33,63,3,16,83,54,20,6,50,79,44,8,80,47,76,37,22,30,35,49,67,21,41,64,55,13,31,4,1}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {1, 83 }
{20,59,64,34,18,71,48,76,44,41,73,26,22,32,53,95,55,21,61,36,86,96,12,39,88,35,60,68,10,2,37,77,31,33,90,98,89,38,79,50,69,13,99,15}

"RRRRRARARRARRRRARRRRAARRARRRRRRARRAAARARRRRR"

Returns: {71, 98 }
{1,26,6,23,5,19,2,10,13,11,17}

"ARRRRRRRRRR"

Returns: {1, 1 }
{56,51,53,57,12,29,55,27,30,6,48,54,32,42,9,23,25,31,16,3,38,10,37,7,24,13,14,5,43,15,19,44,36,61,47,63,8,52,58,39,33,4,49,28,17,22,34}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRR"

Returns: {63, 63 }
{4,12,7,3,10,8,13,14,5,9}

"RRRRRARRRR"

Returns: {8, 8 }
{67,28,79,70,53,90,16,43,6,18,48,3,80,50,65,74,54,68,52,56,14,64,88,27,46,30,19,44,17,45,15,89,59,1,69,57,72,78}

"AARAARAAAAAARAAAAAAAAARAAAAAAAARAAAAAA"

Returns: {1, 78 }
{9,38,28,16,45,25,20,3,51,12,1,4,24,44,37,8,53,50,13,27,32,54,42,21,14,40,52,46,6,18,5}

"AAAAAAARAARRAAAAAAAAAAAAAAAAAAR"

Returns: {6, 54 }
{36,39,59,47,54,61,22,86,51,50,20,84,96,42,40,17,49,58,82,19}

"AAAAAAAAAAAAAAAAAAAA"

Returns: {17, 96 }
{9,47,49,38,36,48,33,21,22,11,24,39,6,27,51,50,2,28,42,46,37,1,18,5,8,17,23,15,41,43,14,31,52,3,45,32,29,25,10,13,20,44,26,12,40,30,19,16,35}

"ARRAARAAAAAARARRRARRARARRAAARRAARRRAAAAAARAAAAAAA"

Returns: {9, 40 }
{50,73,2,64,40,67,10,49,35,65,20,48,9,32,34,56,14,28,5,27,23,1,74,59,7,45,21,75,44,15,72,60,29,3,8,54,47,76,53,77,25,58,6,63,43,55,57,38,71,41}

"RRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRRRRRRRRRRR"

Returns: {1, 1 }
{78,7,87,50,61,55,9,30,31,10,66,92,28,35,21,43,54,25,3,13,91,37,24,15,39,49,80,51,75,96,76,12,65,77,42,46,74,63,95,44,17,36,88,16,73,79,6,71,85,89}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRRR"

Returns: {96, 96 }
{20,21,31,6,10,25,28,41,26,14,13,44,8,38,33,11,58,2,36,60,29,63,34,37,7,48,5,40,39,64,16,46,42,15,56,50,65,57,66,32,9,19,27,17,35,4,62,52,54,59}

"RRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRRRRRRRRRRR"

Returns: {63, 63 }
{20,43,31,11,21,10,29,2,23,15,8,28,25,35,49,5,27,33,46,14,13,44,7,17,47,36,1,12,45,22,38,34,6,30,3,42,50,16,48,39,24,26,9,32,19,18,4,40,37,41}

"RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRR"

Returns: {16, 16 }
{62,83,56,10,82,12,55,89,74,80,40,39,73,32,69,6,24,87,47,76,86,1,50,64,3,46,41,53,42,51,8,85,75,4,65,20,66,79,11,23,59,29,68,28,14,70,91,49,13,7}

"RRRARARRRRRRRARAARRRRARRARRRRRARRARARRAARARAARRRAA"

