TopCoder problem "FactoryManager" used in MM 32 (Division I Level One)



Problem Statement

    

You are the manager (and owner) of a manufacturing company, which has a warehouse and a production factory. Your factory has several automated production lines. Each line can create complex products from others simpler products. You can buy base products and store them with your manufactured products in your limited capacity warehouse. Your task will be to maximize profits by managing the day by day factory operations.

Your Factory

There are B different base products and M different manufactured products. Base products are denoted by integers from 0 to B-1 and manufactured products are denoted by integers from B to B+M-1. Each day, you may produce up to L manufactured products. The prerequisite products must be available in sufficient quantities from the warehouse, and you cannot use a product as a prerequisite on the day it is produced. The output products will be brought to the warehouse, which has a limited capacity: you can store at most C products (including base products).

Your company has a commercial team that negotiates contracts with customers. Each contract is defined by the quantities of products to deliver, a total price, a maximal date of delivery, and a penalty rate in case of delay. You can accept or reject these contracts but your decision is always final.

Your typical day as the Factory manager is (in order):

  1. You accept or reject the contracts negotiated by your commercial team.
  2. You optionally order some base products.
  3. You determine the production quantity of each manufactured product.
  4. The required products for the production process are brought from the warehouse to the production factory.
  5. The factory produces the manufactured products.
  6. The manufactured products created by the production lines are brought to the warehouse.
  7. You optionally decide which contracts are finalized: the corresponding products are taken from the warehouse and you get paid.
  8. You pay penalties for all the contracts that you were supposed to ship today or earlier, and that you did not ship.
  9. Late in the evening, your warehouse receives the base products ordered in the morning.
The order is important to understand the management of the warehouse.

Implementation Details

You will have to manage the factory on a day by day simulation. For this you must provide two functions:

First, an init function that receive the parameters:

  • B -- number of base products,
  • M -- number of manufactured products,
  • L -- production limit in number of products by day,
  • C -- the capacity of the warehouse,
  • processes containing the M manufacturing processes.
processes[i] is a space separated list of products required to produce B+i. The init function may return any integer (which is ignored).

Then a manage function that will be called at each step of the simulation. This function receives several parameters necessary to manage the factory. A int[] warhouse gives the B+M quantities of products in the warehouse. A int[] prices gives the B prices of the base products. A String[] contracts gives the contracts of the day that you have to validate. Each contract contains is formatted as:

"ID PRICE DAYS PENALTY C0 C1 ... CM-1".

ID is a unique contract ID, PRICE is the sale price, DAYS is the number of days you have to fulfill the contract, PENALTY is the penalty rate (mutiplied by 1000) and Ci is the number of products of type B+i to deliver. Example if B=5 and M=9, contract "35 5540 52 24 0 0 10 0 0 17 0 3 0" means: contract ID35 for 10 manufactured products of type "7", 17 manufactured products of type "10" and 3 manufactured products of type "12" for $5540, after 52 days there is a 5540*24/1000 penalty per day.

Your manage function must return a String[] containing 4 elements (lists of integers separated by spaces).

  1. The quantities of each base product that you buy (exactly B integers).
  2. The production quantities of each manufactured product (exactly M integers). Their sum must be less or equal to the production limit L.
  3. The list of accepted contracts (IDs of contracts, this list must be a subset of the IDs given in contracts, if you do not accept any contract use an empty string).
  4. The list of contracts IDs that you ship (IDs of previously accepted contracts).

Money matters

Each base product has a reference price P0. Its market price is updated daily according to the following scheme: newPrice[i] = P0[i]0.01*oldPrice[i]0.99*1.05r where r is a random uniform variable between -1 and 1. The initial price (day 0) is obtained by applying 1000 times this scheme starting from the reference price. Each manufactured product has a price equal to the sum of the prices of its constituting products plus a value factor F multiplied by the complexity of the process (in number of required products). For example if a manufactored product requires one each of products 1, 2, 4 and 13, then its price will be:

Price[22] = 4*F[22] + Price[1]+Price[2]+Price[4]+Price[13]. As the prices of the base products fluctuate, the prices of the manufactured products also fluctuate.

