Statistics

Problem Statement for "Boxing"

Problem Statement

In Olympic boxing, there are five judges who press a button when they think that a particular boxer has just landed a punch. The times of the button presses are recorded, and the boxer receives credit for a punch if at least three of the judges press their buttons within 1 second of each other.

This "algorithm" needs a lot of refinement. Here is the version that you should implement. Find the maximum number of disjoint time intervals that can be chosen such that each interval is of duration 1 second or less and contains button presses from at least 3 different judges. Two intervals are disjoint if every time within one interval is strictly less than every time in the other. We give the boxer credit for one punch during each interval.

The duration of an interval is the amount of time between the instant when it starts and when it ends, and a punch may be included in an interval if its recorded time is at the start, end, or in between. So, for example, the interval from 1 to 4 has duration 3, and a punch recorded at time 1, 2, 3, or 4 is in that interval. The intervals 1 to 4 and 5 to 22 are disjoint, but the intervals 1 to 4 and 4 to 22 are not disjoint.

Create a class Boxing that contains a method maxCredit that is given five int[]s, a, b, c, d, and e, representing the times of the button presses of the five judges in milliseconds. The method returns the maximum credits that can be given to the boxer.

Definition

Class:
Boxing
Method:
maxCredit
Parameters:
int[], int[], int[], int[], int[]
Returns:
int
Method signature:
int maxCredit(int[] a, int[] b, int[] c, int[] d, int[] e)
(be sure your method is public)

Constraints

  • Each of the five arguments will contain between 0 and 50 elements inclusive.
  • Each element of each of the arguments will be between 0 and 180,000 inclusive.
  • The elements within each of the arguments will be in strictly increasing order.

Examples

  1. {1,2,3,4,5,6}

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

    {1,2,3,4,5,6}

    {0,1,2}

    {1,2,3,4,5,6,7,8}

    Returns: 6

    This match had a fast start, with 6 punches credited in the first 6 milliseconds of the match! One way to choose 6 disjoint intervals is to choose [1,1], [2,2], [3,3], [4,4], [5,5], [6,6] each of which contains button presses from judges a, b, and c. There are three button presses in the time interval from 7 through 8, but only from two different judges so no additional credit can be given.

  2. {100,200,300,1200,6000}

    {}

    {900,902,1200,4000,5000,6001}

    {0,2000,6002}

    {1,2,3,4,5,6,7,8}

    Returns: 3

    One way to form three intervals is [0,1000], [1001,2000], [6000,6002]

  3. {5000,6500}

    {6000}

    {6500}

    {6000}

    {0,5800,6000}

    Returns: 1

    Any interval that doesn't include 6000 will not have enough button presses, so we can form only one disjoint interval with credit for a punch.

  4. {}

    {}

    {}

    {}

    {}

    Returns: 0

  5. {180000}

    {1,2,3,4,5,6,179000,179500,179800}

    {5,10,1000,10000}

    {5,10,1000,10000}

    {6,9000}

    Returns: 3

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

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

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

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

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

    Returns: 50

  7. {29000,29005}

    {30000,35000}

    {29815, 180000}

    {29999, 31000}

    {3000,30500}

    Returns: 2

  8. {2699,10692,13011,15965,17741,19186,23392,32495,32890,33294,38153,41040,48392,54352,55114,55658,55960,56201,64961,65481,65515,75634,78801,79643,83789,89641,96181,96216,104873,106920,117908,118745,120013,122753,124907,125091,126876,129105,133341,135052,136473,137495,139277,142103,143967,144712,150713,153393,158784,161182}

    {1595,8642,8954,11045,11249,20771,27970,31274,36528,36892,41520,44978,54877,57368,65224,69869,73501,75231,76272,76423,78302,83535,87222,88010,88361,88945,92000,93747,97352,98511,98960,102550,102990,106636,115539,120722,122265,122430,126235,134111,143167,149823,151733,153758,155472,156083,158202,166624,172914,175590}

