Dynamic Programming Issue - Fibonacci Sequence

问题

I was reading this Wikipedia article, and attempting to implement a 'map' based solution in C, where a 'map' is just an int array, initialized to 0.

For some reason it works up to fib(93), then starts outputting strange numbers. If it matter's I'm specifying -std=c99:

#include <stdio.h>
#include <stdlib.h>

// represents a fib num
typedef unsigned long long fib_t;

// the default value of our 'map'
const int FIB_NULL   = 0;

// could get from input, set here for now
const int FIB_MAX    = 100;

// our 'map' for fib nums
static fib_t *fibMap;

// calculate the fib num n
fib_t fib( unsigned int n )
{
    // if this num, n, is not 0 or 1, and is FIB_NULL, then calculate it
    if( n > 1 && FIB_NULL == fibMap[n] )
    {
        fibMap[n] = fib( n-1 ) + fib( n-2 );
    }

    // get it from the map
    return fibMap[n];
}

// used to setup the 'map' for the fibs
static void initFibMap()
{
    // emulate a map
    fibMap = malloc( sizeof(fib_t) * FIB_MAX);

    // initialize it to 'null'
    memset(fibMap, FIB_NULL, sizeof(fib_t) * FIB_MAX);

    // by definition
    fibMap[0] = 0;
    fibMap[1] = 1;
}

int main(int argc, char *argv[]) 
{
    // setup our 'map'
    initFibMap();

    for( unsigned int i=0; i<FIB_MAX; i++ )
    {
        // breaks on 94
        printf("Fib #%d: %llu\n",i, fib(i));
    }
}

Strange output:

// . . .
// . . .
// Fib #90: 2880067194370816120  // good
// Fib #91: 4660046610375530309  // good
// Fib #92: 7540113804746346429  // good
// Fib #93: 12200160415121876738 // good
// Fib #94: 1293530146158671551  // WHAT?
// Fib #95: 13493690561280548289
// Fib #96: 14787220707439219840
// Fib #97: 9834167195010216513
// Fib #98: 6174643828739884737
// Fib #99: 16008811023750101250

回答1:

With such large numbers, you're getting an unsigned integer overflow, which causes a "wrap around" to result in the original result of the operation, modulo 1 << bits, bits being the bit width of the particular integer type. If you want to represent these numbers, you have to use some kind of bignum library, such as the GNU GMP.

回答2:

As number is getting large so integer is getting overflow so "wrap around" is happening so you can use either GNU GMP library or use string to represent numbers just like i did for factorial of large numbers link to http://codepad.org/bkWNV0JC

来源：https://stackoverflow.com/questions/12413294/dynamic-programming-issue-fibonacci-sequence

标签

dynamic-programming

fibonacci

unsigned-long-long-int