Statistics

Problem Statement for "Salesman"

Problem Statement

There are n people who live on the real axis. The people are numbered 0 through n-1. Person i lives at the position pos[i]. All of these positions are distinct.

Bob is a salesman. He travels along the real axis and he makes trades with the n people who live there. Bob trades items of a single type. Each person has a particular supply or demand of that item. In particular, if delta[i] is positive, the person has a supply of delta[i] units, otherwise the person has a demand of -delta[i] units. It is guaranteed that the sum of all elements of delta is nonnegative.

At the beginning, Bob is at position 0 and he has no items. In one second, he can move left or right by one unit. He can trade with a person if and only if he is exactly at the same position as that person. All trades happen instantly. During each trade Bob can buy or sell as many items as he wants. Of course, he can only sell the items he currently owns. While walking along the real axis, Bob can carry arbitrarily many items at the same time. He can pass through a position with a person without trading with them, if that is what he wants. (he can always come back and trade with them later.)

Bob has a single goal: he wants to trade the items in a way that will satisfy all demands. He can end his travels at any position. Determine and return the smallest amount of time in which Bob can achieve his goal.

Definition

Class:
Salesman
Method:
minMoves
Parameters:
int[], int[]
Returns:
int
Method signature:
int minMoves(int[] pos, int[] delta)
(be sure your method is public)

Constraints

  • pos will have between 1 and 2,500 elements, inclusive.
  • delta will have the same number of elements as pos.
  • Each element of pos,delta will be between -10^5 and 10^5, inclusive.
  • Elements in pos will be distinct and will be strictly increasing.
  • The sum of delta will be nonnegative.

Examples

  1. {-10,1,100}

    {-5,6,-1}

    Returns: 122

    Here we have three people. Person 0 is at position -10 and has a demand of 5 units. Person 1 is at position 1 and has 6 units of supply. Person 2 is at position 100 and has a demand of 1 unit. In this case, one optimal path for Bob is as follows: First, walk to position 1. Since Bob is at the same position as person 1, he can take all their supply. Next, walk to position -10. Bob can satisfy person 0's demands completely, and will be left with 1 unit remaining. Finally, walk to position 100. Bob can satisfy person 2's demands. At this point, Bob can end his walk. The total cost of this walk is 1+11+110 = 122.

  2. {-10,1,100}

    {-5,6,1}

    Returns: 12

    This time, we don't need to visit the rightmost person.

  3. {-100000,-5,-3,0,3,5,100000}

    {123,50,1,-101,1,50,54321}

    Returns: 20

    It is allowed for a person to be at position 0.

  4. {-10,-5,-4,-3,-2,-1,1,5,6,7,8,9}

    {6,-2,1,-2,1,-2,1,-3,1,-2,1,0}

    Returns: 29

    It is allowed for a person's delta to be zero.

