f
/
project-euler
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

C++ solutions 74, 75, 76, 91, 94, 206, 233

This commit is contained in:
User 2019-07-30 16:54:36 +02:00
parent b81b9e6e5e
commit 8e6b92ea9d
7 changed files with 387 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

68
a074.cpp Normal file
View File

@ -0,0 +1,68 @@
#include <iostream>
#include <cmath>
#include <chrono>
using namespace std;
int factorials[10] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
int cycleLength[2200000];
inline int digitFactorial(int a)
{
int sum = 0;
while (a > 0)
{
sum += factorials[a % 10];
a /= 10;
}
return sum;
}
int cycle(int n, int depth)
{
if (depth > 1000)
cout << "{ \"depth\": " << depth << ", \"n\": " << n << " }" << endl;
int cl = cycleLength[n];
if (cl < 0)
return -cl;
if (cl == 0)
{
cl = cycle(digitFactorial(n), depth+1);
cycleLength[n] = cl;
}
return cl+1;
}
int main()
{
auto start = chrono::system_clock::now();
cycleLength[0] = -1;
cycleLength[1] = -1;
cycleLength[2] = -1;
cycleLength[169] = -3;
cycleLength[145] = -1;
cycleLength[871] = -2;
cycleLength[872] = -2;
cycleLength[1454] = -3;
cycleLength[40585] = -3;
cycleLength[45361] = -2;
cycleLength[45362] = -2;
cycleLength[363601] = -3;
cout << "cycle length 69: " << cycle(69,0) << endl;
int sixties = 0;
for (int n = 0; n < 1000000; n++)
{
if (cycle(n,0) == 60)
sixties++;
}
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end - start;
cout << "cycles took: " << elapsed_seconds.count() << endl;
cout << "numbers with 60 cycles: " << sixties;
return 0;
}

75
a075.cpp Normal file
View File

@ -0,0 +1,75 @@
#include <iostream>
#include <cmath>
#include <chrono>
#define lmax 1500000
using namespace std;
typedef unsigned char byte;
inline int isqrt(int n) {
return (int)sqrt((float)n);
}
template<class T>
inline T gcd(T a, T b) {
while(b) {
auto t = a % b;
a = b;
b = t;
}
return a;
}
int main() {
byte arr[lmax+1];
auto start = chrono::system_clock::now();
for (int i = 0; i <= lmax; i++)
arr[i] = 0;
for (int length = 12; length <= lmax; length += 2)
for (int m = isqrt(length)/2+1; m <= isqrt(length/2); m++) {
if (length % (2*m) == 0)
{
int n = length / (2*m) - m;
if (n>0 && n < m && n%2!= m%2 && gcd(m,n) == 1)
arr[length]++;
}
}
auto middle = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = middle-start;
cout << "generating primitives took: " << elapsed_seconds.count() << endl;
for (int length = lmax; length >= 0; length--) {
int sqrtlen = isqrt(length);
for (int prev_length = 2; prev_length <= sqrtlen; prev_length++)
if (length % prev_length == 0) {
arr[length] += arr[prev_length];
arr[length] += arr[length/prev_length];
if (arr[length] > 1)
break;
}
}
auto end = std::chrono::system_clock::now();
elapsed_seconds = end-middle;
cout << "adding multiples took: " << elapsed_seconds.count() << endl;
int singles = 0;
for (int i = 0; i <= lmax; i++)
if (arr[i] == 1)
singles++;
for (int i = 0; i <= 60; i++)
if (arr[i] == 1)
cout << i << ", ";
cout << endl;
cout << singles;
return 0;
}

35
a076.cpp Normal file
View File

@ -0,0 +1,35 @@
#include <iostream>
#include <cmath>
#include <chrono>
using namespace std;
int main() {
int m[101][101];
auto start = chrono::high_resolution_clock::now();
for (int n = 1; n <= 100; n++)
m[1][n] = 1;
for (int t = 1; t <= 100; t++)
m[t][1] = 1;
for (int t = 2; t <= 100; t++)
for (int n = 2; n <= 100; n++) {
if (n > t)
m[t][n] = m[t][n-1];
if (n == t)
m[t][n] = m[t][n-1]+1;
if (n < t)
m[t][n] = m[t][n-1]+m[t-n][n];
}
auto end = std::chrono::high_resolution_clock::now();
std::chrono::duration<double> elapsed_seconds = end-start;
cout << "problem took: " << elapsed_seconds.count() << endl;
cout << m[100][99];
return 0;
}

