💾 Feat: New USACO problems organized.

source/competitions/usaco/2002 January Silver/green.md

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+  GREEN PROBLEMS
+  Four problems numbered 1 through 4
+
+Problems - 2002 Winter Open, Green (Senior Division)
+
+# PROBLEM 1: Pasture Fences [Dominic Battre, 2001]
+
+Farmer John has a long fence made of fence poles and rails. Each of the N (1 <= N <= 3000) 
+fence poles carries a sign with a single number from -1000 through +1000. Some poles might 
+have the same number on their sign as other poles. While chewing their cud, the cows made up
+ a game. The cow who can find the "best fence sum" gets ice cream for dessert.
+
+To win the game, the winning cow must find the longest contiguous set of poles whose sum has 
+the smallest absolute value. Help them determine the winning sum.
+
+PROBLEM NAME: pasture
+
+## INPUT FORMAT:
+
+* Line 1: One line with a single integer: N
+
+* Lines 2..N+1: Each line contains a pole's label. Line 2 contains
+ the value for pole with sequence number 1, etc.
+
+### SAMPLE INPUT (file pasture.in):
+
+```text
+6
+5
+10
+-5
+-6
+2
+4
+```
+
+## OUTPUT FORMAT:
+
+A single line with three numbers:
+ * the sequence number of the pole that is first to be summed,
+ * the sequence number of the pole that is last to be summed, and
+ * the absolute value of the sum of the labels of those poles. If more than one 
+sequence has the same "best fence sum" and same maximum length, report the sequence
+ with the lowest first sequence number.
+
+### SAMPLE OUTPUT (file pasture.out):
+
+```text
+4 6 0
+```
+
+# PROBLEM 2: New Years Party [Hal Burch, 2001]
+
+A group of N (3 <= N <= 200) cows is having a New Year's party. Each cow is able 
+to cook several different kinds of food (in units called a "dish"). There are a 
+total of D (5 <= D <= 100) different kinds of food. Each kind of food is denoted 
+by an integer in the range 1..D.
+
+The cowrdinator wants to maximize the total number of dishes brought to the party, 
+but has specified a limit for the number of dishes of each type. Each cow can bring
+ K (1 <= K <= 5) dishes, but they must be different from each other (she can't bring
+ 3 bovine pies, for example, but she could bring a pie, some bread, and some nice 
+alfalfa in orange sauce). What is the maximum amount of food that can be brought?
+
+PROBLEM NAME: party
+
+## INPUT FORMAT:
+
+* Line 1: Three integers: N, K, and D
+
+* Line 2: D non-negative integers: the limit on total number of each of
+ the various dishes that can be brought to the party
+
+* Lines 3..N+2: Each line contains an initial integer Z (1 <= Z <= D)
+ denoting the number of different dishes a cow can prepare; the rest of
+ the line contains Z integers that are the food identifiers, food type 1
+ first, food type 2 second, etc..
+
+### SAMPLE INPUT [FILE party.in]:
+
+```text
+4 3 5
+2 2 2 2 3
+4 1 2 3 4
+4 2 3 4 5
+3 1 2 4
+3 1 2 3
+```
+
+EXPLANATION OF SAMPLE INPUT:
+
+data...... explanation...................................................
+4 3 5 4 cows, each cow brings up to 3 dishes, 5 different food types
+2 2 2 2 3 max for party of 2 dishes food types 1..4; 3 dishes of food 5
+4 1 2 3 4 This cow can cook 4 different foods (1, 2, 3, 4)
+4 2 3 4 5 This cow can cook 4 different foods (2, 3, 4, 5)
+3 1 2 4 This cow can cook 3 different foods (1, 2, 4)
+3 1 2 3 This cow can cook 3 different foods (1, 2, 3)
+
+## OUTPUT FORMAT:
+
+A single line with a single integer that is the maximum number of dishes that can 
+be brought to the party.
+
+### SAMPLE OUTPUT [FILE party.out]:
+
+```text
+9
+```
+
+[Cow 1 brings foods 3 and 4; cow 2 brings foods 3, 4 and 5;
+cow 3 brings foods 1 and 2; and cow 4 brings foods 1 and 2.]
