TopCoder Statistics - Problem Statement

Problem Statement

Misof recently had an accident in which he managed to cut his left hand on some broken glass. He is now "all right" - meaning that he can only use his right hand for a while. Help him with some issues he has.

In addition to writing problems for programming contests, Misof used to make a living by painting roads. He currently has a job he needs to complete: refresh the paint on the line in the middle of the road for some segments of a long straight road. Ordinarily, this would be easy: he would just load his car, drive to the places where the paint need fixing, and do the job. But with just one good hand he cannot drive, and he cannot even carry a bucket and paint at the same time.

Misof's house is at the beginning of the long straight road. You are given the int[]s dStart and dEnd. For each valid i, one of the segments Misof needs to paint begins exactly dStart[i] meters from his house and ends exactly dEnd[i] meters from his house. The segments are disjoint and they are given in sorted order.

Misof's walking speed is 1 meter per second, regardless of whether he is painting or not. He has a long paintbrush he uses to paint the road. Whenever he is at home, he can dip the paintbrush into a bucket with paint. After that procedure, the paintbrush has enough paint to cover paintPerBrush meters of the road. (Those meters do not have to be contiguous. He can start and stop painting arbitrarily many times, as long as he still has some paint on the paintbrush.)

Misof starts the whole process in his home and he must return back home once he's done. Find and return the shortest time in which Misof can paint all the required road segments.

Definition

Class:: OneHandRoadPainting
Method:: fastest
Parameters:: int[], int[], int
Returns:: long
Method signature:: long fastest(int[] dStart, int[] dEnd, int paintPerBrush)
(be sure your method is public)

Notes

Misof's house is a point and dipping the paintbrush into paint takes no time.

Constraints

dStart will contain between 1 and 500 elements, inclusive.
dEnd will contain the same number of elements as dStart.
All elements of dStart and dEnd will be between 1 and 2*10^9, inclusive.
dStart[0] < dEnd[0] < dStart[1] < dEnd[1] < ...
paintPerBrush will be between 1 and 2*10^9, inclusive.

Examples

{3, 7}

{4, 9}

1

Returns: 42

There are two segments to paint: one is one meter long (3-4) and the other is two meters long (7-9). Misof's paintbrush can only hold enough paint to paint one meter of the road. One optimal schedule looks as follows: Dip the paintbrush (current time: 0). Walk to coordinate 3 (current time: 3). Put down the brush and walk to coordinate 4 while painting the road (current time: 4). Walk back home and dip the paintbrush into the bucket to get more paint (current time: 8). Walk to coordinate 9 (current time: 17). Put down the paintbrush and paint the segment from 9 to 8 (current time: 18). Walk back home, get more paint (current time: 26). Walk to coordinate 7 (current time: 33). Paint segment 7-8 (current time: 34). Walk back home one last time (current time: 42).
{3, 7}

{4, 9}

5

Returns: 18

This is the same scenario but the paintbrush can hold more paint, so Misof can be done much faster.
{1, 10, 20}

{4, 13, 22}

2

Returns: 98
{1}

{2000000000}

1

Returns: 4000000001999999998
{1}

{2000000000}

1999999999

Returns: 4000000000
{1}

{2000000000}

1999999998

Returns: 4000000004
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1520405

Returns: 40577356264
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381202397

Returns: 1997237198
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82962187

Returns: 1998151044
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9598

Returns: 5660516440138
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63226473

Returns: 2613655394
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1

Returns: 71418744767718648
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3

Returns: 25756531767634214
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178343913

Returns: 1999651392
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8702430

Returns: 10376029204
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5748427

Returns: 9677361690
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978743179, 984659659, 985247261, 985954073, 986711006, 989740978, 994662586}

164926991

Returns: 1989325172
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88651

Returns: 667192294490
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4

Returns: 18118171459693536
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15592

Returns: 3669664444346
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18

Returns: 4517760801678722
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295062263

Returns: 1998375956
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44246127

Returns: 2622159874
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942197508, 944187677, 945153690, 946684880, 948396753, 949823966, 954870178, 955746975, 961962286, 964075615, 966034319, 967386178, 968052877, 969376046, 975070251, 976765674, 978031723, 981199378, 982057341, 983445547, 985141449, 988293146, 990168465, 991501061, 991865857, 993590237}

251101

Returns: 376316561376
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2265

Returns: 22213321410008
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977406305, 978542651, 980044309, 981829788, 983594482, 986175743, 991992873, 993549124}

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977431618, 978557745, 980340172, 981899340, 983811401, 986391686, 992028182, 993611572}

394723906

Returns: 1987223144
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975351977, 977095148, 978764277, 980537084, 984396874, 986629694, 991441245, 995567721, 998408323, 998739512}

15115

Returns: 4280990780112
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56233852

