TopCoder Statistics - Problem Statement

Problem Statement

Owaski is another pet dog of Zhangzj. He likes playing on a tree.

The tree has N vertices, labeled from 0 to N - 1. You are given an int[] parent of N - 1 elements. For each i between 0 and N - 2, inclusive, there is an edge between vertex i + 1 and vertex parent[i]. In a single step, Owaski can walk from a vertex to one of its adjacent vertices. You are given an int[] pleasure, element i of which indicates the pleasure Owaski gets when he reaches vertex i. Before entering the tree, his pleasure is 0. Of course, at some moments Owaski's pleasure can be negative, as some vertices can make him unhappy. However, Owaski doesn't like to be unhappy. Thus whenever his pleasure becomes negative, he will make it zero again by playing Overwatch and winning nearly every game. Owaski may enter each vertex arbitrarily many times. However, he doesn't like old things. Thus, if he enters a vertex he visited before, his pleasure remains unchanged. In other words, each vertex only influences Owaski's pleasure when he visits it for the first time.

Owaski enters the tree at vertex 0 (therefore the pleasure of vertex 0 also counts), and can leave the tree whenever he wants. Since all dogs love to be happy, he wants to leave with as much pleasure as possible. Return the maximal pleasure he can get.

Definition

Class:: OwaskiAndTree
Method:: maximalScore
Parameters:: int[], int[]
Returns:: int
Method signature:: int maximalScore(int[] parent, int[] pleasure)
(be sure your method is public)

Constraints

N will be between 1 and 1,000, inclusive.
parent will contain exactly N - 1 elements.
pleasure will contain exactly N elements.
For each i, parent[i] will be between 0 and i, inclusive.
Each element of pleasure will be between -1,000,000 and 1,000,000, inclusive.

Examples

{0, 1, 2, 3, 4, 5, 6, 7, 8}

{1, 1, -1, -1, -1, -1, 1, 1, 1, 1}

Returns: 4

The tree forms a chain of 10 vertices and 9 edges. The optimal way is to walk through the chain. The values of pleasure of Owaski after visiting vertex 0 to 9 are 1, 2, 1, 0, 0, 0, 1, 2, 3, 4, respectively. He can leave the tree after that, yielding net pleasure of 4.
{0, 0, 1, 2}

{2, 3, 4, -1, -1}

Returns: 9

This time his path can be 0 → 1 → 0 → 2. Note that although Owaski visits 0 twice, the pleasure of that vertex only counts once.
{0, 0, 1, 1, 2, 2, 5, 5}

{1, 2, -3, -7, 3, 2, 7, -1, 3}

Returns: 17

One of the optimal paths is 0 → 2 → 5 → 8 → 5 → 2 → 6 → 2 → 0 → 1 → 4.
{0, 1, 1, 1, 0, 3, 1, 3, 4, 4, 3, 6, 8, 0, 12, 12, 11, 7, 7}

{-154011, 249645, 387572, 292156, -798388, 560085, -261135, -812756, 191481, -165204, 81513, -448791, 608073, 354614, -455750, 325999, 227225, -696501, 904692, -297238}

Returns: 3672275
{}

{-1}

Returns: 0
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Returns: 208157266
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Returns: 211326677
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Returns: 208653596
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Returns: 217845506
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Returns: 220844530
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Returns: 209689315
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Returns: 223279906
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Returns: 234430220
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Returns: 200987285
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Returns: 210339433
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Returns: 217493676
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Returns: 212900655
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Returns: 233908469
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Returns: 233320278
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Returns: 240720892
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Returns: 219469453
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Returns: 230166423
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Returns: 225649650
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Returns: 218286603
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Returns: 210433918
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Returns: 215897447
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Returns: 236271445
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Returns: 201630365
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Returns: 215125275
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Returns: 224015497
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Returns: 242947811
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Returns: 228610243
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Returns: 210393205
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Returns: 211672599
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88714, 289623, -364422, -101619, 14372, -711817, -716810, -913878, 830997, 95166, 886400, -206779, -17539, -33863, 373226, 632892, 622109, -882093, 13967, 443438, -881328, 855116, 108905, -783795, -189689, 529060, -599605, 917927, 549812, -875792, 801101, 638973, -777186, 964031, 380372, -360427, -880621, -332434, -735799, -928166, -430914, 381024, -878579, -780988, 820201, -178786, 947890, -302494, -33726, -277669, -38463, -621246, -811098, 800048, 397405, 244282, -564062, 135494, -468807, 829574, 207222, -411576, 765781, -746879, -202342, -369298, -134600, 390885, -725449, 588475, 493318, -423361, -846362, -217100, -995002, -711216, -831692, 196370, -361771, 673444, -337116, 181133, 909556, -786334, 452245, 965560, -94356, 483484, -177409, -283568, 795320, -881604, 472493, 56812, -604886, -305941, -598141, 84443, 617697, 733802, 892358, 98492, -735612, -522722, -80590, 287190, 473662, 695669, 389623, 12621, -838999, -628120, 593835, -986581, 165944, 60637, -278327, 622954, -67976, -672532, -215747, -433944, 657385, 364390, 375690, 44750, 212853, 988036, 434984, -157362, -7446, -641869, 453706, 79929, 330483, 468853, 115355, -441673, 446095, -512954, 466993, 461404, -843061, -234248, -987273, 430656, -193107, -605149, -298641, 999423, 170350, -387949, 667021, 912224, 254314, -881023, -562553, 963594, -450903, -665286, 116445, 657165, -312185, 110106, -961429, -935193, -304715, 548807, -736660, -141897, 59906}