43
a091.cpp Normal file
View File

@ -0,0 +1,43 @@
#include <iostream>
#include <cmath>
#include <chrono>
#define sq 3
using namespace std;
typedef unsigned char byte;
template<class T>
inline T gcd(T a, T b) {
while(b) {
auto t = a % b;
a = b;
b = t;
}
return a;
}
int main() {
auto start = chrono::system_clock::now();
//triangles for which either (x1,y1) == (0,0)
//or x1==0,y1!=0 or x1!=0,y1==0
long count = 3*sq*sq;
for (int vx = 1; vx <= sq; vx++)
for (int vy = 1; vy <= sq; vy++) {
int dx = -vy/gcd(vx,vy);
int dy = vx/gcd(vx,vy);
for (int d = 1; vx+dx*d >= 0 && vy+dy*d <= sq; d++)
count++;
for (int d = -1; vx+dx*d <= sq && vy+dy*d >= 0; d--)
count++;
}
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end-start;
cout << "solving took: " << elapsed_seconds.count() << endl;
cout << "triangles: " << count;
return 0;
}

46
a094.cpp Normal file
View File

@ -0,0 +1,46 @@
#include <iostream>
#include <cmath>
#include <chrono>
#define pmax 1000000000ll
using namespace std;
typedef long long var;
template<typename T> inline bool isSquare(T val) {
T root = (T)sqrt((double)val);
return root*root == val;
}
int main() {
auto start = chrono::system_clock::now();
var perimeterSum = 0;
var count = 0;
for (var equalSide = 3; equalSide <= pmax/3+1; equalSide += 2) {
var otherSide = equalSide-1;
var s = equalSide + otherSide/2;
if (isSquare(s*(s-otherSide)) && 2*s <= pmax) {
perimeterSum += 2*s;
count++;
cout << "(" << equalSide << "," << equalSide << "," << otherSide << ")" << endl;
}
otherSide = equalSide+1;
s = equalSide + otherSide/2;
if (isSquare(s*(s-otherSide)) && 2*s <= pmax) {
perimeterSum += 2*s;
count++;
cout << "(" << equalSide << "," << equalSide << "," << otherSide << ")" << endl;
}
}
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end-start;
cout << "solving took: " << elapsed_seconds.count() << endl;
cout << "perimeter count: " << count << endl;
cout << "perimeter sum: " << perimeterSum;
return 0;
}

33
a206.cpp Normal file
View File

@ -0,0 +1,33 @@
#include <iostream>
#include <cmath>
#include <chrono>
#define lmax 1500000
using namespace std;
typedef unsigned char byte;
inline int isqrt(int n) {
return (int)sqrt((float)n);
}
inline uint64_t isqrt(uint64_t n) {
return (uint64_t)sqrt((double)n);
}
int main() {
auto start = chrono::system_clock::now();
for (uint64_t i = isqrt(10203040506070809ull); i <= isqrt(19293949596979899ull); i++) {
uint64_t square = i*i;
if (square % 10ull == 9 && (square/100ull) % 10ull == 8 && (square/10000ull) % 10ull == 7 && (square/1000000ull) % 10ull == 6 && (square/100000000ull) % 10ull == 5 && (square/10000000000ull) % 10ull == 4 && (square/1000000000000ull) % 10ull == 3 && (square/100000000000000ull) % 10ull == 2 && (square/10000000000000000ull) == 1)
cout << "found " << i << " ^2 = " << square << endl;
}
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end-start;
cout << "iterating took: " << elapsed_seconds.count() << endl;
return 0;
}

87
a233.cpp Normal file
View File

@ -0,0 +1,87 @@
#include <iostream>
#include <vector>
#include <cmath>
#include <chrono>
typedef long long int Int;
using namespace std;
vector<Int> primes;
void generatePrimes() {
primes.push_back(2);
primes.push_back(3);
for (int i = 5; i < 1000000; i += 2) {
bool isPrime = true;
for (auto p : primes) {
if ((int)p*(int)p > i)
break;
if (i % (int)p == 0) {
isPrime = false;
break;
}
}
if (isPrime)
primes.push_back((Int)i);
}
}
bool check420LatticePoints(Int n) {
int latticePoints = 1;
for (auto p : primes) {
if (p*p > n)
p = n;
int multiplicity = 0;
while (n % p == 0) {
multiplicity++;
n /= p;
}
if (multiplicity > 0 && p % 4 == 1) {
latticePoints *= 2*multiplicity+1;
if (latticePoints == 105)
return true;
if (105 % latticePoints != 0)
return false;
}
if (n==1)
return false;
}
return false;
}
int main() {
Int max;
cout << "N = ";
cin >> max;
auto start = chrono::system_clock::now();
generatePrimes();
auto middle = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = middle-start;
cout << "generating primes took: " << elapsed_seconds.count() << endl;
Int count = 0, sum = 0;
for (Int n = 10; n < max; n++) {
if (check420LatticePoints(n)) {
sum += n;
count++;
}
}
auto end = std::chrono::system_clock::now();
elapsed_seconds = end-middle;
cout << "finding 420s took: " << elapsed_seconds.count() << endl << endl;
cout << "sum: " << sum << ", total: " << count;
return 0;
}