algorithm - Calculate this factorial term in C++ with basic datatypes -


i solving programming problem, , in end problem boils down calculating following term:

n!/(n1!n2!n3!....nm!) n<50000 (n1+n2+n3...nm)<n

i given final answer fit in 8 byte. using c++. how should calculate this. able come tricks nothing concrete , generalized.

edit: not use external libraries.

edit1 : added conditions , result 64 bit int.

if result guaranteed integer, work factored representation.

by theorem of legendre, can express these factorials sequence of exponents of primes in range (2,n).

by deducting exponents of factorials in denominator in numerator, obtain exponents whole quotient. computation reduce product of primes never overflow 8 bytes.

for example,

25! = 2^22.3^10.5^6.7^3.11^2.13.17.19.23 15! = 2^11.3^6.5^3.7^2.11.13 10! = 2^8.3^4.5^2.7

yields

25!/(15!.10!) = 2^3.5.11.17.19.23 = 3268760

the exponents of, say, 3 found by

25/3 + 25/9 = 10 15/3 + 15/9 = 6 10/3 + 10/9 = 4

Comments

Post a Comment

Popular posts from this blog

c++ - Difference between pre and post decrement in recursive function argument -

i have following sample code used pre-decrement void function(int c) { if(c == 0) { return; } else { cout << "dp" << c << endl; function(--c); cout << c << endl; return; } } this function give output input 4 : dp3 dp2 dp1 dp0 0 1 2 3 but when use post decrement void function(int c) { if(c == 0) { return; } else { cout << "dp" << c << endl; function(c--); cout << c << endl; return; } } output goes in infinite loop dp4 can explain me in detail why happens ? this happens because function(c--) called same value of c , when finishes c decremented. recursively called, hence called same value no chance of return , hit stack overflow error. assume this, int x = 1, y = 0; y = x++ result y == 1 , x == 2. if y = ++x , bot x , y 2.
Read more

php - Nothing but 'run(); ' when browsing to my local project, how do I fix this? -

i added new project. made mistake in projectname.conf file in sites-available apache2, led me reinstalling apache2. after reinstalling , re-enabling projects on every page of every project .. <body> run(); </body> .. i've run composer update, restarted service, restarted pc, checked config files, tried disabling new project. there nothing in error log, , access.log: 127.0.0.1 - - [15/may/2015:01:40:47 +0200] "get / http/1.1" 304 181 "-" "mozilla/5.0 (x11; ubuntu; linux x86_64; rv:38.0) gecko/20100101 firefox/38.0" maybe i'm forgetting apache2 reinstall? don't think did different last time installed it. looks haven't setup php correctly. take @ this great guide , maybe you're forgetting link php config apache2.
Read more

php - How can I echo out this array? -

i don't know how go grabbing data in variable , put foreach loop. class tree{ private $info = array( array('name'=>'jim','state'=>'nu','company'=>'nu','phone'=>array('cell'=>'5615111111','office'=>'5611111111'),'email'=>array('primary'=>'exs@example.com','ex@there.com')), array('name'=>'joe smith','city'=>'phoenix','phone'=>'4805551111','email'=>'jsmith@some_email.com'), array('name'=>'john doe','city'=>'chandler','company'=>'doe co.','email'=>array('jdoe@gmail.com','personal'=>'email@email.com'),'phone'=>'6025550002') ); } if you're inside of class, can access private variable using $this->variablename . example, i...
Read more