Returns: 230730198
{0, 1, 2, 1, 3, 2, 5, 2, 7, 9, 10, 7}

{1, 1, 0, -1, -1, 0, -1, -1, -1, -1, -1, 0, 0}

Returns: 2
{0, 1, 0, 0, 3, 1, 2, 6, 0, 0, 0, 8, 12}

{47075, -78465, 54291, 89070, 48562, -62622, -67032, 57783, 53453, 81542, -96148, 13664, -44539, 37300}

Returns: 398365
{0, 1, 2, 3, 0, 1, 1, 5, 0, 6}

{4485, -4030, 9034, 8617, 5395, -9829, 9117, 9599, -1726, -141, -6146}

Returns: 42217
{0, 0, 2, 1, 3, 2}

{292357, -233354, 104071, 223049, 734800, -100653, -976357}

Returns: 1120923
{0, 0}

{-494366, 290988, 845185}

Returns: 1136173
{0, 1, 0, 2, 3, 2, 3}

{1, -1, 7, 0, 1, 10, -6, 3}

Returns: 21
{0, 0}

{-734523, -929988, -193527}

Returns: 0
{0, 1, 2, 2, 3, 5, 5, 7, 6}

{0, -1, 0, -1, 1, -1, -1, -1, 0, -1}

Returns: 1
{0, 0, 1, 3, 0, 3, 2, 4}

{-1, -1, 0, -1, 0, 0, 1, 0, -1}

Returns: 1
{0, 0, 1, 3, 1, 5, 5, 6, 8, 0, 7, 7, 1, 8}

{-21, 70, 13, -51, 49, -14, -78, 11, -10, 16, -95, 11, -37, 9, 27}

Returns: 136
{0, 1, 2, 3, 4, 1, 1, 5}

{-1, 0, 0, 0, 1, 0, 1, 1, 1}

Returns: 4
{0, 0, 0, 0, 1, 3, 3, 2, 4, 1, 6, 10, 4, 11, 13, 6}

{85481, -42916, 86754, 77799, 67383, -69701, -45166, 46368, -19724, 66590, -62304, 74753, 76429, -48480, 36046, 80303, -73289}

Returns: 527831
{0, 1, 1, 3, 1, 1, 5, 0, 4, 0, 6, 1, 10, 8, 10}

{-710414, -38698, 597029, 664625, -260804, 750568, -779777, -80419, -614078, 418830, 328131, 885906, -231047, 769708, 120684, -885559}

Returns: 4274677
{0, 0, 0, 0, 4}

{-5953, 6680, 523, 1586, 9656, -1959}

Returns: 18445
{0, 1, 2, 2, 2, 5, 6, 3, 5, 7}

{-888, 929, -104, -102, -272, 571, -914, 454, 625, -491, 521}

Returns: 1980
{0, 0, 1, 1}

{5, -7, -2, 5, 2}

Returns: 7
{0, 0, 0, 0, 2, 0, 5, 2, 8, 9, 9, 8, 3, 1, 2, 12, 14}

{6954, -1318, 2075, 5241, -6253, -9080, 1134, 6347, 3916, -2279, -1992, 3627, 1251, 5116, 1215, 6506, 1246, 1324}

Returns: 36008
{0, 1, 1, 1}

{3, 6, 10, -2, 4}

Returns: 23
{0, 1, 2, 3, 2, 4, 6, 1, 8, 5, 2, 4, 11, 7, 0, 6}

{10, -6, -3, 0, 10, 4, -7, -5, -5, -4, -5, -6, -3, -5, 5, 7, 2}

Returns: 22
{0, 0, 2, 3, 1, 1, 2, 6, 4, 0, 9, 0, 3}

{-9995, 8058, 5508, -5615, 8504, 6426, -1934, -7174, 4100, -8525, 3357, 5161, -4780, 6918}