+
+
+# PROBLEM 3: Strolling Cows [Dan Adkins, 2001]
+
+Before going to the barn for dinner, the cows like to stroll the N (1 <= N <= 30,000)
+ pastures while watching the sun set. Each pasture leads to precisely one pasture, though
+ some pastures have more than one pasture emptying into them. For a valid strolling experience,
+ the cows can start in any pasture and must finish in that same pasture without visiting any 
+other pasture twice. Given a description of the pasture paths, deduce the longest possible 
+valid stroll the cows can take.
+
+PROBLEM NAME: stroll
+
+## INPUT FORMAT:
+
+* Line 1: One integer: N
+
+* Lines 2..N+1: Line M tells the pasture number that pasture M-1 connects
+ to (so line 2 tells which pasture is accessible from pasture 1, etc.)
+
+### SAMPLE INPUT (FILE stroll.in):
+
+```text
+5
+2
+4
+5
+5
+2
+```
+
+## OUTPUT FORMAT:
+
+A single line with the integer that is the largest number of pastures that can be visited 
+on a legal stroll.
+
+### SAMPLE OUTPUT (FILE stroll.out):
+
+```text
+3
+```
+
+[by visiting pasture 2, then 4, then 5]
+
+
+# PROBLEM 4: Grazing Sets [Brian Dean, 2001]
+
+Farmer John's N (4 <= N <= 10,000) cows live at various points within a circular field. 
+FJ wants to partition his cows by building K (3 <= K <= 1000) fences radially outward 
+from the center of the field at evenly-spaced angles (each measuring 360/K degrees). 
+Depending on how he rotates this system of fences, he can partition the cows into K 
+subsets, each containing a different subset of cows (potentially an empty subset). 
+Define the RANGE of this partition as the number of cows in the largest set minus 
+the number of cows in the smallest set. Determine the minimum attainable RANGE value 
+for a given set of cows.
+
+Of course, no cow can straddle a fence. Cows must be in one partition or the other.
+
+To avoid problems with rounding, the input data will not contain cows that are very 
+close to an integer multiple of 360/K degrees apart.
+
+PROBLEM NAME: grazeset
+
+## INPUT FORMAT:
+
+* Line 1: Two integers: N and K
+
+* Lines 2..N+1: Each line contains a single double that tells the angle at
+ which a cow is grazing. Angles are expressed in degrees, 0 <= angle <
+ 360.
+
+### SAMPLE INPUT (FILE grazeset.in):
+
+```text
+4 3
+30
+60
+150.003
+240
+```
+
+## OUTPUT FORMAT:
+
+A single line with the integer that is the minimum attainable RANGE value 
+for the set of cows.
+
+### SAMPLE OUTPUT (FILE grazeset.out):
+
+```text
+1
+```

source/competitions/usaco/2002 January Silver/orange.md

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+  ORANGE PROBLEMS
+  Four problems numbered 5 through 8
+
+# PROBLEM 5: Factorial Power [Piele, 1983]
+
+The factorial power of a whole number N is defined like this:
+
+  N! = 1 * 2 * 3 * ... * N-1 * N
+
+For example, 12! = 1*2*3*4*5*6*7*8*9*10*11*12 = 479001600
+
+The rightmost non-zero digit in 12! is 6; two zeroes follow it. 
+Write a program that will compute the right-most non-zero digit 
+in the decimal representation of N! and also find the number of 
+zeroes after it.
+
+PROBLEM NAME: fact
+
+## INPUT FORMAT:
+
+One line with a single integer: N, 1 <= N <= 1,000,000
+
+### SAMPLE INPUT (file fact.in):
+
+```text
+12
+```
+
+## OUTPUT FORMAT:
+A single line with two numbers:
+
+* The right most non-zero digit of N!
+* The number of zeroes that follow it
+
+### SAMPLE OUTPUT (file fact.out):
+
+```text
+6 2
+```
+
+# PROBLEM 6: Friday the Thirteenth [Traditional; Andree, 1965]
+
+Is Friday the 13th really an unusual event? 
+
+That is, does the 13th of the month land on a Friday less often than on 
+any other day of the week? To answer this question, write a program that 
+will compute the frequency that the 13th of each month lands on Sunday, 
+Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday over a given 
+period of N years. The time period to test will be from January 1, 1900 
+to December 31, 1900+N-1 for a given number of years, N. N is non-negative 
+and will not exceed 400.
