Sorting
– Sorting Applications
 Uniqueness Testing
 Deleting Duplicates
 Prioritizing Events
 Median/Selection
 Frequency Counting
 Reconstructing the Original Order
 Set Intersection/Union
 Finding a target Pair
 Efficient Searching
1
Program Design Example: Rating the Field
– Pretty Polly has no shortage of gentlemen suitors who come a’
courting. Indeed, her biggest problem is keeping track of who the best
ones are. She is smart enough to realize that a program which ranks
the men from most to least desirable would simplify her life. She is
also persuasive enough to have talked you into writing the program.
– Polly really likes to dance, and has determined the optimal partner
height is 180 centimeters tall. Her first criteria is finding someone
who is as close as possible to this height; whether they are a little
taller or shorter doesn’t matter. Among all candidates of the same
height, she wants someone as close as possible o 75 kilograms without
going over. If all equal-height candidates are over this limit, she will
take the lightest of the bunch. If two or more people are identical by
all these characteristics, sort them by last name, then by first name if it
is necessary to break the tie.
2
Polly is only interested in seeing the candidates ranked by name, so the input file:
George Bush 195
Harry Truman 180
Bill Clinton 180
John Kennedy 180
Ronald Reagan 165
Richard Nixon 170
Jimmy Carter 180
110
75
75
65
110
70
77
yields the following output:
Clinton, Bill
Truman, Harry
Kennedy, John
Carter, Jimmy
Nixon, Richard
Bush, George
Reagan, Ronald
3
#include <stdio.h>
#include <string.h>
#define NAMELENGTH 30
#define NSUITORS 100
#define BESTHEIGHT 180
#define BESTWEIGHT 75
typedef struct {
char first[NAMELENGTH];
char last[NAMELENGTH];
int height;
int weight;
} suitor;
suitor suitors[NSUITORS];
int nsuitors;
main()
{
int i;
int suitor_compare();
read_suitors();
qsort(suitors,nsuitors,sizeof(suitor),suitor_compare);
for(i=0;i<nsuitors;i++)
printf(“%s, %s\n”,suitors[i].last,suitors[i].first);
}
4
read_suitors()
{
char first[NAMELENGTH],last[NAMELENGTH];
int height,weight;
nsuitors=0;
while(scanf(“%s %s %d %d\n”,suitors[nsuitors].first,
suitors[nsuitors].last,&height,&weight)!=EOF) {
suitors[nsuitors].height=abs(height-BESTHEIGHT);
if(weight>BESTWEIGHT)
suitors[nsuitors].weight=weight-BESTWEIGHT;
else
suitors[nsuitors].weight=-weight;
nsuitors++;
}
}
5
int suitor_compare(suitor *a,suitor *b)
{
int result;
if(aheight<bheight) return (-1);
if(aheight>bheight) return (1);
if(aweight<bweight) return (-1);
if(aweight>bweight) return (1);
if((result=strcmp(alast,blast))!=0) return result;
return (strcmp(afirst,bfirst));
}
6
Exercises:
http://online-judge.uva.es/problemset/
7
Problem : Vito’s Family
UVa ID: 10041, Popularity: A. Success rate: high Level: 1
Background
The world-known gangster Vito Deadstone is moving to New York. He
has a very big family there, all of them living in Lamafia Avenue.
Since he will visit all his relatives very often, he is trying to find a
house close to them.
Problem
Vito wants to minimize the total distance to all of them and has
blackmailed you to write a program that solves his problem.
Input
The input consists of several test cases. The first line contains the
number of test cases. For each test case you will be given the integer
number of relatives r ( 0 < r < 500) and the street numbers (also
integers) where they live ( 0 < si < 30000 ). Note that several relatives
could live in the same street number.
8
Output
For each test case your program must write the
minimal sum of distances from the optimal Vito's
house to each one of his relatives. The distance
between two street numbers si and sj is dij= |si-sj|.