Prices are simulated internly with double precision. However we provide rounded integer values to your function. The actual prices of your transactions will always be the rounded value. The balance of your account is initially 0 and it is allowed to have a negative balance.

End of simulation and scoring

After a very long period of very hard work (5000 days), you decide to sell you factory in order to buy a private island to retire. You negotiated that all the current accepted contract will be honoured by your successor in exchange of the entire stock in the warehouse. The simulation will end after 5000 steps. At the end ot the 5000th day, after receiving the money for the contracts you just shipped and paying the penalties for the delays of the current late contracts, you gather your money and leave forever, leaving the current contracts (late or not) and the current stock to be handled by your successor.

For each test case your score is your profits measured by the amount of money on your account when you leave. If you have lost money then your score will be 0. Your total score will be the sum of your relative scores (your score / best score)

Any invalid action will give you a 0 score. For example exceeding the warehouse capacity; insufficient quantities of necessary products; produce more than L products; ship several times the same contract; refer to a inexistent or rejected contract; refer to an inexistent product; bad size of the returned vector; etc...

Parameter generation

Base parameters: The following parameters are chosen randomly and uniformly in the following inclusive ranges:

  • B (number of base products) between 5 and 25.
  • M (number of manufactured products) between 5 and 25.
  • L (production limit by day) between 100 and 1000.
  • C (capacity of the warehouse) between 1000 and 10000.
  • The reference price P0 of each base product is equal to 50*2r where r is between -1 and 1.
  • The value factor F of each manufactured product is equal to 5*2r where r is between -1 and 1.

Process specifications: The number of products required to make a manufactured product is randomly chosen as floor(1.5 + 6*r2) where r is between 0 and 1. Each required products is randomly and independently chosen among all the products having a lower number than the output product with possible repetition.

Contracts:

  • The number of contracts that you receive each day is randomly chosen between 0 and 10, inclusive.
  • The contract IDs will be unique integers.
  • The number of different products ordered is randomly chosen between 1 and 5, inclusive.
  • The requested products are then randomly chosen among the M possible products, without repetitions.
  • For each product, the quantity ordered is ceil(1000*r3) where r is a random uniform variable in [0, 1].
  • The maximal number of days to honor the contract is chosen between 0 and 100, inclusive. A maximal number of days equals to 1 means that you have to ship the products at the end of the next day.
  • The penalty rate is chosen between 0 and 50 (i.e. between 0% to 5% per day).
  • The amount of the contract is equal to the current market price of the products multiplied by two modifying factors. The first one depends on the negotiation skill of your commercial team, this factor is chosen as 1.5r where r is a random uniform variable between -1 and 1. The second one is a stress factor equals to min(1.5, 1+(number_of_products_requested/maximal_number_of_days)*penalty_rate/10000). If maximal_number_of_days = 0 then the stress factor is 1.5 (or 1.0 if rate also equals zero)

Tools

A jar file and the source are available for offline testing. To use this tool, you will need to create an executable out of your submission. The executable must communicate with the tool via standard out and standard in. You should read the parameters from standard in, and write your outputs to standard out. You may write debugging statements to standard error. To run the tool, open a console, and run "java -jar Tester.jar <command> <seed>". <command> is the command for your executable (Java users must do something like "java class") and <seed> is a seed for the random number generator (examples are 1-10).



You should first read the init parameters. B, M, L and C will first be given on one line. The next M lines will contain the M elements of processes. You should not output anything after receiving the init parameters. You will then receive the manage parameters exactly 5000 times. Each time, the elements of warehouse will be given on one line, and the elements of prices will be given on the next line. A single line will then contain N, the number of contracts. The following N lines will contain the N contracts. Each reading the parameters to manage, you should print exactly four lines to standard out, containing the four elements of your return.