  5. {2018}

    {2017}

    Returns: 0

  6. {-1001,-1000}

    {-1,33333}

    Returns: 1001

  7. {-9, -8, -4, 0, 1}

    {-3, -2, 9, 9, -7}

    Returns: 11

  8. 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    Returns: 299684

  9. 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    Returns: 299489

  10. 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    Returns: 328611

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    Returns: 285170

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    Returns: 297889

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    Returns: 337890

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    Returns: 290400

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    Returns: 297768

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    Returns: 297855

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    Returns: 389479

  18. 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    Returns: 299238

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    Returns: 314922

  20. 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    Returns: 396251

  21. 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    Returns: 365704

  22. 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    Returns: 346879

  23. 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    Returns: 299468

  24. 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    Returns: 312777

  25. 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    Returns: 303062

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    Returns: 353434

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    Returns: 324838

  28. 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    Returns: 335608

  29. 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    Returns: 299516

  30. 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    Returns: 312348

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    Returns: 388463

  32. 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    Returns: 301340

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    Returns: 393127

  34. 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    Returns: 345766

  35. 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    Returns: 347492

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    Returns: 299174

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    Returns: 294441

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    Returns: 353038

  39. 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    Returns: 299700

  40. 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    Returns: 301393

  41. 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    Returns: 324335

  42. 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    Returns: 353205

  43. 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    Returns: 314019

  44. 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    Returns: 302279

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    Returns: 316064

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    Returns: 304361

  47. 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    Returns: 299074

  48. 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    Returns: 299652

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    Returns: 316384

  50. 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    Returns: 308082

  51. 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    Returns: 382011

  52. 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    Returns: 365003

  53. 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    Returns: 306533

  54. 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    Returns: 299083

  55. 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    Returns: 310633

  56. 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    Returns: 299418

  57. 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9}

    Returns: 299232

  58. 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    Returns: 299564

  59. 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    Returns: 363500

  60. 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    Returns: 309861

  61. 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    Returns: 330800

  62. 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    Returns: 305257

  63. 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    Returns: 355755

  64. 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    Returns: 361623

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    Returns: 299858

  66. 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    Returns: 316826

  67. 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    Returns: 299359

  68. 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    Returns: 381966

  69. 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    Returns: 394540

  70. 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    Returns: 396542

  71. 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    Returns: 397710

  72. 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    Returns: 396696

  73. 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    Returns: 396907

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    Returns: 397006

  75. 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    Returns: 397404

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    Returns: 398528

  77. 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    Returns: 383516

  78. 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    Returns: 388077

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    Returns: 393813

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    Returns: 395591

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    Returns: 387649

  82. 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    Returns: 389027

  83. 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    Returns: 392559

  84. 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    Returns: 398494

  85. 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    Returns: 397470

  86. 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    Returns: 396985

  87. 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    Returns: 390049

  88. 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    Returns: 390287

  89. 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    Returns: 395878

  90. 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    Returns: 384077

  91. 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    Returns: 399112

  92. 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    Returns: 397341

  93. 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    Returns: 387110

  94. 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    Returns: 390069

  95. 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    Returns: 393561

  96. 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    Returns: 389754

  97. 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    Returns: 385556

  98. 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    Returns: 343242

  99. 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    Returns: 394109

  100. 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    Returns: 388786

  101. 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    Returns: 391639

  102. 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    Returns: 391905

  103. 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10204,10028,9890,10060}

    Returns: 379166

  104. 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    Returns: 394016

  105. 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    Returns: 399484

  106. 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    Returns: 386864

  107. 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    Returns: 390228

  108. 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    Returns: 393843

  109. 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    Returns: 396678

  110. 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    Returns: 394502

  111. 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    Returns: 397614

  112. 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    Returns: 386978

  113. 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    Returns: 380928

  114. 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    Returns: 392196

  115. 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    Returns: 385252

  116. 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    Returns: 390810

  117. 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    Returns: 397909

  118. 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    Returns: 386756

  119. 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    Returns: 385234

  120. 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    Returns: 394759

  121. 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    Returns: 396901

  122. 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    Returns: 385387

  123. 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    Returns: 397242

  124. 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    Returns: 397864

  125. 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    Returns: 396131

  126. 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    Returns: 387767

  127. 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    Returns: 392908

  128. 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    Returns: 388311

  129. 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    Returns: 350727

  130. 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    Returns: 391249

  131. 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    Returns: 380017

  132. 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    Returns: 359418

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    Returns: 386074

  134. 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    Returns: 387061

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    Returns: 373525

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    Returns: 375670

  137. 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    Returns: 364704

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    Returns: 383134

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    Returns: 366230

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    Returns: 383096

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    Returns: 381743

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    Returns: 391781

  143. 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    Returns: 393647

  144. 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    Returns: 382732

  145. 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    Returns: 353507

  146. 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    Returns: 368095

  147. 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    Returns: 376914

  148. 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    Returns: 359827

  149. 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    Returns: 351487

  150. 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    Returns: 352142

  151. 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    Returns: 370486

  152. 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    Returns: 354461

  153. 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    Returns: 379857

  154. 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    Returns: 383663

  155. 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    Returns: 351829

  156. 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    Returns: 395324

  157. 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    Returns: 386962

  158. 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    Returns: 395726

  159. 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    Returns: 397497

  160. 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    Returns: 393508

  161. 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    Returns: 396782

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    Returns: 394734

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    Returns: 392897

  164. 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    Returns: 397724

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    Returns: 394536

  166. 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    Returns: 397387

  167. 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    Returns: 394678

  168. {-9, 47, 54, 65, 66, 83, 85 }

    {96, 8, -54, -93, 59, 14, -27 }

    Returns: 105

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    Returns: 299631

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