    {3780,9366,13367,23559,24191,24831,25786,26391,26794,26852,31798,37596,38421,48740,49811,56623,62882,77821,82774,85865,87313,91804,92493,92818,95129,95923,104007,110764,113758,114294,115821,122485,126932,133926,136982,138418,138999,145410,149647,150652,151485,153397,156791,156801,159556,160288,161454,161636,166235,178516}

    {5054,10277,11234,13012,17143,20271,22171,23615,28055,35313,48476,53922,59118,61729,64751,65548,68138,74352,85808,87073,90894,90962,95082,101435,102635,103405,104385,104656,104760,110629,130051,134159,135014,136227,140978,141735,143163,149823,149917,154906,158519,160314,162052,168874,170552,172221,175517,176894,177644,177679}

    {2388,3005,5419,7320,8811,8870,10630,21793,22133,23869,35905,37104,37474,37490,37978,39589,43939,44835,49094,50658,57209,59529,70009,74916,81029,87448,89111,89635,91942,97418,100352,104035,107523,113736,114910,123639,124246,126071,135449,136225,141088,142377,155102,156125,163533,163921,164128,164941,167598,168811} {2388,3005,5419,7320,8811,8870,10630,21793,22133,23869,35905,37104,37474,37490,37978,39589,43939,44835,49094,50658,57209,59529,70009,74916,81029,87448,89111,89635,91942,97418,100352,104035,107523,113736,114910,123639,124246,126071,135449,136225,141088,142377,155102,156125,163533,163921,164128,164941,167598,168811} {2388,3005,5419,7320,8811,8870,10630,21793,22133,23869,35905,37104,37474,37490,37978,39589,43939,44835,49094,50658,57209,59529,70009,74916,81029,87448,89111,89635,91942,97418,100352,104035,107523,113736,114910,123639,124246,126071,135449,136225,141088,142377,155102,156125,163533,163921,164128,164941,167598,168811}

    Returns: 32

  9. {2699,10692,13011,15965,17741,19186,23392,32495,32890,33294,38153,41040,48392,54352,55114,55658,55960,56201,64961,65481,65515,75634,78801,79643,83789,89641,96181,96216,104873,106920,117908,118745,120013,122753,124907,125091,126876,129105,133341,135052,136473,137495,139277,142103,143967,144712,150713,153393,158784,161182}

    {1595,8642,8954,11045,11249,20771,27970,31274,36528,36892,41520,44978,54877,57368,65224,69869,73501,75231,76272,76423,78302,83535,87222,88010,88361,88945,92000,93747,97352,98511,98960,102550,102990,106636,115539,120722,122265,122430,126235,134111,143167,149823,151733,153758,155472,156083,158202,166624,172914,175590}

    {3780,9366,13367,23559,24191,24831,25786,26391,26794,26852,31798,37596,38421,48740,49811,56623,62882,77821,82774,85865,87313,91804,92493,92818,95129,95923,104007,110764,113758,114294,115821,122485,126932,133926,136982,138418,138999,145410,149647,150652,151485,153397,156791,156801,159556,160288,161454,161636,166235,178516}

    {5054,10277,11234,13012,17143,20271,22171,23615,28055,35313,48476,53922,59118,61729,64751,65548,68138,74352,85808,87073,90894,90962,95082,101435,102635,103405,104385,104656,104760,110629,130051,134159,135014,136227,140978,141735,143163,149823,149917,154906,158519,160314,162052,168874,170552,172221,175517,176894,177644,177679}

    {2388,3005,5419,7320,8811,8870,10630,21793,22133,23869,35905,37104,37474,37490,37978,39589,43939,44835,49094,50658,57209,59529,70009,74916,81029,87448,89111,89635,91942,97418,100352,104035,107523,113736,114910,123639,124246,126071,135449,136225,141088,142377,155102,156125,163533,163921,164128,164941,167598,168811}