For example, the text below gives the contents you must read from standard in for the call to init, and the first call to manage for example 0: 
21 14 876 7426
14 7
14 7 5 2 1
12 1 22 8
17 23 15 5 20 18
1 11 7 17 11 15 19
21 0 24 19 6 9
8 15
11 0 7
9
5 28 29
19 27
2 27
19 26
12 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 43 70 34 44 32 35 50 64 58 66 80 21 65 37 39 98 76 52 60 41
6
0 211338 73 35 0 1 0 0 300 0 0 266 0 0 0 0 0 34
1 655720 1 15 0 0 0 0 0 446 0 0 0 0 0 0 0 1
2 101436 59 37 0 1 143 0 37 0 0 0 900 1 0 0 0 0
3 320 84 31 0 1 0 0 0 0 0 0 0 0 0 0 0 0
4 4830 100 25 0 0 0 0 0 0 0 0 0 0 30 0 0 0
5 20920 36 15 0 0 0 35 0 0 0 0 0 0 0 0 0 0
 

Definition

    
Class:FactoryManager
Method:init
Parameters:int, int, int, int, String[]
Returns:int
Method signature:int init(int B, int M, int L, int C, String[] processes)
 
Method:manage
Parameters:int[], int[], String[]
Returns:String[]
Method signature:String[] manage(int[] warhouse, int[] prices, String[] contracts)
(be sure your methods are public)
    
 

Notes

-Time limit is 30 seconds.
-Memory limit is 1GB.
 

Examples

0)
    
"1"
Returns: 
"B = 21
M = 14
L = 876
C = 7426
Product 0: P=30.467057930553647 P0=33.006314788649775
Product 1: P=43.481783596104044 P0=47.845366073188664
Product 2: P=69.56655575272202 P0=93.76896164038025
Product 3: P=33.67938336794847 P0=33.36908959363036
Product 4: P=43.65861493607287 P0=27.85634704408539
Product 5: P=31.564949927614162 P0=33.088036912740456
Product 6: P=35.3081606366463 P0=35.743061584806554
Product 7: P=50.19182908882418 P0=59.96794871085762
Product 8: P=64.11956864880528 P0=81.26844543438246
Product 9: P=57.72714854722601 P0=42.169786968566
Product 10: P=65.73358207712664 P0=89.45981852482852
Product 11: P=79.88578054217935 P0=85.00778467304987
Product 12: P=21.105545663065868 P0=26.3968875207382
Product 13: P=65.07741989225501 P0=54.33421422778455
Product 14: P=36.54261431045972 P0=36.02592453123869
Product 15: P=38.8825541055492 P0=34.29358922388757
Product 16: P=97.9281039385543 P0=94.79166739434143
Product 17: P=75.52508597127817 P0=72.33723047718561
Product 18: P=51.61296062330573 P0=52.70677796642459
Product 19: P=59.94954098584402 P0=55.63548438998127
Product 20: P=41.188483810703815 P0=46.86391458866739
Product 21: P=95.63324677771831 F=4.449401689217211 (21=14+7)
Product 22: P=260.367097876033 F=5.80387304006177 (22=14+7+5+2+1)
Product 23: P=421.8492982698891 F=8.193825621470229 (23=12+1+22+8)
Product 24: P=684.9954423337102 F=4.062018270895007 (24=17+23+15+5+20+18)
Product 25: P=451.7574419665015 F=3.4221553049347397 (25=1+11+7+17+11+15+19)
Product 26: P=989.7226045688892 F=4.273667892865123 (26=21+0+24+19+6+9)
Product 27: P=117.30374537504716 F=7.1508113103463415 (27=8+15)
Product 28: P=169.91244422693424 F=3.1225922217923543 (28=11+0+7)
Product 29: P=63.64637651579069 F=5.919227968564682 (29=9)
Product 30: P=273.5599264105531 F=2.8120519134046775 (30=5+28+29)
Product 31: P=185.75916791464988 F=4.252940776879345 (31=19+27)
Product 32: P=192.6728025338334 F=2.901250703032099 (32=2+27)
Product 33: P=1058.1683778795912 F=4.248116162428947 (33=19+26)
Product 34: P=69.54474034601071 F=3.6253554361205143 (34=12+20)
"
1)
    
