Question

use the code and change it

Task

This assignment is very straight-forward and quick to do since BigInteger supports integer operations just as long does!

1. Start by downloading the code below (scroll down). (Certainly compile and run the code to see what it does.)
2. Add "import java.math.BigInteger;" to the top of the file.
3. Replace all "Long" types with "BigInteger" in the entire file. (This works because long was intentionally only used for computed values.)
4. Replace all "long" types with "BigInteger" in the entire file. (This works because long was intentionally only used for computed values.)
5. Delete all occurrences of ".longValue()" in the value. (Java collections must store objects. Long is a Java-provided class so long values can be stored as objects.)
6. Replace the two occurrences of 1L passed in to fib_cache.add() with BigInteger.ONE.
7. Delete the if statements throwing exceptions in fib() and fact().
8. Delete the "throws AirthmeticException" clauses on the fib() and fact() functions.
9. Delete the try..catch blocks in main() --but leave the code that is inside the try blocks.
10. Replace "valueNew = value1 + value2; // fib(i)" with "valueNew = value1.add(value2); // fib(i)". (BigInteger must use its add() method to add values.)
11. Replace "valueNew = prev*i; // fact(i)" with "valueNew = prev.multiply(BigInteger.valueOf(i)); // fact(i)". (BigInteger must use its multiply() method to multiply values. Note that to convert an int to a BigIInteger one must use the valueOf() static function in BigInteger.)

After these edits, the code will produce the output shown in Sample Output. Notice that the code now shows all iterations of the two for loops. Prof. X' provided code stopped when the result would exceed the maximum value of long.

Sample Output

The following is what will be output from the completed program:

fib(0) = 1
fib(1) = 1
fib(2) = 2
fib(3) = 3
fib(4) = 5
fib(5) = 8
fib(6) = 13
fib(7) = 21
fib(8) = 34
fib(9) = 55
fib(10) = 89
fib(11) = 144
fib(12) = 233
fib(13) = 377
fib(14) = 610
fib(15) = 987
fib(16) = 1597
fib(17) = 2584
fib(18) = 4181
fib(19) = 6765
fib(20) = 10946
fib(21) = 17711
fib(22) = 28657
fib(23) = 46368
fib(24) = 75025
fib(25) = 121393
fib(26) = 196418
fib(27) = 317811
fib(28) = 514229
fib(29) = 832040
fib(30) = 1346269
fib(31) = 2178309
fib(32) = 3524578
fib(33) = 5702887
fib(34) = 9227465
fib(35) = 14930352
fib(36) = 24157817
fib(37) = 39088169
fib(38) = 63245986
fib(39) = 102334155
fib(40) = 165580141
fib(41) = 267914296
fib(42) = 433494437
fib(43) = 701408733
fib(44) = 1134903170
fib(45) = 1836311903
fib(46) = 2971215073
fib(47) = 4807526976
fib(48) = 7778742049
fib(49) = 12586269025
fib(50) = 20365011074
fib(51) = 32951280099
fib(52) = 53316291173
fib(53) = 86267571272
fib(54) = 139583862445
fib(55) = 225851433717
fib(56) = 365435296162
fib(57) = 591286729879
fib(58) = 956722026041
fib(59) = 1548008755920
fib(60) = 2504730781961
fib(61) = 4052739537881
fib(62) = 6557470319842
fib(63) = 10610209857723
fib(64) = 17167680177565
fib(65) = 27777890035288
fib(66) = 44945570212853
fib(67) = 72723460248141
fib(68) = 117669030460994
fib(69) = 190392490709135
fib(70) = 308061521170129
fib(71) = 498454011879264
fib(72) = 806515533049393
fib(73) = 1304969544928657
fib(74) = 2111485077978050
fib(75) = 3416454622906707
fib(76) = 5527939700884757
fib(77) = 8944394323791464
fib(78) = 14472334024676221
fib(79) = 23416728348467685
fib(80) = 37889062373143906
fib(81) = 61305790721611591
fib(82) = 99194853094755497
fib(83) = 160500643816367088
fib(84) = 259695496911122585
fib(85) = 420196140727489673
fib(86) = 679891637638612258
fib(87) = 1100087778366101931
fib(88) = 1779979416004714189
fib(89) = 2880067194370816120
fib(90) = 4660046610375530309
fib(91) = 7540113804746346429
fib(92) = 12200160415121876738
fib(93) = 19740274219868223167
fib(94) = 31940434634990099905
fib(95) = 51680708854858323072
fib(96) = 83621143489848422977
fib(97) = 135301852344706746049
fib(98) = 218922995834555169026
fib(99) = 354224848179261915075
fib(100) = 573147844013817084101
fib(101) = 927372692193078999176
fib(102) = 1500520536206896083277
fib(103) = 2427893228399975082453
fib(104) = 3928413764606871165730
fib(105) = 6356306993006846248183
fib(106) = 10284720757613717413913
fib(107) = 16641027750620563662096
fib(108) = 26925748508234281076009
fib(109) = 43566776258854844738105
fact(0) = 1
fact(1) = 1
fact(2) = 2
fact(3) = 6
fact(4) = 24
fact(5) = 120
fact(6) = 720
fact(7) = 5040
fact(8) = 40320
fact(9) = 362880
fact(10) = 3628800
fact(11) = 39916800
fact(12) = 479001600
fact(13) = 6227020800
fact(14) = 87178291200
fact(15) = 1307674368000
fact(16) = 20922789888000
fact(17) = 355687428096000
fact(18) = 6402373705728000
fact(19) = 121645100408832000
fact(20) = 2432902008176640000
fact(21) = 51090942171709440000
fact(22) = 1124000727777607680000
fact(23) = 25852016738884976640000
fact(24) = 620448401733239439360000
fact(25) = 15511210043330985984000000
fact(26) = 403291461126605635584000000
fact(27) = 10888869450418352160768000000
fact(28) = 304888344611713860501504000000
fact(29) = 8841761993739701954543616000000
fact(30) = 265252859812191058636308480000000
fact(31) = 8222838654177922817725562880000000
fact(32) = 263130836933693530167218012160000000
fact(33) = 8683317618811886495518194401280000000
fact(34) = 295232799039604140847618609643520000000
fact(35) = 10333147966386144929666651337523200000000
fact(36) = 371993326789901217467999448150835200000000
fact(37) = 13763753091226345046315979581580902400000000
fact(38) = 523022617466601111760007224100074291200000000
fact(39) = 20397882081197443358640281739902897356800000000

