Small trick, more STL, Prime algorithm

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Small trick, more STL,Prime algorithm

• Small trick for your coding
• STL Powerful C tools
• Prime numbers algorithm

2
Plan

• Some simple tricks
• More STL vector, set, map, queue,
• Iterator
• Compare function for STL
• Prime numbers algorithm

3
Programming style

• Short variable names are usually okay
• Quote from Issacs notes
• With proper indentation for every
• Your partner may read your code when debugging
• For eye-ball debug

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Coding

• Coding speed is very important
• The program only need to be fast enough for
  judge to accept it. Dont over-optimize.
• The operation of the program should not over 109

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Array

• Always give more space to the array
• If you think the array will store 100 elements,
  please set the array size to be 105.
• To avoid invalid memory access.
• Use int a100 instead of inta new100
• To avoid memory management
• Unless you are the expert in memory management
• Just for ACM, you may deduct mark if you apply it
  in assignment p

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Input

• To detect end of file,
• while (cin gtgt in)
• while (scanf(d,n)!EOF)
• To detect zero terminate,
• while (cin gtgt in, in)
• To read line,
• while (getline(cin,str))
• To ignore white space,
• cin gtgt ws

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Floating point

• Handle precision error
• Assume error not more then 1e-8
• const double e 1e-8
• check a equal to b
• fabs(a-b) lt e
• check a less than or equal to b
• a lt b fabs(a-b) lt e

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Dummy element

• Add one dummy element at the front or back of an
  array may help your coding easier
• Handle the special case

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Testing you program

• Make use of command promote
• In Windows
• ..gt ExecuteFile lt Input_File gt Output_File
• Eg. C\gt 100.exe lt 100.txt gt output.txt
• In Linux
• ./ExecuteFile lt Input_File gt Output_File
• Eg. ./100 lt 100.txt gt output.txt

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Structure
struct st int i // member variable string
s int arr10 st()s(testing) // if you
have other constructer, // you should
add this line st(int a, string b)i(a),s(b) //
the constructor you want memset(arr,0,sizeof(a
rr)) bool operatorlt(const st ss) //
will be very useful return i lt ss.i i
ss.i s lt ss.s
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Structure
void sortArr() // member function
sort(arr,arrsizeof(arr)/sizeof(int))
int main() st temp1 st
temp2(10,AAA) temp1.sortArr() // can sort
arr cout ltlt temp1.s ltlt ltlt temp2.s ltlt endl
// testing AAA
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STL include
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STL include
If you are not sure which library you should
include, please include all related library.
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STL vector and deque

• Useful member functions
• push_back add an element to the back
• pop_back remove the last element
• clear clear the container (erase all element)
• size return the size of the container
• erase delete one element or a range of element
• Difference between vector and deque
• vector is more efficient
• deque have push_front and pop_front, but vector
  doesnt

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STL set and multiset

• All elements inside set and multiset are already
  sorted
• Useful member function
• insert insert an element to set . O(log n)
• find return the iterator point to element x
• if (s.find(x) ! s.end()) / s has x /
• size return the size of the container
• clear clear the container (delete all element)
• begin, end return the begin/end iterator

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STL set and multiset

• Difference between set and multiset
• set will eliminate element that already inside
  that set
• multiset will not
• The element must be comparable
• bool operatorlt(const type t) const
• Usage
• Find all of distinct elements
• Check the element is appeared before
• Sort all elements in every step (every insert
  operation)

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STL queue and priority_queue

• queue first in first out
• priority_queue the largest element always on
  top
• Useful member function
• push insert an element to queue
• front() / top() return the first element of the
  queue / priority_queue
• pop remove the first element
• size return the size of the queue
• empty return (size() 0)
• Reset the queue
• q queuelttypegt() // assume we want to clear
  q

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STL queue and priority_queue