"2"
Returns: 
"B = 11
M = 17
L = 543
C = 5324
Product 0: P=33.476148795494225 P0=32.955982909225604
Product 1: P=56.81892923962181 P0=73.64283167603583
Product 2: P=21.883764533194736 P0=30.68375637488481
Product 3: P=38.20272728625397 P0=43.00475972491574
Product 4: P=31.435631049908014 P0=25.14965975858976
Product 5: P=64.25115614494297 P0=61.03111259643422
Product 6: P=78.83407129232229 P0=83.23303834189075
Product 7: P=100.3758516814169 P0=99.86217124936097
Product 8: P=64.31277314031621 P0=68.64528756376869
Product 9: P=95.11863948203627 P0=85.00190178497206
Product 10: P=31.836877393952204 P0=35.395253498985404
Product 11: P=181.4463658597204 F=7.969866931527193 (11=2+6+1)
Product 12: P=143.85417155890076 F=5.798961327705654 (12=3+4+1)
Product 13: P=41.88196361150912 F=3.679236325255153 (13=3)
Product 14: P=484.69495710293086 F=9.849116826886812 (14=9+2+9+13+11)
Product 15: P=85.17493299970272 F=6.340861707380428 (15=6)
Product 16: P=394.2508414648499 F=2.8476874929500635 (16=0+1+8+12+1+2)
Product 17: P=561.3018340861714 F=7.7314689887494845 (17=4+11+2+11+1+13)
Product 18: P=258.0552506773243 F=3.383075378534665 (18=0+6+10+7)
Product 19: P=45.21664960824362 F=3.3346859967345024 (19=13)
Product 20: P=166.66436273690258 F=2.8298209187532706 (20=4+0+19+19)
Product 21: P=213.136427353591 F=4.134668665217218 (21=20+3)
Product 22: P=891.1480255433789 F=3.6627906282859994 (22=4+9+2+17+8+9)
Product 23: P=461.7514689700231 F=5.339604727294515 (23=8+11+9+0+0+2)
Product 24: P=959.8834927590874 F=5.958268988043339 (24=22+1)
Product 25: P=573.9168601725329 F=5.193915888639864 (25=14+6)
Product 26: P=35.57743133702424 F=3.7405539430720305 (26=10)
Product 27: P=207.4695088348561 F=2.973074489706835 (27=4+13+7+2)
"
2)
    