Returns: {1, 32 }
{3,66,28,2,49,29,55,38,14,56,60,63,61,30,52,50,39,19,59,1,12,51,35,57,13,45,65,53,17,26,67,54,31,24,58,33,8,34,22,47,40,5,23,21,4,43,36,64,18,11}

"ARAARARRARRRRARRRARAARRRARRRAARRAARAARARRAAAARRRAA"

Returns: {1, 33 }
{85,52,46,74,83,50,33,77,17,78,2,29,22,54,11,61,73,45,58,60,62,44,55,23,21,26,72,82,70,59,53,4,7,6,71,28,24,49,51,47,39,40,14,69,67,79,56,16,18,37}

"ARRAARRARARRRRRRARRRRRRRRRAAARRRRRARRRRRRRRRRARRRR"

Returns: {70, 85 }
{37,11,73,26,40,35,39,13,36,10,63,12,15,6,30,27,46,31,29,59,44,32,70,49,8,48,1,17,69,43,4,58,55,45,79,9,54,78,51,16,33,71,67,72,25,64,61,2,24,56}

"RRARARARRRARRRRRARRAARAARARRAARAAAARAAARRAAARAARRA"

Returns: {39, 79 }
{74,6,80,13,41,55,22,30,44,40,73,18,50,9,23,68,43,1,71,20,75,78,15,4,53,2,28,58,77,7,48,64,17,34,49,33,16,60,14,19,61,63,82,57,10,47,25,54,24,69}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {1, 82 }
{4,35,28,16,37,55,20,21,36,49,6,39,26,31,56,33,58,47,5,43,34,25,1,12,17,54,29,41,3,22,7,15,9,38,10,18,32,40,46,13,23,14,50,53,52,11,19,2,48,24}

"RRARRRRRRRRRRARARRRRRRRRRRARRRRRRRRRARRRRRRRRRRRRR"

Returns: {28, 33 }
{45,27,55,38,9,42,48,41,86,10,28,63,65,5,15,62,6,81,31,37,83,47,67,17,72,50,23,7,74,12,52,49,24,4,82,90,22,64,16,46,34,3,36,35,71,84,61,32,43,54}

"RRARRRRRARRAARRARARRARARARRRARARRRARRARRRRRRAAARRA"

Returns: {52, 86 }
{31,43,48,1,47,40,11,50,22,29,37,23,20,30,5,16,26,41,18,13,34,38,19,46,3,49,36,25,8,21,14,12,32,28,24,51,7,52,9,27,42,44,45,17,10,6,4,15,33,35}

"RRRRRRRRARRAARRRRRRRRRRRRRRRRARRRRARRRRRRRRRRRRRRR"

Returns: {20, 24 }
{55,33,31,18,24,11,39,27,34,50,14,1,43,36,47,3,54,9,17,10,48,45,40,44,32,4,26,56,37,19,23,2,16,41,28,38,30,46,52,49,35,53,12,13,15,8,29,20,21,51}

"RAARRRARAARRAAARRRRRAAAAARRRARRRRARAAARAARRRRRRRRA"

Returns: {30, 51 }
{28,32,83,45,10,81,99,2,88,5,37,21,38,62,33,78,9,55,42,34,14,75,35,60,4,1,47,16,25,44,53,77,57,63,89,46,39,6,36,24,49,100,26,13,90,69,66,41,52,11}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {1, 100 }
{100,94,26,82,45,13,97,74,96,69,4,59,63,12,73,65,85,91,6,2,38,1,55,76,28,57,99,51,92,19,52,15,43,61,71,17,48,86,95,14,20,66,7,5,37,87,90,64,70,60}

"RAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {1, 99 }
{68,37,95,77,67,100,29,35,92,46,98,73,83,69,45,61,44,60,10,24,71,62,30,94,11,31,76,79,2,21,1,82,80,75,91,9,72,13,7,96,58,93,74,18,38,56,52,63,51,65}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAARAAAAAAAAAAAAAAAAAAA"