• Difference between queue and priority_queue

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STL map

• Map one type to another type
• Useful member functions
• find return the iterator point to index x
• if (m.find(x)m.end()) mx y // not found x
• clear clear the container (delete all
  index/element)
• size return the number of index of the map
• The indexs type must be comparable
• bool operatorlt(const type t) const

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STL map

• Usage
• Mapping between two types using O(log n)
• Just like a hash table
• Sometimes you need mapltint,intgt
• If the problem given a graph have at most 100
  node,
• the id of the every node is lt 231 1
• Use map to help you give the new id (1n) to
  every node .
• Limit the memory size
• Just like the above example, we use O(n) memory
  to store the node instead of 231-1

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STL iterator

• Just like a pointer
• Basically, nearly (every?) iterator has following
  operator
• , , --
• Every STLs .begin() and .end() are iterators
• Which are constant iterators
• Dont apply or -- to it
• Random access iterator vector and deques
  iterator
• Very similar to pointer
• Can use , , iter5 // iter is a random access
  iterator
• V.erase(V.begin() 3) // assume V is a vector

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STL Compare function

• Why we need compare function
• For sorting using STL sort
• For using some STLs structure map,
  priority_queue, set
• For binary search using STL lower_bound,
  upper_bound
• For your own convenient P

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STL Compare function

• We only need less than compare function in most
  cases
• There are few way to write it
• See compare_ex.cpp

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Prime numbers algorithm

• Basic algorithm good for individual query
• Testing if a number n is prime or not
• Assuming that you already have a array of primes
• int upper (int)sqrt((double)n)
• for (i 0 primeiltupper i)
• if (nprimei0) return false
• return true

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Prime numbers algorithm

• How about asking a range of prime number?
• Lets say all prime numbers from 1 to 1000000???
• We can use more efficient algorithm

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Prime numbers algorithm

• Generate 1100 prime number

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Prime numbers algorithm

• First step assume all element multiply by 2 is
  not prime

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Prime numbers algorithm

• Second step
• For every odd number gt 3 and lt sqrt(n)
• If P is prime // assume current number is P
• Eliminate all element which is P(2k1) where k
  1,2,

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Prime numbers algorithm

• P 3, Since 3 is not eliminated, so 3 is prime

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Prime numbers algorithm

• P 5, Since 5 is not eliminated, so 5 is prime

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Prime numbers algorithm

• P 7, Since 7 is not eliminated, so 7 is prime

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Prime numbers algorithm

• P 9, Since 9 is eliminated, so 9 is not a prime.

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Prime numbers algorithm

• bool nonprime1000006 // in global, all
  element already set to 0 (false)
• int main()
• int n 1000000
• int upper (int)sqrt((double)n)
• for (int i 3 i lt upper i2)
• if (!nonprimei)
• int offset i2
• for (int j i3 j lt n joffset)
• nonprimej true

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Prime numbers algorithm

• How about finding all prime factors for
  11000000??
• In previous slides, we use bool to mark the
  primes
• Actually we can use int instead of bool
• Initial all value to 0
• When eliminate, set that element to the current
  prime number

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Prime numbers algorithm
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Prime numbers algorithm

• Since we assume 2 is eliminated, we should have
  special handle for 2
• void print_factor(int n)
• if (n lt 1) return
• while (n 2 0)
• cout ltlt "2 "
• n/2
• if (n 1) return
• while (nonprimen)
• cout ltlt nonprimen ltlt ' '
• n/nonprimen
• cout ltlt n

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Prime numbers algorithm

• int nonprime1000006 // in global, all element
  already set to 0
• int main()
• int n 1000000
• int upper (int)sqrt((double)n)
• for (int i 3 i lt upper i2)
• if (!nonprimei)
• int offset i2
• for (int j i3 j lt n joffset)
• nonprimej i

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Practice

• STL
• 136,146,156,482,484,10098,10107,10282,10896,10954
• Prime
• 884,897,10006,10015(Joseph Number),
  10235,10699,10738,10789,10856