"3"
Returns: 
"B = 24
M = 17
L = 294
C = 4064
Product 0: P=38.65130158197142 P0=26.556182291114226
Product 1: P=74.47919714550947 P0=82.76253031804238
Product 2: P=65.61933711880552 P0=73.01307093796466
Product 3: P=89.44556974768923 P0=81.22312435268304
Product 4: P=55.48578812468421 P0=55.158187440601345
Product 5: P=35.96931422814248 P0=41.53827466846898
Product 6: P=31.58419834179683 P0=25.068425719913467
Product 7: P=53.94611058807457 P0=42.304574894738266
Product 8: P=80.01029067386135 P0=91.34237757998129
Product 9: P=33.65216435603129 P0=30.307411243179715
Product 10: P=73.32867262664242 P0=55.48032719604608
Product 11: P=26.52130927496994 P0=26.37474104898355
Product 12: P=38.60664248379992 P0=45.713010421599044
Product 13: P=31.088564926894637 P0=26.929024353199278
Product 14: P=78.20329056841291 P0=88.09979662092289
Product 15: P=40.72650443636486 P0=38.53070382804417
Product 16: P=36.4291906083585 P0=30.178851936434526
Product 17: P=79.28972808999642 P0=63.37322448684793
Product 18: P=43.128267317171705 P0=48.54822461113692
Product 19: P=32.29212044342042 P0=35.004061865173405
Product 20: P=86.47159597334513 P0=92.19177800633852
Product 21: P=35.61940055647144 P0=44.47873490333926
Product 22: P=54.612970966399544 P0=64.03835592365648
Product 23: P=55.748187950153344 P0=67.79351506926619
Product 24: P=148.31048533444283 F=2.641311184254429 (24=10+5+13)
Product 25: P=361.27693027199484 F=9.162146070222217 (25=4+15+0+24+19)
Product 26: P=153.81700879787965 F=5.50652346343683 (26=24)
Product 27: P=408.3822989361855 F=3.0294287743018735 (27=0+26+4+24)
Product 28: P=39.55080783230212 F=3.931407275830678 (28=21)
Product 29: P=190.30041304123085 F=3.0103067393227745 (29=5+24)
Product 30: P=161.6626810964005 F=8.376807943799282 (30=2+17)
Product 31: P=440.72258540189745 F=2.9179481181063025 (31=30+2+28+8+17)
Product 32: P=130.39113169761316 F=7.8410181807501145 (32=19+12+5)
Product 33: P=308.8486677397809 F=3.1347070152810503 (33=18+2+8+13+10)
Product 34: P=122.49593782663061 F=5.712223587097709 (34=13+0+21)
Product 35: P=144.89621590203814 F=5.830188611983582 (35=17+7)
Product 36: P=189.33907906407842 F=3.6882146868021426 (36=9+24)
Product 37: P=237.69306251557575 F=4.393003495272491 (37=12+29)
Product 38: P=479.77403114120034 F=2.6831008731239407 (38=29+9+1+4+16+10)
Product 39: P=413.06200310356627 F=6.589215173885755 (39=25+12)
Product 40: P=118.80635846166732 F=3.435521675612498 (40=10+12)
"
3)
    
"4"
Returns: 
"B = 5
M = 8
L = 373
C = 8538
Product 0: P=89.3765106841046 P0=83.13122042912711
Product 1: P=55.737617072257656 P0=51.413508608860894
Product 2: P=34.26032367496541 P0=31.864964663532884
Product 3: P=48.8787548206847 P0=39.21585332955063
Product 4: P=44.32997356409447 P0=60.34143574301969
Product 5: P=208.15145306685147 F=4.719523496601508 (5=0+1+3)
Product 6: P=155.471468095342 F=8.608101295276345 (6=0+3)
Product 7: P=53.046159114496206 F=4.167404293811506 (7=3)
Product 8: P=310.58876242028884 F=4.394648094018293 (8=4+4+6+3)
Product 9: P=314.5280932866052 F=3.9393308663163835 (9=8)
Product 10: P=65.05920412130523 F=9.321587049047569 (10=1)
Product 11: P=56.99788503433386 F=3.951725919837654 (11=7)
Product 12: P=163.75040190096004 F=8.27893380561803 (12=6)
"
4)
    
"5"
Returns: 
"B = 22
M = 5
L = 209
C = 6585
Product 0: P=39.97720766552882 P0=49.17810891471672
Product 1: P=100.52320261016708 P0=74.6891916522258
Product 2: P=39.20677653716936 P0=38.611274834622215
Product 3: P=35.443660007348285 P0=33.02252166478518
Product 4: P=82.16966552067379 P0=84.94094398669714
Product 5: P=56.964360721681196 P0=71.67666705642664
Product 6: P=53.650621511314135 P0=54.01365471765429
Product 7: P=57.66124546179076 P0=52.613556392946556
Product 8: P=20.778721420432767 P0=28.824580952278545
Product 9: P=32.15415224996614 P0=41.61188797840493
Product 10: P=25.346105372684796 P0=28.290221250730855
Product 11: P=50.78057355314793 P0=52.633101075595924
Product 12: P=54.875737865691995 P0=56.25999649876026
Product 13: P=52.23453830745965 P0=37.79973345719665
Product 14: P=30.288402329569017 P0=30.495956523999347
Product 15: P=122.86791092363514 P0=95.77365869084313
Product 16: P=34.9520954824441 P0=42.98488515625064
Product 17: P=90.1497154263361 P0=69.9818436591882
Product 18: P=51.64581232578584 P0=38.02494323314488
Product 19: P=37.26847321914346 P0=33.25622941683438
Product 20: P=80.87455465993273 P0=82.58475203338351
Product 21: P=44.18711394582331 P0=38.80375440954096
Product 22: P=307.0592859740742 F=4.371060896910054 (22=1+12+12+0+16)
Product 23: P=341.3238713826175 F=4.459240017929249 (23=22+10)
Product 24: P=259.1757781063878 F=9.099426421107491 (24=4+11+16+12)
Product 25: P=529.3873207089586 F=6.7170572642769475 (25=8+20+18+3+22)
Product 26: P=410.74476809002186 F=6.582152758354831 (26=6+22+14)
"
5)
    