Returns: 2107220614
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2547969

Returns: 34255678134
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55

Returns: 1195724490101544
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133015813

Returns: 1998252836
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1400

Returns: 70869929977720
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7394733

Returns: 14088433964
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1711383327

Returns: 1996258952
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1923728

Returns: 28154699904
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30647

Returns: 2533096482702
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133350453

Returns: 1996803068
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4

Returns: 21037505558404838
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491955679

Returns: 1982134910
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9971176

Returns: 10294036856
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9

Returns: 12139770123019862
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2

Returns: 25528771068745974
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28021116

Returns: 3794082250
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1716126339

Returns: 1998557550
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6913499

Returns: 15598104212
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92673

Returns: 1061368731882
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169

Returns: 260693630060178
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1

Returns: 90379331992953942
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595013

Returns: 130782291048
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472989

Returns: 209505307784
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1

Returns: 73443156833653824
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16716793

Returns: 6041985908
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245

Returns: 260923272083380
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1

Returns: 62433902973989286
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27037631

Returns: 4994173054
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4

Returns: 20873711827529804
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432693906

Returns: 1999332632
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16

Returns: 3359503236620484
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3055823

Returns: 25560964530
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230691010

Returns: 1996500280
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5224

Returns: 15738939005088
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16573

Returns: 4211379553458
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2050

Returns: 37665224625944
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687064818

Returns: 1998459492
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32967963

Returns: 3397678022
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13

Returns: 8499308513351114
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1234567

Returns: 1637417269212
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1

Returns: 3021119539184637112
{1 }

{4 }

2

Returns: 12
{1 }

{2000000000 }

2000000000

Returns: 4000000000
{1 }

{2000000000 }

1

Returns: 4000000001999999998
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{1213351, 2712182, 11686843, 18026019, 30369186, 31171954, 32832422, 32889408, 40273456, 43067380, 48368909, 49817061, 51114392, 51793315, 52306992, 54015160, 58496774, 61460745, 64834558, 65910475, 68033390, 69532443, 76534975, 79832815, 81684890, 86217059, 93217812, 96152664, 98826831, 100955455, 106480309, 110353183, 117736787, 120233933, 121036874, 127004918, 130127806, 138520395, 140346545, 143119840, 144133435, 148326747, 150744804, 151413437, 155978366, 160379683, 165231165, 169408868, 173474046, 177397109, 178643639, 181332206, 184592510, 195035291, 195422124, 199905068, 201499298, 207254643, 207796523, 226811998, 229821522, 235084290, 237482087, 247390831, 252286321, 258570895, 259645356, 261409529, 266087332, 271876199, 275470680, 279586507, 282745481, 284582405, 289420199, 298313276, 306458353, 309083967, 310614611, 311913646, 313615452, 323090033, 325844024, 330327419, 334401426, 336569869, 340326703, 342213058, 343514652, 343925520, 345741970, 348449373, 350164907, 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1

Returns: 3996554695240208866
{1900000000 }

{2000000000 }

1

Returns: 390000000100000000
{1 }

{1900000000 }

1

Returns: 3610000001899999998
{10, 50 }

{20, 60 }

8

Returns: 252
{1999999999 }

{2000000000 }

1

Returns: 4000000000
{1, 4, 7, 10 }

{3, 6, 9, 12 }

3

Returns: 46
{19, 551, 1490, 3000, 5959, 7682, 11524, 19583, 37946, 67411, 92572, 109697, 129499, 152787, 281415, 417133, 770170, 969733, 1491828, 1895028, 2507429, 4967369, 8334589, 8574831, 9652206, 15808693, 21816188, 40440785, 59547803, 106692022, 151285886, 197816709, 303340968, 503490854, 1005271636 }

{508, 768, 1664, 3160, 6244, 7708, 11776, 19715, 38318, 67596, 92915, 110116, 129763, 153228, 281648, 417320, 770457, 969866, 1492127, 1895133, 2507712, 4967441, 8334724, 8574951, 9652231, 15808973, 21816288, 40441035, 59548056, 106692229, 151285971, 197817195, 303341032, 503490946, 1005271734 }

5

Returns: 133278335148
{1999999997 }

{2000000000 }

2

Returns: 7999999996
{1, 1000000005 }

{1000000000, 2000000000 }

1

Returns: 3999999991999999968
{1, 11 }

{10, 20 }

13

Returns: 52
{745440656 }

{1798802438 }

1560412158

Returns: 3597604876
{1, 7, 9 }

{5, 8, 10 }

5

Returns: 24
{1 }

{1000000000 }

1

Returns: 1000000000999999998
{1, 1000000001 }

{1000000000, 2000000000 }

1

Returns: 3999999999999999996

Statistics

Problem Statement for "OneHandRoadPainting"

Problem Statement

Definition

Notes

Constraints

Examples