Returns: {2, 100 }
{24,8,37,10,23,13,15,16,7,20,36,33,26,12,27,34,3,35,19,21,31,22,1,32,28,9,5,2}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: {1, 37 }
{26,81,9,14,43,77,55,57,12,34,29,79,40,25,50}

"ARAAARRARARARAA"

Returns: { }
{10,23,26,27,8,1,22,16,30,20,7,5,19,29,18,38,9,36,34,35}

"AAAAAAAAAAAAAAAAARAA"

Returns: { }
{4,2,11,19,14,8,29,13,6,5,22,7}

"ARARAARAAARA"

Returns: {4, 14 }
{33,20,41,24,36}

"RARAA"

Returns: { }
{51,22,13,62,41,46}

"AARAAA"

Returns: {22, 62 }
{16,40,24,23,25,32,39,45,21,36,51,41,44,43,27,5,47,12}

"RAARRAAAAARRAAAARR"

Returns: { }
{52,10,63,75,42,85,8,18,15,26,33,56,44,64,46,47,29,1,16,30,13,79,21,84,43,81,36,61,6,11,66,73,51,74,58,40,48,27,82,67,78,55,12,54}

"RAARAAARRAAAAAAARARAAAAARAARAAAAAAARRRAAAAAA"

Returns: { }
{23,27,16,12,1,4,15,28,6,9,44,42,24,26,17,2,20,46,51,10,47,3,13,21,18,32,37,22,8,38,33,43,41,14,39,45,48,49,30,25,7,34}

"AAAAAAAARRARAAAAAAAAAAAAAARAAAAAARAAAAARAA"

Returns: { }
{39,37,42,36,46,54,26,19,2,11,53,45,47,30,18}

"RAAAARAAAAAAAAA"

Returns: { }
{25,52,40,37,61,56,42,62,53,73,35,41,28,9,33,65,22,13,66,2,84,29,44,81,58,85,80,70,10,50,43,75,77,1,78,8,49,20,14,59,48,55,76,47,3,71,4,60,31,39}

"RAAAAAAARAAAAAAAAAAAAAAAAAAAAAAAAAAARAAAAAAAAAAAAA"

Returns: { }
{21,34,3,35,36,11,50,44,5,14,2,42,58,57,17,55,45,48,29,39,59,15,43,47,46,32,12,33,9,54,40,10,1,13,53,31,18,27}

"AAAAAAAAAARAAAAAAAARAAAAAAAARARRAARRAA"

Returns: { }
{10,29,21,41,53,52,32,17,7,56,44,4,42,27,25,26,2,54,47,59,34,48,57,51,45,49,14,55,20,12,23,6,39,15,22,36,33,11,58,46,38,13,40,28,35,5,31}

"ARAAARAAAAARARAAAARAAAARRAAAAAARAAAAARAARARRARA"

Returns: { }
{63,10,46,19,23,48,17,1,59,67,4,60,8,3,28,53,65,29,30,43}

"AAARARAAAAAAAARRRAAA"

Returns: { }
{57,13,70,73,56,38}

"AAAAAA"

Returns: {13, 73 }
{7,43,8,23,18,40,49,39,1,35,41,26,34,11,13,22,12,2,32,33,42,44,20,36,10,48,27,29,17,31,3,24,16,30,21,15,37,25,14,47,46,9,19,4,38,45,6,28,5,50}

"RRRRRARRARRRRRRRRRRRRRRARRRARRRAAAARRRAAAARRARRARA"

Returns: { }
{66,60,39,6,62,72,2,9,56,73,14,45,74,4,15,76,68,32,71,63,33,46,35,50,26,51,12,20,59,53,24,58,31,17,19,5,49,69,7,10,21,23,16,29,41,75,30,37,34,3}

"AAAAAAAAARAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: { }
{1,39,52,50,65,44,24,75,43,42,48,3,13,36,57,15,45,68,55,16,22,59,32,26,73,69,40,7,66,35,81,41,17,78,54,12,79,14,61,37,33,46,10,11,67,6,62,21,5,34}

"RRRRRRRARRARRRRRRRRRRARRRRRRRRRRRARRRRRRRRRARARRRR"

Returns: { }
{48,59,56,44,51,54,35,47,1,49,30,17,32,18,61,22,33,26,43,28,8,40,37,27,2,52,13,23,42,25,62,38,24,4,3,12,41,7,57,19,10,46,14,5,31,50,45,39,29,58}

"RRRRRARRARARARRRRRAARRARRRARRARRARRRRARRRRRAAARRRA"

Returns: { }
{24,17,9,56,57,12,6,53,18,45,22,34,69,7,11,41,47,20,5,66,3,23,26,58,61,28,40,2,15,21,72,49,63,38,1,32,64,27,14,54,65,50,31,13,59,46,19,8,71,39}

"RRRRRAARRRRRRRRRRRRARRRRRRRRRRRRRRARRRRRRRRRRRRARR"

Returns: { }
{66,33,31,62,48,24,67,71,51,20,54,23,61,27,10,30,2,65,29,39,56,50,4,68,16,53,43,14,36,17,25,59,55,1,57,52,38,37,6,7,63,19,5,13,18,3,28,41,73,40}

"RRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRRARRRR"

Returns: { }
{40,21,34,8,48,65,61,38,2,64,52,44,20,73,13,1,72,54,63,43,69,19,59,9,51,17,67,45,23,30,12,24,39,68,41,71,56,55,27,58,6,74,22,53,46,15,57,35,49,33}

"AAARAAARRRRAAARRAAAAAARAARRAARRARARRARRAAAAAAAARAA"

Returns: { }
{53,69,60,14,47,22,29,6,42,70,21,25,5,61,16,9,41,56,38,15,46,40,39,19,18,54,17,51,55,59,33,11,31,66,63,48,23,20,43,71,68,12,4,57,1,2,52,36,37,67}

"AAAAAAAAAAAAAAAAAAAAAAAAAAAAARAAAAAAAAAAAAAAAAAAAA"

Returns: { }
{52,21,14,59,28,3,23,40,78,94,62,54,75,53,95,17,12,31,65,44,15,76,9,33,49,74,88,26,16,47,22,2,73,38,51,11,81,84,1,93,18,34,30,92,56,24,10,91,7,69}

"RRRRRRRRRRARRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRRRRRR"

Returns: { }
{41,15,19,2,48,46,37,51,7,45,44,1,9,40,3,52,30,57,4,34,55,12,61,10,60,25,21,36,28,32,47,26,11,43,24,56,18,6,35,50,31,53,54,23,29,38,13,27,20,22}

"ARRRRARRRRRRRARRRRRRARAAARRRRRRRRRRRRAARRRRARARRAR"

Returns: { }
{56,52,37,49,26,19,57,20,63,34,22,17,58,13,16,38,25,2,18,43,27,40,59,60,24,33,53,5,4,23,7,10,8,54,29,35,50,61,44,45,15,46,62,32,21,39,9,28,11,1}

"AAAARRRAARARRAAAARRAAAAAARAAARRRRARARAARRARRAARAAA"

Returns: { }
{46,10,51,28,57,53,27,56,64,44,11,26,12,39,37,54,17,4,31,3,33,49,35,16,30,25,29,55,7,21,43,36,13,15,8,48,58,23,14,5,47,18,22,62,19,45,34,52,63,59}

"AARRRRRARRAARRRRRRRRRRRARRRRRARRRRRAARRRRRARARRRRR"

Returns: { }
{16,15,7,65,29,13,31,25,5,54,9,53,52,26,34,22,48,21,28,20,44,27,8,19,17,40,51,6,66,23,41,30,62,14,42,39,24,58,2,33,63,59,36,60,61,4,46,3,64,45}