"6"
Returns: 
"B = 8
M = 17
L = 497
C = 5738
Product 0: P=36.3860163867334 P0=35.42105357563672
Product 1: P=47.63559415835839 P0=40.860951667954446
Product 2: P=82.11817577516202 P0=67.87148262528426
Product 3: P=18.895234885002566 P0=25.534614293843426
Product 4: P=78.44333007200864 P0=94.35063490587953
Product 5: P=45.30903073579938 P0=48.51229099519235
Product 6: P=68.51849498192495 P0=63.63003968676904
Product 7: P=26.882550749066116 P0=37.4313428619823
Product 8: P=92.77443687547576 F=2.680353504274122 (8=3+6)
Product 9: P=41.47227678931647 F=5.086260402583068 (9=0)
Product 10: P=21.421392193310254 F=2.5261573083076874 (10=3)
Product 11: P=51.70447093929622 F=4.068876780937837 (11=1)
Product 12: P=148.08089889656725 F=2.9875660301145004 (12=3+11+6)
Product 13: P=195.31165851819364 F=3.9722505605277014 (13=0+7+1+6)
Product 14: P=306.54834621726513 F=2.6092486068263563 (14=11+11+13)
Product 15: P=749.3149738441846 F=5.341280378062889 (15=11+14+10+0+14)
Product 16: P=402.20408744028276 F=6.76878272392781 (16=14+2)
Product 17: P=600.5664696117968 F=5.645121785623559 (17=4+4+16+3)
Product 18: P=46.83587132678598 F=5.363594537469512 (18=9)
Product 19: P=758.6074052086769 F=9.292431364492382 (19=15)
Product 20: P=765.302062013604 F=6.694656804926983 (20=19)
Product 21: P=32.21846118566408 F=5.335910436597969 (21=7)
Product 22: P=1088.4037554238498 F=3.6763828294389778 (22=21+13+15+11+9)
Product 23: P=49.2150977240359 F=7.742820934719433 (23=9)
Product 24: P=455.6178787129583 F=4.0523802684380845 (24=5+16)
"
6)
    