    Returns: 32

    {2699,10692,13011,15965,17741,19186,23392,32495,32890,33294,38153,41040,48392,54352,55114,55658,55960,56201,64961,65481,65515,75634,78801,79643,83789,89641,96181,96216,104873,106920,117908,118745,120013,122753,124907,125091,126876,129105,133341,135052,136473,137495,139277,142103,143967,144712,150713,153393,158784,161182} {1595,8642,8954,11045,11249,20771,27970,31274,36528,36892,41520,44978,54877,57368,65224,69869,73501,75231,76272,76423,78302,83535,87222,88010,88361,88945,92000,93747,97352,98511,98960,102550,102990,106636,115539,120722,122265,122430,126235,134111,143167,149823,151733,153758,155472,156083,158202,166624,172914,175590} {3780,9366,13367,23559,24191,24831,25786,26391,26794,26852,31798,37596,38421,48740,49811,56623,62882,77821,82774,85865,87313,91804,92493,92818,95129,95923,104007,110764,113758,114294,115821,122485,126932,133926,136982,138418,138999,145410,149647,150652,151485,153397,156791,156801,159556,160288,161454,161636,166235,178516} {5054,10277,11234,13012,17143,20271,22171,23615,28055,35313,48476,53922,59118,61729,64751,65548,68138,74352,85808,87073,90894,90962,95082,101435,102635,103405,104385,104656,104760,110629,130051,134159,135014,136227,140978,141735,143163,149823,149917,154906,158519,160314,162052,168874,170552,172221,175517,176894,177644,177679} {2388,3005,5419,7320,8811,8870,10630,21793,22133,23869,35905,37104,37474,37490,37978,39589,43939,44835,49094,50658,57209,59529,70009,74916,81029,87448,89111,89635,91942,97418,100352,104035,107523,113736,114910,123639,124246,126071,135449,136225,141088,142377,155102,156125,163533,163921,164128,164941,167598,168811}

  10. {1520,1846,7333,8112,20247,27916,39498,41761,46386,47793,56674,57549,61237,61738,61807,65566,69075,71904,74585,80694,84588,86505,88568,89512,91125,99605,104067,105132,109113,111132,112180,112192,124246,125499,132535,136731,137175,143796,144887,145500,146398,150481,154549,154625,159865,163845,164236,175503,175900,176126}

    {2573,2723,5513,5935,8194,12985,23445,29571,31423,31487,40780,51677,56402,59271,60194,60478,66049,70507,73577,74547,75331,77356,80258,81166,83826,87223,88214,89516,97263,102691,111577,117020,118327,119370,119660,125980,130251,139707,142443,148094,157423,166045,167681,167759,167818,168658,169568,170767,175423,175720}

    {959,4395,7172,8529,9331,14385,23960,25489,31966,35544,36902,43935,45973,50360,51612,60847,62728,64504,69043,69729,70709,70853,73450,73670,78050,78098,84248,85529,94807,95321,96076,99179,100936,104392,106920,107507,110199,113120,129867,131702,140539,142123,142408,145029,146598,158440,162276,163556,165301,176549}

    {6720,7433,7788,11690,17426,20105,23451,26032,36674,38158,39144,41710,42534,44682,48068,52603,58238,59746,60568,68524,80900,83011,87298,88995,91297,94327,95120,96803,106949,108191,108590,116531,120351,122883,124316,129214,129599,135157,140186,142868,143710,143892,146237,150549,151505,153595,154854,155600,156528,170935}

    {2234,15006,18258,19351,20627,25780,27578,28999,29014,30624,35196,35837,36317,41041,51208,58629,62003,62009,65021,68516,68598,83627,92390,97218,103272,110723,119850,120544,122313,124948,125626,127582,128559,132029,132666,136231,137211,140195,143206,143535,146053,148029,160479,161179,163014,165505,169279,171856,176947,179620}