Returns: 35429
{0}

{-92017, 80120}

Returns: 80120
{0, 1, 2, 1, 3, 1, 1, 7, 3, 5, 6, 8, 9, 1, 6, 7, 1, 2}

{-6646, 5266, -3731, 7971, 2555, -4387, 8462, -4067, 2190, 3714, -2779, 8035, -5697, 8721, 7946, -3812, 7983, 9763, 720}

Returns: 68060
{0, 1, 2, 3, 1, 4, 5, 2, 4, 9, 4, 2, 4, 6, 4, 5}

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

Returns: 20
{0, 1, 2, 0, 2}

{8, -1, -2, 10, -5, 8}

Returns: 23
{0, 1, 2, 2, 2, 5, 6, 0, 1}

{7, -4, 10, 5, -1, -3, -2, 5, -2, -5}

Returns: 18
{0, 0, 1, 0, 3, 5}

{7507, -6507, -8223, -8500, 6284, 460, 330}

Returns: 13791
{0, 0, 0, 2, 4, 0}

{391399, 378825, -256819, -948128, -341996, -288908, 543360}

Returns: 1313584
{0, 0, 0, 2, 4, 4, 2, 1, 5, 5, 0, 7, 6, 11, 6, 15, 7, 17}

{1671, -3266, -5834, 3309, 2795, -6333, 6429, -7516, -496, 5137, -1528, -3801, -1087, 7400, -5373, -2573, -5522, -1921, -3429}

Returns: 22275
{0, 1, 2, 3, 0, 2, 6}

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

Returns: 28
{0, 0, 1, 0, 4, 1, 2, 4, 2, 9, 8, 3}

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

Returns: 38
{0, 1, 0, 0, 2, 1, 6}

{-970, 209, 973, 513, 889, -533, -763, -632}

Returns: 2584
{0, 0, 1, 0, 0, 1, 5, 2, 0, 0, 8, 0, 2, 4, 12}

{-73, -91, -6, -9, -14, 58, -32, 19, 24, -78, -33, 43, -21, -61, -58, -58}

Returns: 144
{0, 1, 0}

{-1, -1, 1, -1}

Returns: 1
{0, 1, 0, 2, 0, 0, 2, 1, 3}

{-9604, 7078, 806, -3937, -9968, -3540, 8972, 7732, -5723, -9894}

Returns: 24588
{0, 1, 0, 1, 1, 0, 2, 6, 6, 0, 9, 0, 4, 8, 1, 11, 5}

{621, 950, 729, 921, -745, 281, -41, -789, 938, -275, 958, 865, 566, 56, 527, -966, -404, -632}

Returns: 7040
{0, 0, 1, 2, 1, 3, 4, 5, 7}

{7423, 6992, 7317, 4390, 3312, 5469, -1439, 5513, 2242, 1086}

Returns: 43744
{0, 1, 1, 3, 0, 1, 2, 5}

{-926, 911, -432, 199, -68, -185, 560, -552, -787}

Returns: 1670
{0, 1, 1, 2, 3}

{-1, 1, -1, 0, 1, -1}

Returns: 1
{0, 1}

{-48, 83, -77}

Returns: 83
{0, 1}

{-589, 748, 224}

Returns: 972
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Returns: 51992646
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Returns: 49168035
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Returns: 15233645
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Returns: 33830971
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Returns: 22259303
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Returns: 240270727
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Returns: 264372105
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Returns: 242491557
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Returns: 252333470
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Returns: 242892803
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Returns: 243887578
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Returns: 251216141
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Returns: 254267224
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Returns: 242696602
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Returns: 256737747
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Returns: 256299705
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Returns: 180172163
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Returns: 263264516
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Returns: 172830198
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Returns: 171940243
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Returns: 156903734
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Returns: 176436202
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Returns: 182812579
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-953040, -504380, 38645, 213700, -362674, -412969, -762232, -95613, -356916, 353656, -945946, -994176, -956727}

Returns: 214576604
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-858901, -852125, -946933, -975869}

Returns: 186580861
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Returns: 59116261
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Returns: 176879685
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Returns: 209581219
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Returns: 241268402
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Returns: 200123059
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Returns: 231652337
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Returns: 230607659
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Returns: 143112641
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Returns: 111920745
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Returns: 220790609
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Returns: 279935803
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Returns: 206676430
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Returns: 199412452
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Returns: 227237926
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Returns: 177324702
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Returns: 212802111
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Returns: 218649015
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Returns: 253962751
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855485, 710502, 641834, -563367, 6656, 248582, 70147}