Sample Input
2
224
3246
Sample Output
2
4
9
Problem : Stacks of Flapjacks
UVa ID: 120, Popularity: B. Success rate: high Level: 2
Background
Stacks and Queues are often considered the bread and butter of data structures and
find use in architecture, parsing, operating systems, and discrete event simulation.
Stacks are also important in the theory of formal languages.
This problem involves both butter and sustenance in the form of pancakes rather
than bread in addition to a finicky server who flips pancakes according to a unique,
but complete set of rules
Problem
Given a stack of pancakes, you are to write a program that indicates how the
stack can be sorted so that the largest pancake is on the bottom and the smallest
pancake is on the top. The size of a pancake is given by the pancake's diameter. All
pancakes in a stack have different diameters.
Sorting a stack is done by a sequence of pancake ``flips''. A flip consists of
inserting a spatula between two pancakes in a stack and flipping (reversing) the
pancakes on the spatula (reversing the sub-stack). A flip is specified by giving the
position of the pancake on the bottom of the sub-stack to be flipped (relative to the
whole stack). The pancake on the bottom of the whole stack has position 1 and the
pancake on the top of a stack of n pancakes has position n.
A stack is specified by giving the diameter of each pancake in the stack in the
10
order in which the pancakes appear.
For example, consider the three stacks of pancakes
below (in which pancake 8 is the top-most
pancake of the left stack):
8
7
2
4
6
5
6
4
8
7
8
4
5
5
6
2
2
7
The stack on the left can be transformed to the
stack in the middle via flip(3). The middle stack
can be transformed into the right stack via the
command flip(1).
11
The Input
The input consists of a sequence of stacks of pancakes. Each stack will consist of
between 1 and 30 pancakes and each pancake will have an integer diameter between
1 and 100. The input is terminated by end-of-file. Each stack is given as a single line
of input with the top pancake on a stack appearing first on a line, the bottom
pancake appearing last, and all pancakes separated by a space.
The Output
For each stack of pancakes, the output should echo the original stack on one line,
followed by some sequence of flips that results in the stack of pancakes being sorted
so that the largest diameter pancake is on the bottom and the smallest on top. For
each stack the sequence of flips should be terminated by a 0 (indicating no more
flips necessary). Once a stack is sorted, no more flips should be made.
Sample Input
12345
54321
51234
Sample Output
12345
0
54321
10
51234
120
12
Problem : Bridge
UVa ID: 10037, Popularity: B. Success rate: low Level: 3
n people wish to cross a bridge at night. A group of at most two
people may cross at any time, and each group must have a flashlight.
Only one flashlight is available among the n people, so some sort of
shuttle arrangement must be arranged in order to return the flashlight
so that more people may cross. Each person has a different crossing
speed; the speed of a group is determined by the speed of the slower
member. Your job is to determine a strategy that gets all n people
across the bridge in the minimum time.
Input
The input begins with a single positive integer on a line by itself
indicating the number of the cases following, each of them as
described below. This line is followed by a blank line, and there is
also a blank line between two consecutive inputs.
The first line of input contains n, followed by n lines giving the
crossing times for each of the people. There are not more than 1000
people and nobody takes more than 100 seconds to cross the bridge.
13
Output
For each test case, the output must follow the description below. The outputs of two
consecutive cases will be separated by a blank line.
The first line of output must contain the total number of seconds required for all n people to
cross the bridge. The following lines give a strategy for achieving this time. Each line
contains either one or two integers, indicating which person or people form the next group to
cross. (Each person is indicated by the crossing time specified in the input. Although many
people may have the same crossing time the ambiguity is of no consequence.) Note that the
crossings alternate directions, as it is necessary to return the flashlight so that more may cross.
If more than one strategy yields the minimal time, any one will do.