"AAARAAAAAAAAAAAAAAAAAARRRAAAAAAAAARARRAAAAAAAAAARA"

Returns: { }
{73,61,51,23,50,54,75,9,85,28,84,33,66,62,88,86,32,19,83,43,18,14,94,96,7,11,76,2,16,8,97,21,69,46,30,68,13,60,25,70,1,87,41,56,89,82,53,31,47,90}

"ARRARRAARRRRRRRARAARARRRRARRRARARARRRRRRAARRRRRRRR"

Returns: { }
{48,53,68,5,30,85,55,61,24,16,59,41,15,60,9,4,72,64,49,81,20,7,31,37,57,35,44,12,14,73,23,52,86,94,70,1,77,45,92,58,32,87,88,75,62,89,90,39,42,3}

"AARAAAARAARARRAAARAAARRRAAARRARAARAARAARAARAAAAAAA"

Returns: { }
{13,6,21,33,35}

"RRARA"

Returns: { }
{9,1,34,5,69,31,67,59,21,40,38,41,17,2,63,66,4,7,60,22,27,53,58,55}

"RRARRAAARAARRRAAARAAARAA"

Returns: { }
{56,31,46,54,62,17,3,76,12,57,49,4,59,85,69,25,18,29,43,21,13}

"RRRAARRRRRRRARARARRRR"

Returns: { }
{67,13,54,19,61,90,82,43,84,55,36,85,17,4,66,30,96}

"RAAAARRRAARRAARAR"

Returns: { }
{15,5,30,37,10,50,19,65,23,45,48,1,9,38,2,55,8,14,52,29,56,58,4,3,46,39,32,59,60,31,11,49,6,27,12,51,33,35,40,41,17,21}

"RRARRRRRARRRRRRRRARARRRRRRARRARRRARRRRRRRR"

Returns: { }
{39,57,20,16,61,65,30,58,19,38,50,10,37,60,8,43,67,42,15,55,25,59,31,52,14,18,44,51,66,17}

"RRRRARRRRAARRRRRRRRARRRARRAARR"

Returns: { }
{24,69,9,53,58,71,30,55,76,41,19,42,28,37,18,52,70,4,11,35,50,49,75,47,51,29,56,14}

"RARRARRRRRRRRRRRARRRRRRRRRAR"

Returns: {56, 70 }
{6,48,68,16,1,34,69,17,7,28,46,45,37,54,52,53,22,24,44,43,61,47,63,60,49,29,26,56,30,21,27,62,51,14,58,12,31,10,42,8,13}

"RRRRRARRRRRRRRRRRRRRRRRRRARRARRRARRRARRRR"

Returns: { }
{13,20,9,28,10,30,41,3,15,12,16,7,27,24,42,26,38,43,19,34,22,8,1,37,32}

"ARARARRARAAARRRRRRARRAARR"

Returns: { }
{9,36,41,31,27,13,2,38,24,6,17,19,40,35,16,39,18,30,32,12,7,10,4,14,21}

"RARAARRRARAAARRAAARRRRRRA"

Returns: { }
{12,54,63,40,7,44,59,77,57,45,15,50,35,27,13,70,16,62,66,4}

"RAAAAAARAAAAAARRAAAA"

Returns: { }
{24,29,6,17,22,15}

"RRRRAA"

Returns: { }
{16,53,46,7,18,30,48,35,78,8,62,28,33,5,23,47,29,22,14,9,12,79,73,40,72,27,69,34,1,50,13,68,64,49,65,74,42,58}

"RAARRRARRRAARRRARRARRRRARRRRRARRAARRRA"

Returns: { }
{43,36,27,57,8,48,17,59,44,61,54,2,58,55,14,19,6,7,5,37,25,53,28,40,16,63,30,15}

"RARRRRARRARRRRRRRRRARRAARRAR"