    Returns: 31

    {1520,1846,7333,8112,20247,27916,39498,41761,46386,47793,56674,57549,61237,61738,61807,65566,69075,71904,74585,80694,84588,86505,88568,89512,91125,99605,104067,105132,109113,111132,112180,112192,124246,125499,132535,136731,137175,143796,144887,145500,146398,150481,154549,154625,159865,163845,164236,175503,175900,176126} {2573,2723,5513,5935,8194,12985,23445,29571,31423,31487,40780,51677,56402,59271,60194,60478,66049,70507,73577,74547,75331,77356,80258,81166,83826,87223,88214,89516,97263,102691,111577,117020,118327,119370,119660,125980,130251,139707,142443,148094,157423,166045,167681,167759,167818,168658,169568,170767,175423,175720} {959,4395,7172,8529,9331,14385,23960,25489,31966,35544,36902,43935,45973,50360,51612,60847,62728,64504,69043,69729,70709,70853,73450,73670,78050,78098,84248,85529,94807,95321,96076,99179,100936,104392,106920,107507,110199,113120,129867,131702,140539,142123,142408,145029,146598,158440,162276,163556,165301,176549} {6720,7433,7788,11690,17426,20105,23451,26032,36674,38158,39144,41710,42534,44682,48068,52603,58238,59746,60568,68524,80900,83011,87298,88995,91297,94327,95120,96803,106949,108191,108590,116531,120351,122883,124316,129214,129599,135157,140186,142868,143710,143892,146237,150549,151505,153595,154854,155600,156528,170935} {2234,15006,18258,19351,20627,25780,27578,28999,29014,30624,35196,35837,36317,41041,51208,58629,62003,62009,65021,68516,68598,83627,92390,97218,103272,110723,119850,120544,122313,124948,125626,127582,128559,132029,132666,136231,137211,140195,143206,143535,146053,148029,160479,161179,163014,165505,169279,171856,176947,179620}

  11. {0,4244,8627,9903,31479,40959,44573,45119,45998,46078,47150,47833,49210,50070,56274,56982,58247,59485,77334,81949,91133,98080,102696,105045,105079,111421,113613,118602,124653,134545,136564,137813,138060,141547,151108,151348,156210,166236,174986,177342,177710}

    {0,2430,7853,13088,21832,24275,30409,36233,49393,51785,54662,55725,56628,60462,63882,66856,67212,74681,74957,87425,89567,97859,97958,105136,106213,107656,108554,111029,113202,119091,119684,124691,126694,132821,144116,146492,147893,151953,155306,164568,164748}

    {0,6842,13439,13936,16259,24061,24247,24852,35161,40211,41246,43182,46628,46750,56598,60779,62036,62447,65024,70049,74411,78506,79298,80462,80797,83909,89970,99032,103158,116140,118861,121203,121884,133335,145983,150611,154531,160319,166847,176077,176980}

    {0,4278,4521,14703,15142,15530,19172,19265,21880,25585,26615,28314,31481,31977,33593,37475,39154,49434,60148,63581,68149,68737,73341,73367,84830,84848,89726,91857,94920,109318,110430,112129,115111,119117,122739,126402,147254,149053,151834,168627,174675}

    {0,2148,4367,10640,18035,18487,21629,26109,31283,40380,40730,52166,59667,60313,64014,66510,68348,68609,71314,75624,88972,96476,98137,98788,106141,109176,114246,117649,126005,127893,128583,131962,132113,134437,140498,144765,150567,151156,151584,161092,179359}

    Returns: 18

  12. {58247,59485,77334,81949,91133,98080,102696,105045,105079,111421,113613,118602,124653,134545,136564,137813,138060,141547,151108,151348,156210,166236,174986,177342,177710}

    {0,4278,4521,14703,15142,15530,19172,19265,21880,25585,26615,28314,31481,31977,33593,37475,39154,49434,60148,63581,68149,68737,73341,73367,84830,84848,89726,91857,94920,109318,110430,112129,115111,119117,122739,126402,147254,149053,151834,168627,174675}