Sample Input
1
4
1
2
5
10
Sample Output
17
12
1
5 10
2
12
14
Problem : Longest Nap
UVa ID: 10191, Popularity: B. Success rate: average Level: 1
The Problem
As you may already know, there are professors very busy with a filled schedule of work
during the day. Your professor, let's call him Professor P, is a bit lazy and wants to take a nap
during the day, but as his schedule is very busy, he doesn't have a lot of chances of doing this.
He would REALLY like, however, to take one nap every day. Because he'll take just one nap,
he wants to take the longest nap that it's possible given his schedule. He decided to write a
program to help him in this task but, as we said, Professor P is very lazy. So, he finally
decided that YOU must write the program!
The Input
The input will consist on an arbitrary number of test cases, each test case represents
one day. The first line of each set contains a positive integer s (not greater than 100)
representing the number of scheduled appointments during that day. In the next s lines
there are the appointments in the following format:
time1 time2 appointment Where time1 represents the time which the appointment starts and
time2 the time it ends. All times will be in the hh:mm format, time1 will always be strictly
less than time2, they will be separated by a single space and all times will be greater than or
equal to 10:00 and less than or equal to 18:00. So, your response must be in this interval as
well (i.e. no nap can start before 10:00 and last after 18:00). The appointment can be any
sequence of characters, but will always be in the same line. You can assume that no line will
be longer than 255 characters, that 10 <= hh <= 18 and that 0 <= mm < 60. You CAN'T
assume, however, that the input will be in any specific order. You must read the input until
you reach the end of file.
15
The Output
For each test case, you must print the following line:
Day #d: the longest nap starts at hh:mm and will last for [H hours and] M
minutes. Where d stands for the number of the test case (starting from 1) and
hh:mm is the time when the nap can start. To display the duration of the nap,
follow these simple rules:
if the total duration X in minutes is less than 60, just print "M minutes",
where M = X.
if the total duration X in minutes is greater or equal to 60, print "H hours and
M minutes", where H = X div 60 (integer division, of course) and M = X
mod 60.
Notice that you don't have to worry with concordance (i.e. you must print "1
minutes" or "1 hours" if it's the case). The duration of the nap is calculated
by the difference between the ending time free and the begining time free.
That is, if an appointment ends at 14:00 and the next one starts at 14:47, then
you have (14:47)-(14:00) = 47 minutes of possible nap. If there is more than
one longest nap with the same duration, print the earliest one. You can
assume that there won't be a day all busy (i.e. you may assume that there will
be at least one possible nap).
16
Sample Input
4
10:00 12:00 Lectures
12:00 13:00 Lunch, like always.
13:00 15:00 Boring lectures...
15:30 17:45 Reading
4
10:00 12:00 Lectures
12:00 13:00 Lunch, just lunch.
13:00 15:00 Lectures, lectures... oh, no!
16:45 17:45 Reading (to be or not to be?)
4
10:00 12:00 Lectures, as everyday.
12:00 13:00 Lunch, again!!!
13:00 15:00 Lectures, more lectures!
15:30 17:15 Reading (I love reading, but should I schedule it?)
1
12:00 13:00 I love lunch! Have you ever noticed it? :)
Sample Output
Day #1: the longest nap starts at 15:00 and will last for 30 minutes.
Day #2: the longest nap starts at 15:00 and will last for 1 hours and 45 minutes.
Day #3: the longest nap starts at 17:15 and will last for 45 minutes.
Day #4: the longest nap starts at 13:00 and will last for 5 hours and 0 minutes.
17
Problem : CDVII
UVa ID: 10138, Popularity: C. Success rate: low Level: 2
Roman roads are famous for their longevity and sound engineering. Unfortunately, sound
engineering does not come cheap, and a number of neo-Caesars have decided to recover the
costs through automated tolling. A particular toll highway, the CDVII, has a fare structure that
works as follows: travel on the road costs a certain amount per km travelled, depending on the
time of day when the travel begins. Cameras at every entrance and every exit capture the
license numbers of all cars entering and leaving. Every calendar month, a bill is sent to the
registered owner for each km travelled (at a rate determined by the time of day), plus one
dollar per trip, plus a two dollar account charge. Your job is to prepare the bill for one month,
given a set of license plate photos.