"7"
Returns: 
"B = 23
M = 7
L = 843
C = 1489
Product 0: P=65.39747424449513 P0=75.61547796565704
Product 1: P=40.52920100364615 P0=33.71512593463487
Product 2: P=40.67979612399307 P0=37.65362680491842
Product 3: P=33.103955548239824 P0=31.781321651058718
Product 4: P=35.45234797381355 P0=32.54222639030798
Product 5: P=29.069608806425784 P0=38.13223741005848
Product 6: P=80.40397430979178 P0=79.94341212399485
Product 7: P=90.86672276129048 P0=95.52674092455817
Product 8: P=33.861962063741004 P0=30.94808900952203
Product 9: P=79.68961533758782 P0=76.47615957199247
Product 10: P=29.582519859697243 P0=31.631837380625132
Product 11: P=31.7679231843823 P0=35.32880590952081
Product 12: P=90.77840229163581 P0=96.19344613622465
Product 13: P=44.98216349863044 P0=40.66260012007911
Product 14: P=38.589793130591495 P0=38.78754674292166
Product 15: P=26.847240412840144 P0=30.441524773749233
Product 16: P=90.85885184524554 P0=72.77798727339608
Product 17: P=41.538090991612606 P0=40.209143318702594
Product 18: P=42.88993149513911 P0=35.93568297121617
Product 19: P=112.499458224725 P0=95.14451655159947
Product 20: P=41.003937146361245 P0=44.987022291053
Product 21: P=20.294968602046247 P0=26.29429083854741
Product 22: P=51.54471423506227 P0=51.99506607616495
Product 23: P=178.24468042864015 F=3.8014265353116388 (23=4+16+1)
Product 24: P=475.79082990359836 F=7.339515546976816 (24=1+15+1+23+3+19)
Product 25: P=224.81648797103898 F=8.302685430739063 (25=9+9+1)
Product 26: P=33.33041534751097 F=4.26080654108519 (26=5)
Product 27: P=390.3860433098215 F=5.30710408643435 (27=5+2+14+23+5+18)
Product 28: P=191.76827737135793 F=9.693340538213937 (28=15+13+16)
Product 29: P=127.99830837205745 F=2.7093807696652625 (29=9+18)
"
7)
    
"8"
Returns: 
"B = 9
M = 11
L = 902
C = 1158
Product 0: P=88.82776858207922 P0=85.24825652023821
Product 1: P=31.82229270089032 P0=27.150141262627063
Product 2: P=44.05872017792101 P0=62.596718464822864
Product 3: P=32.179023506869285 P0=44.36780596203697
Product 4: P=59.72482319513359 P0=68.26749009680803
Product 5: P=52.561117395229005 P0=44.838725993394384
Product 6: P=40.84277984915369 P0=26.197914184945425
Product 7: P=96.95611249410733 P0=99.52899991401705
Product 8: P=37.72574875566561 P0=44.64465738143755
Product 9: P=40.0648403711694 F=8.242547670279084 (9=1)
Product 10: P=106.76787335008848 F=7.432013324042809 (10=3+4)
Product 11: P=415.63155022418215 F=2.5748791299511 (11=3+0+8+7+8+10)
Product 12: P=104.78889672783299 F=4.084529577341486 (12=2+5)
Product 13: P=687.1123792099213 F=6.940060214960386 (13=6+1+8+11+4+4)
Product 14: P=858.9967646305532 F=8.182975403685335 (14=0+4+10+3+10+11)
Product 15: P=1016.2202430038956 F=2.8902955320432184 (15=0+14+4)
Product 16: P=168.77307247635866 F=9.627921293511164 (16=5+7)
Product 17: P=97.99705845267151 F=9.169289870592294 (17=0)
Product 18: P=137.43586983426218 F=3.141084975900648 (18=8+5+8)
Product 19: P=43.943221800022485 F=3.1004419508687886 (19=6)
"
8)
    