    {0,6842,13439,13936,16259,24061,24247,24852,35161,40211,41246,43182,46628,46750,56598,60779,62036,62447,65024,70049,74411,78506,79298,80462,80797,83909,89970,99032,103158,116140,118861,121203,121884,133335,145983,150611,154531,160319,166847,176077,176980}

    {0,2430,7853,13088,21832,24275,30409,36233,49393,51785,54662,55725,56628,60462,63882,66856,67212,74681,74957,87425,89567,97859,97958,105136,106213,107656,108554,111029,113202,119091,119684,124691,126694,132821,144116,146492,147893,151953,155306,164568,164748}

    {68348,68609,71314,75624,88972,96476,98137,98788,106141,109176,114246,117649,126005,127893,128583,131962,132113,134437,140498,144765,150567,151156,151584,161092,179359}

    Returns: 10

  13. {0,981,3613,26000,26176,37010,38435,39040,40685,42425,46970,59261,67421,67920,82003,85701,87573,91240,93491,107579,112368,113824,116747,121687,125755,127324,132032,140824,143746,144757,146730,155636,156018,157475,162649,163964,165479,170919,177957,179764,179965}

    {0,1217,4153,5425,17053,19129,43622,46089,48103,50301,53492,56102,68174,84843,85637,87136,87185,88702,95409,95797,101068,104223,106991,108238,108955,117189,119639,121061,124599,125297,126114,134470,138386,145528,147670,152412,162297,164351,165708,168293,172580}

    {0,11051,13830,19854,30421,36371,36535,36897,37306,38723,38925,41350,46265,48062,58292,64193,68744,70567,72253,76984,82827,95247,101210,101222,102896,108648,109826,110615,119751,127846,131990,138495,141718,145700,146602,146685,147124,150007,172043,177263,179134}

    {0,1348,7290,9987,12606,13130,15817,22158,30099,30741,37397,38311,59532,72507,82249,84112,84427,85130,92552,95084,95409,97456,101816,104606,106746,111065,112492,113485,116757,117245,118106,118496,124949,135786,136212,151069,157902,161266,167618,175037,179129}

    {0,6109,7876,8417,9118,15800,15935,21154,26751,30028,34785,35328,38739,39685,42901,49852,56923,63140,67867,83832,92868,93990,95129,99411,100246,106167,106358,109043,109910,118188,118844,123839,128368,137816,154556,154889,158067,168585,173068,175219,175501}

    Returns: 24

    {5990,6985,17723,18784,20958,26433,27925,29068,34574,39404,39961,52385,61619,67571,69079,71683,76016,77748,79929,79942,83772,86008,90871,92029,92895,95040,99406,106093,109832,111714,114326,115461,118375,123873,124070,127204,130167,134872,135251,139682,141782,142837,151104,158085,160856,163874,170734,173038,173124,179615} {12605,13835,16403,18397,18568,19172,19645,23229,25607,31723,32089,32436,33012,42898,44695,55663,60634,64704,65858,66595,67057,67500,69060,69671,70288,75940,79076,79608,94714,114741,118019,123599,130401,131280,136012,138743,141284,142172,148411,149675,150070,152978,153206,157338,157356,159875,162145,163073,173452,174169} {6314,11673,18740,32338,36256,38728,39063,42030,45585,46830,52297,61046,61085,66019,72246,73199,73617,85000,91849,97412,97723,100716,100927,102447,103616,116332,120475,123782,139454,143663,144075,150883,151120,152183,153475,153661,154452,157076,159166,161365,165992,171242,171868,172309,172784,175837,175902,178248,178859} {7540,13808,17898,19074,19394,27970,40304,48853,49506,50631,52266,52473,54344,55260,59663,60235,62136,63861,67360,67520,67660,72177,74169,77411,83827,88394,89716,93588,98557,104525,106318,110903,116276,118109,119318,119392,122442,122623,125319,129273,137152,137260,141872,147669,148620,151715,154407,163392,163960,168826} {1307,3302,3646,6741,10217,24069,25045,25617,36166,38588,40843,49777,51433,51524,63389,65744,69457,70002,71456,73600,74296,74620,75943,78866,82864,83867,85497,85517,90879,94100,95914,105759,108018,110401,112565,114407,115743,116012,119734,126263,135184,137207,144413,145286,146748,147420,150406,151795,154445,170406}