Returns: { }
{88,67,24,53,27,11,47,14,85,28,46,64,48,29,30,22,73,81,91,49,17,69,76,78,71,61,90,13,43,83,68,31,41,12,6,26,36,5,63,7}

"RRARAARARRRRRRAARRRRARRRRRRARRRRAARARRRR"

Returns: { }
{48,6,61,2,51,19,55,30,70,1,17,47,16,4,63,58,57,13,62,67,11,26,39,18,21,60,65,42,8,29,69,12,9,15,45,5,73,40,23,34,10,66,59,53,46,56,25,41,49,44}

"RARRRARRRRARAARRRRRRARRAARRRAARAAARARRRRARRRRRRRRR"

Returns: { }
{65,4,19,58,62,43,48,8,33,42,45,73,9,5,2,17,46,66,10,59,24,60,57,71,21,72,55,44,13,3,25,70,50,26,6,53,37,22,36,16,31,28,47,14,49,32,54,29,68,41}

"RRARRARRAARARRRARRRRRRRRARRRRRARRARRRAAAAARARARARA"

Returns: { }
{51,1,28,80,3,32,55,57,40,33,37,9,82,47,53,31,44,11,77,19,42,13,49,73,67,74,59,20,5,48,22,65,24,72,15,64,16,50,75,18,83,63,21,29,68,6,17,25,30,45}

"RRRRRRRRRRRAARRRRARRRARRRRRRARRRRRARARRRRRRRRAARRR"

Returns: { }
{66,12,68,46,4,52,38,22,21,39,58,3,37,11,71,31,63,67,34,69,17,44,29,64,15,55,49,16,57,30,36,50,28,2,23,25,60,48,74,40,65,72,18,70,1,33,47,6,10,19}

"ARRRRARRRRRRRRRRRRRRRRRRRRRRRRRRARRRRRRRRRRRRRRRRR"

Returns: { }
{70,63,67,34,38,57,30,43,65,29,1,96,76,75,80,68,56,64,40,86,18,32,71,17,46,62,10,59,2,77,61,54,4,7,26,73,78,50,39,90,19,91,25,72,53,88,66,60,27,16}

"RAAAAARAARRRRRRAAAARRARRAARARRAAARRRRAARRRRRARAARR"

Returns: { }
{24,61,13,8,57,18,16,23,17,56,68,42,26,38,19,12,66,53,58,44,40,47,35,39,67,70,36,3,33,21,43,1,5,45,51,31,29,11,4,48,28,10,27,59,30,14,32,20,50,41}

"ARARRAAAARRRARARRRRRRRARRRRRRARRRRRRRARRARARRARARR"

Returns: { }
{59,34,63,55,52,66,5,36,4,15,17,60,14,41,26,6,20,48,24,13,9,40,8,54,68,2,50,56,53,23,62,21,1,65,43,69,7,22,42,32,19,30,27,39,10,28,29,58,16,11}

"AAAAAARRRAAAAAARAAAAAAAARRAAAAAARAARAAAAAAAAAAAAAA"

Returns: { }
{81,39,32,71,10,46,61,44,28,70,80,31,4,36,78,92,64,9,2,50,65,73,37,56,41,22,75,15,5,33,45,72,82,55,18,29,48,26,7,14,68,17,60,23,13,69,35,90,8,59}

"RAARRARARRRARARRRRRRRRARARRRRAARRRRRARRRRRRRRRARRR"

Returns: {31, 48 }
{45,16,31,88,15,70,90,53,95,61,28,20,75,44,81,84,14,76,52,33,59,5,92,85,12,57,50,18,94,87,93,23,46,3,82,66,34,21,60,63,38,83,2,62,42,19,80,39,43,58}

"RAARARRRRRAARARRRRRARRRRRRRARRRARRRAAARRARRRAARAAR"

Returns: { }
{10,15,39,13,52,44,57,28,11,49,54,26,50,40,56,45,51,41,36,6,3,55,43,37,1,12,46,33,9,47,30,31,25,42,58,7,4,5,22,23,24,32,17,29,34,48,8,21,16,20}