import java.util.ArrayList;

public class BigFibFact
{
private static ArrayList<Long> fib_cache = new ArrayList<Long>();
private static ArrayList<Long> fact_cache = new ArrayList<Long>();

public static long fib(int N) throws ArithmeticException
{
int size = fib_cache.size();

if (N < size)
return fib_cache.get(N).longValue(); // return previously computed answer
else if (fib_cache.isEmpty())
{
// ensure fib_cache contains "base case" entries...
fib_cache.add(0, 1L);
fib_cache.add(1, 1L);
size = fib_cache.size();
}

// Ensure that N >= size...
if (N < size)
return fib_cache.get(N).longValue(); // return previously computed answer

// It is safe to start at size-2 since base case values are present...
int i = size-2;

// Add the first two previously computed values...
long value1 = fib_cache.get(i++).longValue();
long value2 = fib_cache.get(i++).longValue();
long valueNew;

// and then compute fib(i) until i == N...
do
{
if ((Long.MAX_VALUE-value1) < value2)
throw new ArithmeticException("fib("+i+") is too large for long.");

valueNew = value1 + value2; // fib(i)
fib_cache.add(i++, valueNew); // store fib(i) result

// Adjust last two values...
value1 = value2;
value2 = valueNew;
}
while (i <= N);
return valueNew;
}

public static long fact(int N) throws ArithmeticException
{
int size = fact_cache.size();

if (N < size)
return fact_cache.get(N).longValue(); // return previously computed answer
else if (fact_cache.isEmpty())
{
// ensure fact_cache contains "base case" entry...
fact_cache.add(0, 1L);
size = fact_cache.size();
}

// Ensure that N >= size...
if (N < size)
return fact_cache.get(N).longValue(); // return previously computed answer

// It is safe to start at size-1 since base case value is present...
int i = size-1;

// Add the first two previously computed values...
long prev = fact_cache.get(i++).longValue();
long valueNew;

// and then compute fib(i) until i == N...
do
{
if ((Long.MAX_VALUE - prev) / i < prev)
throw new ArithmeticException("fact("+i+") is too large for long.");

valueNew = prev*i; // fact(i)
fact_cache.add(i++, valueNew); // store fact(i) result

// Adjust prev...
prev = valueNew;
}
while (i <= N);
return valueNew;
}

public static final void main(String[] args)
{
try
{
for (int i=0; i != 110; ++i)
System.out.println("fib("+i+") = "+fib(i));
}
catch (ArithmeticException e)
{
}

try
{
for (int i=0; i != 40; ++i)
System.out.println("fact("+i+") = "+fact(i));
}
catch (ArithmeticException e)
{
}
}
}

Answer 1

CODE:

import java.math.BigInteger;

public class Exercise
{
   // Returns n-th Fibonacci number
   static BigInteger fib(int n)
   {
       BigInteger value1 = BigInteger.valueOf(1);
       BigInteger value2 = BigInteger.valueOf(1);
       BigInteger valueNew;
  
       for (int j=0 ; j<n ; j++)
       {
if(j==0)
System.out.println("fib(0) = 1");
else if(j==1)
System.out.println("fib(1) = 1");
else{
valueNew = value1.add(value2);
value1 = value2;
value2 = valueNew;
System.out.println("fib(" + j + ") = " + valueNew);
}
}
return BigInteger.valueOf(0);
   }
  
static BigInteger fact(int N)
{
// Initialize result
BigInteger prev = new BigInteger("1"); // Or BigInteger.ONE
BigInteger valueNew;
// Multiply f with 2, 3, ...N
for (int i = 0; i < N; i++)
{
if(i==0)
System.out.println("fact(0) = 1");
else if(i==1)
System.out.println("fact(1) = 1");
else
{
valueNew = prev.multiply(BigInteger.valueOf(i));
prev = valueNew;
System.out.println("fact(" + i + ") = " + valueNew);
}
}
return BigInteger.valueOf(0);
}

   public static void main(String[] args)
   {
       fib(110);
fact(40);
   }
}

OUTPUT:

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