CodingKnight's blog

By CodingKnight, 5 weeks ago, In English,

The following are C++11 classes huge_unsigned and binomial_coefficient for computing huge Binomial coefficients C( n, k ), where n and k are positive integers.

The class implements the iterative multiplicative formula:

def binomialCoefficient(n, k):
    if k < 0 or k > n:
        return 0
    if k == 0 or k == n:
        return 1
    k = min(k, n - k) # take advantage of symmetry
    c = 1
    for i in range(k):
        c = c * (n - i) / (i + 1)
    return c

reported in Binomial coefficient without overflow, and without using the modulus arithmetic operator. Items of the STL base class vector< uint32_t > are used to store the successive digits of a base-4,294,967,296 representation of C( n, k ). C( 32000, 16000 ) has been computed using 1000 huge_unsigned digits in 1.873 sec. on Intel Core i3 processor with 3 GB RAM running at 2.4 GHz. Comments and votes (like or do not like) are thankfully and gratefully appreciated.


#include <bits/stdc++.h> using namespace std; struct huge_unsigned: public vector< uint32_t > { uint64_t carry; huge_unsigned() : carry( 0 ) {} huge_unsigned& operator *= ( uint32_t i ) { register uint64_t p, q, x = i; for( register size_t k = 0, l = size(); k < l; at( k++ ) = q, carry = ( q >> 32 ) ) { p = at( k ), q = p * x; if ( carry != 0 ) q += carry; } if ( carry != 0 ) push_back( carry ), carry = 0; return *this; } huge_unsigned& operator /= ( uint32_t j ) { register uint64_t p, q, x = j; for ( register size_t k = size(); k > 0; at( k ) = q, carry = p - q * x ) p = ( carry << 32 ) | at( --k ), q = p / x; while( size() > 0 && back() == 0 ) pop_back(); return *this; } void write() { for( register size_t k = size() - 1; k > 0; k-- ) printf( "%u ", at( k ) ); printf( "%u", at( 0 ) ); } }; struct binomial_coefficient: public huge_unsigned { binomial_coefficient( uint32_t n, uint32_t k ) { if ( k > n ) { push_back( 0 ); return; } register uint32_t p = n - k, q = min( k, p ); if ( q == 0 ) { push_back( 1 ); return; } push_back( n-- ); for( register uint32_t i = 2; i <= q; *this /= i++ ) *this *= n--; } }; int main() // A sample test program { uint32_t n, k; scanf( "%u %u", &n, &k ); clock_t start_time = clock(); binomial_coefficient c( n, k ); clock_t end_time = clock(); double elapsed_time = ( end_time - start_time ) * 1000.0 / CLOCKS_PER_SEC; printf( "Computed c( %u, %u ) = ", n, k ), c.write(), putchar( '\n' ), printf( "Using %u huge unsigned digits(s)\n", c.size() ), printf( "Elapsed time = %f msec.\n", elapsed_time ); }
 
 
 
 
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