Input
The input begins with a single positive integer on a line by itself indicating the number of
the cases following, each of them as described below. This line is followed by a blank line,
and there is also a blank line between two consecutive inputs.
Standard input has two parts: the fare structure, and the license photos. The fare structure
consists of a line with 24 non-negative integers denoting the toll (cents/km) from 00:00 00:59, the toll from 01:00 - 00:59, and so on for each hour in the day. Each photo record
consists of the license number of the vehicle (up to 20 alphanumeric characters), the time and
date (mm:dd:hh:mm), the word "enter" or "exit", and the location of the entrance or exit (in
km from one end of the highway). All dates will be within a single month. Each "enter"
record is paired with the chronologically next record for the same vehicle provided it is an
"exit" record. "enter" records that are not paired with an "exit" record are ignored, as are
"exit" records not paired with an "enter" record. You may assume that no two records for the
same vehicle have the same time. Times are recorded using a 24-hour clock. There are not
18
more than 1000 photo records.
Output
For each test case, the output must follow the description below. The outputs of
two consecutive cases will be separated by a blank line.
Print a line for each vehicle indicating the license number, and the total bill, in
alphabetical order by license number. Vehicles that don't use the highway shouldn't
be listed.
Sample Input
1
10 10 10 10 10 10 20 20 20 15 15 15 15 15 15 15 20 30 20 15 15 10 10 10
ABCD123 01:01:06:01 enter 17
765DEF 01:01:07:00 exit 95
ABCD123 01:01:08:03 exit 95
765DEF 01:01:05:59 enter 17
Sample Input
765DEF $10.80
ABCD123 $18.60
19
Problem : ShellSort
UVa ID: 10152, Popularity: B. Success rate: average Level: 2
The Problem
King Yertle wishes to rearrange his turtle throne to place his highest-ranking nobles and
closest advisors nearer to the top. A single operation is available to change the order of the
turtles in the stack: a turtle can crawl out of its position in the stack and climb up over the
other turtles to sit on the top.
Given an original ordering of a turtle stack and a required ordering for the same turtle
stack, your job is to determine a minimal sequence of operations that rearranges the original
stack into the required stack.
The first line of the input consists of a single integer K giving the number of test cases.
Each test case consist on an integer n giving the number of turtles in the stack. The next n
lines specify the original ordering of the turtle stack. Each of the lines contains the name of a
turtle, starting with the turtle on the top of the stack and working down to the turtle at the
bottom of the stack. Turtles have unique names, each of which is a string of no more than
eighty characters drawn from a character set consisting of the alphanumeric characters, the
space character and the period (`.'). The next n lines in the input gives the desired ordering of
the stack, once again by naming turtles from top to bottom. Each test case consists of exactly
2n+1 lines in total. The number of turtles (n) will be less than or equal to two hundred.
For each test case, the output consists of a sequence of turtle names, one per line,
indicating the order in which turtles are to leave their positions in the stack and crawl to the
top. This sequence of operations should transform the original stack into the required stack
and should be as short as possible. If more than one solution of shortest length is possible, any
of the solutions may be reported. Print a blank line after each test case.
20
Sample Input
2
3
Yertle
Duke of Earl
Sir Lancelot
Duke of Earl
Yertle
Sir Lancelot
9
Yertle
Duke of Earl
Sir Lancelot
Elizabeth Windsor
Michael Eisner
Richard M. Nixon
Mr. Rogers
Ford Perfect
Mack
Yertle
Richard M. Nixon
Sir Lancelot
Duke of Earl
Elizabeth Windsor
Michael Eisner
Mr. Rogers
Ford Perfect
Mack
21
Sample Output
Duke of Earl
Sir Lancelot
Richard M. Nixon
Yertle
22