Returns: 255919316
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Returns: 230261221
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Returns: 234233438
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Returns: 185492327
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Returns: 111575303
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Returns: 243511394
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Returns: 215622084
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Returns: 194043702
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703663}

Returns: 242664878
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Returns: 173708511
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Returns: 133738819
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Returns: 156258331
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Returns: 240557538
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Returns: 229000411
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Returns: 178964529
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Returns: 153045860
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Returns: 226116663
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Returns: 246057262
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Returns: 209669853
{0, 1, 0, 2, 0, 0, 2, 1, 4, 6, 7, 0, 1, 1, 5, 0, 0, 5, 7, 4, 3, 2, 0, 8, 0, 4, 0, 4, 1, 14, 2, 11, 3, 1, 18, 12, 13, 19, 4, 0, 21, 1, 3, 7, 21, 1, 25, 8, 12, 30, 0, 6, 1, 19, 27, 36, 0, 23, 9, 43, 0, 4, 24, 10, 12, 5, 2, 16, 2, 57, 10, 4, 23, 21, 5, 18, 12, 5, 7, 26, 17, 11, 11, 25, 1, 30, 3, 21, 27, 53, 27, 49, 12, 75, 47, 1, 44, 14, 14, 11, 46, 27, 9, 38, 33, 29, 22, 55, 67, 51, 6, 38, 2, 27, 3, 18, 39, 20, 36, 12, 67, 73, 11, 15, 4, 74, 34, 73, 14, 7, 21, 32, 11, 59, 56, 26, 34, 40, 80, 10, 2, 94, 18, 52, 13, 30, 23, 68, 55, 36, 26, 15, 60, 10, 58, 33, 15, 34, 40, 28, 18, 15, 41, 40, 28, 17, 8, 1, 46, 1, 39, 37, 4, 57, 24, 109, 67, 30, 18, 67, 3, 25, 4, 51, 3, 89, 23, 30, 24, 40, 16, 47, 81, 16, 30, 33, 25, 16, 58, 0, 21, 27, 50, 67, 42, 38, 4, 79, 111, 5, 29, 65, 31, 57, 144, 98, 8, 18, 68, 8, 28, 2, 30, 3, 4, 56, 46, 63, 70, 54, 40, 90, 40, 28, 102, 102, 101, 90, 10, 55, 84, 27, 66, 17, 76, 46, 23, 14, 140, 5, 3, 29, 33, 29, 103, 40, 86, 6, 138, 32, 23, 21, 123, 38, 144, 52, 43, 203, 41, 34, 159, 59, 102, 49, 10, 18, 100, 35, 15, 60, 65, 109, 61, 107, 164, 104, 70, 159, 36, 162, 80, 18, 135, 137, 16, 56, 65, 168, 45, 38, 10, 63, 50, 72, 208, 27, 122, 141, 50, 66, 205, 14, 72, 39, 81, 32, 103, 138, 0, 29, 96, 60, 143, 94, 166, 128, 198, 17, 205, 3, 132, 6, 127, 0, 3, 125, 107, 51, 3, 170, 23, 8, 104, 102, 122, 73, 58, 12, 230, 40, 15, 13, 72, 74, 1, 34, 13, 219, 3, 0, 4, 14, 158, 13, 19, 38, 51, 60, 18, 177, 5, 65, 249, 165, 29, 122, 119, 134, 170, 32, 10, 76, 22, 83, 33, 14, 76, 80, 82, 47, 146, 156, 0, 91, 228, 69, 39, 3, 128, 104, 292, 165, 24, 65, 254, 72, 32, 138, 116, 14, 110, 21, 260, 0, 45, 175, 65, 40, 140, 59, 160, 27, 158, 103, 212, 27, 70, 33, 120, 55, 115, 81, 123, 30, 28, 61, 28, 81, 97, 4, 41, 3, 188, 368, 282, 239, 27, 127, 76, 39, 165, 101, 53, 96, 242, 34, 63, 66, 50, 149, 67, 49, 49, 41, 233, 107, 84, 6, 319, 20, 1, 73, 216, 5, 26, 238, 9, 92, 312, 3, 55, 51, 187, 205, 32, 282, 117, 119, 122, 285, 7, 156, 35, 9, 90, 294, 103, 48, 245, 2, 67, 19, 358, 84, 23, 64, 203, 64, 2, 307, 38, 271, 33, 151, 88, 194, 74, 248, 83, 320, 278, 225, 51, 18, 24, 99, 93, 148, 46, 197, 285, 106, 104, 103, 169, 31, 105, 8, 54, 222, 37, 16, 157, 175, 198, 142, 283, 111, 279, 89, 321, 97, 13, 37, 47, 198, 240, 446, 328, 261, 384, 38, 29, 78, 339, 19, 3, 189, 126, 0, 240, 436, 24, 464, 171, 291, 130, 145, 99, 211, 107, 209, 205, 286, 154, 31, 108, 152, 24, 99, 43, 219, 110, 1, 58, 48, 68, 107, 338, 140, 324, 240, 134, 139, 312, 28, 76, 13, 157, 106, 119, 126, 144, 141, 64, 163, 67, 8, 267, 301, 56, 68, 249, 341, 6, 195, 227, 459, 309, 352, 0, 102, 45, 85, 178, 328, 167, 139, 52, 65, 81, 231, 257, 32, 182, 33, 43, 48, 131, 148, 246, 248, 37, 46, 468, 22, 50, 154, 74, 1, 22, 310, 30, 59, 50, 63, 102, 116, 286, 349, 502, 280, 106, 58, 48, 160, 308, 334, 62, 45, 93, 534, 82, 72, 86, 41, 35, 158, 430, 15, 266, 189, 119, 0, 316, 41, 62, 48, 67, 81, 208, 135, 0, 63, 119, 233, 371, 127, 297, 36, 405, 0, 100, 226, 139, 458, 12, 58, 169, 217, 12, 14, 331, 28, 127, 165, 316, 239, 248, 311, 35, 154, 115, 244, 153, 113, 360, 189, 113, 125, 138, 156, 76, 240, 130, 175, 276, 512, 239, 335, 199, 418, 241, 10, 388, 76, 26, 492, 125, 57, 99, 354, 361, 384, 259, 252, 21, 493, 417, 5, 287, 284, 13, 383, 19, 157, 230, 477, 251, 434, 128, 183, 147, 24, 130, 305, 377, 75, 120, 317, 460, 431, 64, 57, 226, 446, 487, 234, 11, 64, 110, 162, 495, 80, 402, 122, 158, 173, 153, 250, 188, 189, 124, 455, 322, 32, 249, 47, 584, 37, 250, 248, 255, 224, 267, 360, 12, 469, 217, 73, 276, 101, 167, 553, 90, 319, 1, 39, 509, 81, 9, 133, 314, 91, 131, 136, 207, 202, 485, 38, 286, 28, 163, 561, 73, 104, 618, 269, 331, 222}

