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Added Fast Power in Number Theory #76

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merged 11 commits into from
Jul 20, 2017
Merged

Added Fast Power in Number Theory #76

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860bd1d
Added Fast Power
ahmad307 Jul 5, 2017
546bc5b
Updated fast Power
ahmad307 Jul 6, 2017
348ad07
Edited fastPower.cpp
ahmad307 Jul 7, 2017
60b4356
Added fastPower test file
ahmad307 Jul 7, 2017
e0d5338
Merge branch 'master' of https://github.com/ahmad307/Algos
ahmad307 Jul 7, 2017
98fd22b
Issues Fixed
ahmad307 Jul 8, 2017
f61dcfd
Renamed fastPower.test.cpp to FastPower.test.cpp
ahmad307 Jul 8, 2017
ea182d5
Duplicate removed
ahmad307 Jul 8, 2017
7bee107
Updated FastPower.cpp & FastPower.test.cpp
ahmad307 Jul 19, 2017
e90a43e
Updated FastPower.cpp
ahmad307 Jul 20, 2017
c4255a0
Updated FastPower.test.cpp
ahmad307 Jul 20, 2017
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21 changes: 16 additions & 5 deletions NumberTheory/FastPower.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -16,23 +16,24 @@

*/
#include <iostream>
#include <cmath>

using namespace std;
typedef unsigned long long ull;

//Function that returns base raised to the exponent
ull fast_power (ull base,ull exponent)
ull fast_power (ull base,ull exponent,ull mod)
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Give mod the default value ULLONG_MAX so that it doesn't need to be passed to the function if modulus of the result is not required.

{
if (exponent==0) return 1;

if (exponent%2==1) //If the power is odd
{
return fast_power(base,exponent-1) * base;
return (fast_power(base,exponent-1,mod) * base)%mod;
}
else //If the power is even
{
base = fast_power(base,exponent/2);
return (base*base);
base = fast_power(base,exponent/2,mod);
return (base*base)%mod;
}
}

Expand All @@ -52,7 +53,17 @@ int main()
}
else
{
cout<<endl<<fast_power(base,exponent)<<endl;
int digits_required = floor(exponent * log10(base)) + 1;

if (digits_required > 19)
{
cout<<endl<<fast_power(base,exponent,1000000007)<<endl;
cout<<"*The output is modulo 10^9+7"<<endl;
}
else
{
cout<<endl<<fast_power(base,exponent,ULLONG_MAX)<<endl;
}
}

return 0;
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20 changes: 10 additions & 10 deletions Test/NumberTheory/FastPower.test.cpp
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Expand Up @@ -7,22 +7,22 @@

TEST_CASE("Base cases", "[fast_power]") {
//REQUIRE(fast_power(0,0) == undefined);
REQUIRE(fast_power(0,1) == 0);
REQUIRE(fast_power(1,0) == 1);
REQUIRE(fast_power(1,1) == 1);
REQUIRE(fast_power(0,1,ULLONG_MAX) == 0);
REQUIRE(fast_power(1,0,ULLONG_MAX) == 1);
REQUIRE(fast_power(1,1,ULLONG_MAX) == 1);
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ULLONG_MAX should be removed from the tests too. You missed this.

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Sure! Sorry for this.

}

TEST_CASE("Normal cases", "[fast_power]") {
REQUIRE(fast_power(2,2) == 4);
REQUIRE(fast_power(2,4) == 16);
REQUIRE(fast_power(3,4) == 81);
REQUIRE(fast_power(7,9) == 40353607);
REQUIRE(fast_power(15,10) == 576650390625);
REQUIRE(fast_power(2,2,ULLONG_MAX) == 4);
REQUIRE(fast_power(2,4,ULLONG_MAX) == 16);
REQUIRE(fast_power(3,4,ULLONG_MAX) == 81);
REQUIRE(fast_power(7,9,ULLONG_MAX) == 40353607);
REQUIRE(fast_power(15,10,ULLONG_MAX) == 576650390625);
}

TEST_CASE("Overflow cases", "[fast_power]") {
REQUIRE(fast_power(2,100) == 68719476736);
REQUIRE(fast_power(10,99) == 4440381706574496940U);
REQUIRE(fast_power(2,100,1000000007) == 976371285);
REQUIRE(fast_power(10,99,1000000007) == 22673271);
}

#undef FAST_POWER_TEST