"RRRRRRRRRRARRRARARRRRARRRRRRRRRRRRRRRRRRRRRRRRRRRR"

Returns: { }
{59,80,87,71,37,2,19,82,58,32,26,49,55,30,33,21,53,75,66,84,17,23,96,61,77,90,67,13,47,72,42,14,48,22,81,24,43,4,78,91,29,28,40,79,88,10,8,83,63,86}

"ARRARRAAARRAARRRAAARRRRAARARAARRARRRARARRRRARRRRAR"

Returns: { }
{67,38,7,11,48,5,24,25,15,19,20,14,6,47,36,63,4,52,33,44,22,78,77,73,35,3,21,46,27,34,2,65,60,12,1,16,71,62,69,51,29,10,58,64,18,56,42,66,53,54}

"RRRRRRRRRRRRRRRRRRARRRRRRRRRRARRRRRRRRRRRRARRRRRRR"

Returns: { }
{89,7,86,9,25,73,47,90,69,1,40,6,55,37,34,82,61,30,66,64,84,67,33,31,42,17,39,28,23,76,49,21,15,52,60,12,78,77,50,56,75,16,65,58,91,81,2,83,22,18}

"ARARAAARARAAAAAAAAAAAAAAAAAARAAAAAAAAAAAAAARRARAAA"

Returns: { }
{80,38,56,13,49,87,74,27,18,78,42,88,47,30,43,54,32,17,97,29,37,10,22,31,26,82,76,8,57,53,14,36,79,5,65,85,20,91,11,69,35,33,94,86,51,19,68,72,9,41}

"ARARAAARRARRRRRARRRRRRRRRAARAARRARAARRRARRRAARAARR"

Returns: {49, 87 }
{22,41,62,68,17,74,47,65,25,24,48,6,73,36,42,26,5,51,35,19,27,58,11,8,43,33,52,54,1,10,50,55,61,45,70,20,30,13,63,69,64,53,12,2,46,15,31,56,9,72}

"AARRARARAAARRAAARAAAARAAAAAARAAARARAARRRRAARAAARAR"

Returns: { }
{68, 57, 7, 41, 76, 53, 43, 77, 84, 52, 34, 48, 27, 75, 36 }

"RARRRARRRARARRR"

Returns: {48, 57 }
{26, 81, 9, 14, 43, 77, 55, 57, 12, 34, 29, 79, 40, 25, 50 }

"ARAAARRARARARAA"

Returns: { }
{26, 81, 9, 14, 43, 77, 55, 57, 12, 34, 29, 79, 40, 25, 50 }

"ARAAARRARARARAR"

Returns: { }
{1, 2, 3, 4, 5 }

"ARAAR"

Returns: { }
{1, 2, 3, 4, 5 }

"RRARA"

Returns: { }
{72, 52, 70 }

"ARA"

Returns: {70, 72 }
{3, 4, 5, 6, 7 }

"AARAA"

Returns: { }
{2, 1 }

"AA"

Returns: {1, 2 }
{3, 7, 2 }

"AAA"

Returns: {2, 7 }
{1, 2, 3, 4, 5, 6 }

"RARARA"

Returns: { }
{3, 4, 5, 6, 7 }

"RRRRA"

Returns: {7, 7 }
{5, 6 }

"AR"

Returns: {5, 5 }
{3, 6, 4 }

"ARA"

Returns: {3, 4 }
{4 }

"A"

Returns: {4, 4 }
{1, 3, 5 }

"AAA"

Returns: {1, 5 }
{49, 31, 26, 13, 7, 12, 14, 4, 8 }

"ARARAAAAA"

Returns: { }
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

"RRAARRAARR"

Returns: { }
{100 }

"A"

Returns: {100, 100 }

Statistics

Problem Statement for "Filtering"

Problem Statement

Definition

Constraints

Examples