  14. {5990,6985,17723,18784,20958,26433,27925,29068,34574,39404,39961,52385,61619,67571,69079,71683,76016,77748,79929,79942,83772,86008,90871,92029,92895,95040,99406,106093,109832,111714,114326,115461,118375,123873,124070,127204,130167,134872,135251,139682,141782,142837,151104,158085,160856,163874,170734,173038,173124,179615}

    {12605,13835,16403,18397,18568,19172,19645,23229,25607,31723,32089,32436,33012,42898,44695,55663,60634,64704,65858,66595,67057,67500,69060,69671,70288,75940,79076,79608,94714,114741,118019,123599,130401,131280,136012,138743,141284,142172,148411,149675,150070,152978,153206,157338,157356,159875,162145,163073,173452,174169}

    {6314,11673,18740,32338,36256,38728,39063,42030,45585,46830,52297,61046,61085,66019,72246,73199,73617,85000,91849,97412,97723,100716,100927,102447,103616,116332,120475,123782,139454,143663,144075,150883,151120,152183,153475,153661,154452,157076,159166,161365,165992,171242,171868,172309,172784,175837,175902,178248,178859}

    {7540,13808,17898,19074,19394,27970,40304,48853,49506,50631,52266,52473,54344,55260,59663,60235,62136,63861,67360,67520,67660,72177,74169,77411,83827,88394,89716,93588,98557,104525,106318,110903,116276,118109,119318,119392,122442,122623,125319,129273,137152,137260,141872,147669,148620,151715,154407,163392,163960,168826}

    {1307,3302,3646,6741,10217,24069,25045,25617,36166,38588,40843,49777,51433,51524,63389,65744,69457,70002,71456,73600,74296,74620,75943,78866,82864,83867,85497,85517,90879,94100,95914,105759,108018,110401,112565,114407,115743,116012,119734,126263,135184,137207,144413,145286,146748,147420,150406,151795,154445,170406}

    Returns: 32

  15. {0,33,61,64,74,78,83,87,98,111,115,122,126,133,135,141,155,163,170}

    {20,39,46,53,58,66,74,80,95,110,123,124,125,127,133,134,138,144,145,168}

    {3,4,9,21,29,54,76,84,86,88,94,102,112,115,127,134,140,152,169,175}

    {8,9,20,21,22,23,34,45,57,59,87,90,97,117,120,139,149,152,153,171}

    {12,15,20,28,34,43,45,52,64,71,73,76,88,91,127,138,167}

    Returns: 26

  16. { 1, 1008 }

    { 1, 3 }

    { 1, 3 }

    { }

    { }

    Returns: 1

  17. { 0 }

    { 0 }

    { 1000 }

    { }

    { }

    Returns: 1

  18. { 5 }

    { 5555 }

    { 9999, 10000 }

    { }

    { }

    Returns: 0

  19. { 0 }

    { 2000 }

    { 4000 }

    { 6000 }

    { 8000 }

    Returns: 0

  20. { 1 }

    { 1 }

    { 6000 }

    { }

    { }

    Returns: 0

  21. { 10000 }

    { 20000 }

    { 30000 }

    { 40000 }

    { 50000 }

    Returns: 0

  22. { 0, 10000, 20000, 30000, 40000 }

    { 0, 10000, 20000, 30000, 40000 }

    { 1000, 11001, 21000, 31001, 41000 }

    { }

    { }

    Returns: 3

  23. { 0 }

    { 0 }

    { }

    { 20000 }

    { 30000 }

    Returns: 0

  24. { 1000 }

    { 3000 }

    { 5000 }

    { 7000 }

    { 9000 }

    Returns: 0

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