"9"
Returns: 
"B = 15
M = 20
L = 278
C = 2525
Product 0: P=67.19398844824225 P0=85.66029640188628
Product 1: P=35.51830741346755 P0=25.198432128900205
Product 2: P=32.73228492365504 P0=54.481161660687704
Product 3: P=51.920114942729725 P0=42.71787183215023
Product 4: P=55.39840472565144 P0=55.121979001988365
Product 5: P=45.63881586672027 P0=58.21485853753528
Product 6: P=43.46797864061991 P0=44.90295637008834
Product 7: P=37.51635933233866 P0=38.402985678407596
Product 8: P=27.54156625555124 P0=39.855793046134124
Product 9: P=22.259032176228555 P0=27.977366003535582
Product 10: P=37.60577109771973 P0=31.61330940342112
Product 11: P=41.97188612057414 P0=33.39095980535855
Product 12: P=52.96530264684559 P0=63.781842549713595
Product 13: P=17.8302983907773 P0=28.20547999110316
Product 14: P=56.80038863262895 P0=51.371125712416564
Product 15: P=287.9971056133796 F=9.847052281998126 (15=9+6+1+2+12+11)
Product 16: P=106.80408193957672 F=4.716895546675573 (16=11+4)
Product 17: P=49.69467593930376 F=7.722789818729616 (17=11)
Product 18: P=461.6561538762852 F=3.351525896899984 (18=16+15+14)
Product 19: P=249.7194083386562 F=7.453427097980839 (19=8+10+10+11+8+2)
Product 20: P=203.6969265737668 F=3.022158059207445 (20=12+10+4+5)
Product 21: P=100.16817522852625 F=7.757887681070744 (21=3+2)
Product 22: P=53.64923803716512 F=4.138686695418291 (22=8+13)
Product 23: P=44.91548563578838 F=2.9435995152142373 (23=11)
Product 24: P=464.57255251490824 F=2.9163986386230265 (24=18)
Product 25: P=73.4344740250799 F=6.240485576837647 (25=0)
Product 26: P=612.0452953679453 F=6.3345401304771265 (26=1+14+18+2)
Product 27: P=354.0020162205779 F=6.177836285016609 (27=15+22)
Product 28: P=49.62857304874247 F=4.713087412954092 (28=23)
Product 29: P=120.19239786663817 F=7.549658600841489 (29=4+17)
Product 30: P=105.98752542468488 F=6.536380683347387 (30=4+7)
Product 31: P=665.2429414509058 F=8.26829771301643 (31=4+14+24+4)
Product 32: P=363.4674986655808 F=6.740882333298944 (32=12+4+7+16+10+2)
Product 33: P=238.14315346130218 F=3.2201982817638104 (33=4+1+16+8)
Product 34: P=109.59231804433732 F=2.7882361047605944 (34=16)
"
9)
    
"10"
Returns: 
"B = 9
M = 15
L = 323
C = 9146
Product 0: P=27.492190268144938 P0=31.236829732058624
Product 1: P=107.55208918872971 P0=95.79384064243415
Product 2: P=104.61061212076584 P0=87.1004696780129
Product 3: P=27.700517761193115 P0=34.713457593946664
Product 4: P=39.93963455671486 P0=35.207336378312405
Product 5: P=68.85472281664039 P0=73.91243714688865
Product 6: P=89.4336061094451 P0=76.40492231588654
Product 7: P=53.03897262678645 P0=68.32998427812953
Product 8: P=98.26178354207231 P0=62.36409829812241
Product 9: P=349.70244650175306 F=3.296289901090843 (9=7+6+5+5+7)
Product 10: P=772.1666740621114 F=2.7555918333436304 (10=8+9+8+2+1)
Product 11: P=201.6737407373873 F=3.8147612535881814 (11=6+2)
Product 12: P=101.34790359645586 F=3.086120054383554 (12=8)
Product 13: P=1348.8401623550164 F=9.818913034908691 (13=10+9+6+8)
Product 14: P=110.12720929303397 F=5.516597172268131 (14=2)
Product 15: P=453.1993130192064 F=2.617541487690502 (15=9+8)
Product 16: P=1807.2880996095441 F=2.624312117660602 (16=13+15)
Product 17: P=466.6857132681494 F=3.4280287366811835 (17=14+9)
Product 18: P=1812.1906757628972 F=4.902576153353124 (18=16)
Product 19: P=2149.1625550267645 F=8.886491335577386 (19=7+6+14+18+4)
Product 20: P=817.6394922554299 F=2.702463319629915 (20=9+14+9)
Product 21: P=1816.645240056567 F=4.45456429366992 (21=18)
Product 22: P=1820.1221791452303 F=7.93150338233327 (22=18)
Product 23: P=5481.110823693461 F=6.367679400415368 (23=5+19+13+3+13+15+4)
"

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8472

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12198&pm=8472

Writer:

Unknown

Testers:

Problem categories:

Simulation