+
+There are few facts you need to know before you can solve this
+problem: 
+* January 1, 1900 was on a Monday. 
+* Thirty days has September, April, June, and November, all the rest have
+ 31 except for February which has 28 except in leap years
+ when it has 29.
+* Every year evenly divisible by 4 is a leap year (1992 = 4*498 so 1992
+ will be a leap year, but the year 1990 is not a leap year)
+* The rule above does not hold for century years. Century years divisible
+ by 400 are leap years, all other are not. Thus, the century years 1700,
+ 1800, 1900 and 2100 are not leap years, but 2000 is a leap year.
+
+Do not use any built-in date functions in your computer language. 
+
+Don't just precompute the answers, either. 
+
+PROGRAM NAME: friday
+
+## INPUT FORMAT:
+
+One line with the integer N. 
+
+### SAMPLE INPUT (file friday.in):
+
+```text
+20
+```
+
+## OUTPUT FORMAT:
+
+Seven space separated integers on one line. These integers represent the 
+number of times the 13th falls on Saturday, Sunday, Monday, Tuesday, ..., Friday.
+
+### SAMPLE OUTPUT (file friday.out):
+
+```text
+36 33 34 33 35 35 34
+```
+
+# PROBLEM 7: Beef McNuggets [Hubert Chen, 1998]
+
+Farmer Brown's cows are up in arms, having heard that McDonalds is considering 
+the introduction of a new product: Beef McNuggets. The cows are trying to find 
+any possible way to put such a product in a negative light.
+
+One strategy the cows are pursuing is that of `inferior packaging'. ``Look,'' say 
+the cows, ``if you have Beef McNuggets in boxes of 3, 6, and 10, you can not satisfy 
+a customer who wants 1, 2, 4, 5, 7, 8, 11, 14, or 17 McNuggets. Bad packaging: bad product.''
+
+Help the cows. Given N (the number of packaging options, 1 <= N <= 10), and a set 
+of N positive integers (1 <= i <= 256) that represent the number of nuggets in the 
+various packages, output the largest number of nuggets that can not be purchased by 
+buying nuggets in the given sizes. Print 0 if all possible purchases can be made or 
+if there is no bound to the largest number.
+
+The largest impossible number (if it exists) will be no larger than 2,000,000,000.
+
+PROGRAM NAME: nuggets
+
+## INPUT FORMAT:
+
+* Line 1: N, the number of packaging options
+
+* Line 2..N+1: The number of nuggets in one kind of box 
+
+### SAMPLE INPUT (file nuggets.in) :
+
+```text
+3
+3
+6
+10
+```
+
+## OUTPUT FORMAT:
+
+The output file should contain a single line containing a single integer that 
+represents the largest number of nuggets that can not be represented or 0 if all 
+possible purchases can be made or if there is no bound to the largest number.
+
+### SAMPLE OUTPUT (file nuggets.out):
+
+```text
+17
+```
+
+# PROBLEM 8: Calf Flac [Traditional; Brian Dean 2001]
+
+PROBLEM NAME: calfflac
+
+It is said that if you give an infinite number of cows an infinite number of 
+heavy-duty laptops (with very large keys), that they will ultimately produce 
+all the world's great palindromes. Your job will be to detect these bovine beauties.
+
+Ignore punctuation, whitespace, and case when testing for palindromes, but 
+keep these extra characters around so that you can print them out as the 
+answer; just consider the letters `A-Z' and `a-z'.
+
+Find any largest palindrome in a string no more than 20,000 characters long. 
+The largest palindrome is guaranteed to be at most 2,000 characters long before 
+whitespace and punctuation are removed.
+
+## INPUT FORMAT:
+
+A file with no more than 20,000 characters.
+
+### SAMPLE INPUT (file calfflac.in):
+
+```text
+Confucius say: Madam, I'm Adam.
+```
+
+## OUTPUT FORMAT:
+
+The first line of the output should be the length of the longest palindrome found. 
+The next line or lines should be the actual text of the palindrome (without any 
+surrounding white space or punctuation but with all other characters) printed on a line 
+(or more than one line if newlines are included in the palindromic text). If there are 
+multiple palindromes of longest length, outputthe one that appears first.
+
+### SAMPLE OUTPUT (file calfflac.out):
+
+```text
+11
+Madam, I'm Adam
+```