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Returns: 206803403
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Returns: 265760922
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Returns: 196729566
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Returns: 156651858
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Returns: 252839356
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-775937, 566428, 908454}

Returns: 225201914
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Returns: 257935411
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Returns: 194561963
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Returns: 162519032
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Returns: 111468335
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Returns: 62607581
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Returns: 226961120
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Returns: 193770994
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Returns: 112678642
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Returns: 193869266
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Returns: 197994541
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Returns: 256024384
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Returns: 217196674
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Returns: 195370285
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Returns: 185758040
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Returns: 97964383
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499143, 274619}

Returns: 47554020
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Returns: 187466687
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Returns: 203281416
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Returns: 249500559
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Returns: 152861245
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Returns: 220494367
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Returns: 187122906
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Returns: 232416632
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Returns: 184836696
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Returns: 122348137
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-839240, 13093, -764295, -109243, -825193, -896963, -605549, -337600, -393029, -846390, 127343, -718417, -626758}

Returns: 275148749
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Returns: 227558138
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Returns: 226553563
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Returns: 201423795
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Returns: 204408401
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Returns: 240278707
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Returns: 150135550
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Returns: 180068972
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Returns: 238280845
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-730098, -273968, -358106, -936822, -47601, 71838, -783825, -865319, 111751, -752242, -391089}

Returns: 243643429
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Returns: 193392874
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Returns: 250910031
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Returns: 240573740
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Returns: 236411958
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Returns: 98972906
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Returns: 161564196
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Returns: 266585995
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Returns: 160164112
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Returns: 249232821
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Returns: 249170574
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Returns: 182151295
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Returns: 257103373
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1000000}

Returns: 1000000000
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1000000}

Returns: 1000000000
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1000000}

Returns: 1000000000
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Returns: 307322931
{0, 0, 1, 2 }

{2, 3, 4, -1, -1 }

Returns: 9

Statistics

Problem Statement for "OwaskiAndTree"

Problem Statement

Definition

Constraints

Examples