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probleme010.cpp
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#include <cstdlib>
#include <iostream>
#include "math.h"
#include <sstream>
#include <fstream>
#include <vector>
#include "bignum.h"
#include <gmp.h>
#include "functions.hpp"
using namespace std;
void Problem10() {
double sum=0, number=1;
while (number<2000000) {
number++;
if (isprime(number))
sum += number;
}
cout << fixed << sum << endl;
}
void Problem11() {
int sum, max=0;
int numbers[400] = { 8,2 , 22,97,38,15,40,75,4,5,7,78,52,12,50,77,91,8
,49 , 49 , 99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62
,81 , 49 , 31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65
,52 , 70 , 95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91
,22 , 31 , 16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80
,24 , 47 , 32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50
,32 , 98 , 81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70
,67 , 26 , 20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21
,24 , 55 , 58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72
,21 , 36 , 23,9,75,76,44,20,45,35,14,61,33,97,34,31,33,95
,78 , 17 , 53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92
,16 , 39 , 5,42,96,35,31,47,55,58,88,24,17,54,24,36,29,85,57
,86 , 56 , 0,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58
,19 , 80 , 81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40
,4, 52 , 8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66
,88 , 36 , 68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69
,4, 42 , 16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36
,20 , 69 , 36 , 41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16
,20 , 73 , 35 , 29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54
,1, 70 , 54 , 71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48 };
for (int i=0; i<395;i++) {
if (i%20 <= 16) {
//right
sum = numbers[i] * numbers[i+1] * numbers[i+2] * numbers[i+3];
if (sum > max) max = sum;
if (i < 339) {
//diagonal right down
sum = numbers[i] * numbers[i+21] * numbers[i+42] * numbers[i+63];
if (sum > max) max = sum;
}
}
if (i<=339) {
// down
sum = numbers[i] * numbers[i+20] * numbers[i+40] * numbers[i+60];
if (sum > max) max = sum;
}
if (i%20 >= 3 && i < 339) {
// diagonal left down
sum = numbers[i] * numbers[i+19] * numbers[i+38] * numbers[i+57];
if (sum > max) max = sum;
}
}
cout << fixed << max << endl;
}
void Problem12() {
int i=1, number=0, divisors = 0;
while (divisors < 500) {
number += i;
i++;
divisors = num_divisors(number);
// if (divisors > 100)
// cout << number << " " << divisors << endl;
}
cout << fixed << number << endl;
}
void Problem13() {
double hilf, sum=0;
char numbers[5000];
fstream file_op("numbers 13.txt", ios::in);
while(file_op >> numbers) {
std::stringstream val;
val << numbers;
val >> hilf;
sum+=hilf;
}
file_op.close();
cout.precision(10);
cout << sum << endl;
}
void Problem14() {
double max_number=0, steps, akt, max_steps=0;
for (double i=1; i<1000000; i++) {
akt=i;
steps=0;
while (akt!=1) {
if (fmod(akt, 2)==0)
akt = akt/2;
else
akt = 3*akt+1;
steps++;
}
if (steps > max_steps) {
max_steps = steps;
max_number = i;
}
}
cout << max_number << endl;
}
int pascaltriangle(double column, double row) {
if (row==1 and (column==1 or column == 2))
return 1;
else if (row==1)
return 0;
if (row > 22)
cout << row << endl;
return pascaltriangle(column-1, row-1) + pascaltriangle(column, row-1);
}
void Problem15() {
int dimension=20;
double triangle[dimension*2+1][dimension*2+1];
for (int i=0;i<dimension*2+1;i++)
for (int j=0;j<dimension*2+1;j++)
triangle[i][j]=0.;
triangle[0][1]=1.;
triangle[0][2]=1.;
for (int i=1;i<41;i++)
{
triangle[i][0]=1;
for (int j=1; j<i+1; j++)
triangle[i][j]=triangle[i-1][j-1] + triangle[i-1][j];
}
cout << fixed << triangle[dimension*2][dimension] << endl;
}
/*
void Problem16() {
BIGNAT rest, number;
int grenze = 1000;
//number = 2^grenze
string2bignat(&rest, "2");
string2bignat(&number, "2");
for (int i=1;i<grenze;i++)
number = mul_bignat(number, rest);
int sum = sum_of_digits(number);
cout << sum << endl;
}
*/
int digit_count_letters(int i) {
switch(i%10) {
case 1: case 2: case 6: return 3;
case 4: case 5: case 9: return 4;
case 3: case 7: case 8: return 5;
default: return 0;
}
}
int digit_count_letters_ten(int i) {
switch(i%10) {
case 1: return 4;
case 4: case 5: case 6: return 5;
case 2: case 3: case 8: case 9: return 6;
case 7: return 7;
default: return 0;
}
}
void Problem17() {
//one thousand
long long int sum=11;
for (int i=1;i<=999;i++) {
if (i%100 == 10) sum += 3;
else if (i%100 == 11) sum +=6;
else if (i%100 == 12) sum +=6;
else if (i%100 == 13) sum +=8;
else if (i%100 == 14) sum +=8;
else if (i%100 == 15) sum +=7;
else if (i%100 == 18) sum +=8;
else {
sum+=digit_count_letters(i%10);
sum+=digit_count_letters_ten((i%100-i%10)/10);
}
//hundred and
if (i>99) {
sum += 10;
sum += digit_count_letters((i-i%100)/100);
}
//Bei runden hundertern gibts kein and
if (i%100 == 0)
sum -= 3;
}
cout << sum << endl;
}
void Problem18() {
int dim=16;
int dreieck[dim][dim];
for (int i=0;i<dim;i++)
for (int j=0;j<dim;j++)
dreieck[i][j]=0;
dreieck[0][0] =75; dreieck[8][4] =83; dreieck[12][2 ]=52;
dreieck[1][0] =95; dreieck[8][5] =40; dreieck[12][3 ]=38;
dreieck[1][1] =64; dreieck[8][6] =80; dreieck[12][4 ]=17;
dreieck[2][0] =17; dreieck[8][7] =70; dreieck[12][5 ]=14;
dreieck[2][1] =47; dreieck[8][8] =33; dreieck[12][6 ]=91;
dreieck[2][2] =82; dreieck[9][0] =41; dreieck[12][7 ]=43;
dreieck[3][0] =18; dreieck[9][1] =48; dreieck[12][8 ]=58;
dreieck[3][1] =35; dreieck[9][2] =72; dreieck[12][9 ]=50;
dreieck[3][2] =87; dreieck[9][3] =33; dreieck[12][10]=27;
dreieck[3][3] =10; dreieck[9][4] =47; dreieck[12][11]=29;
dreieck[4][0] =20; dreieck[9][5] =32; dreieck[12][12]=48;
dreieck[4][1] =4 ; dreieck[9][6] =37; dreieck[13][0]=63;
dreieck[4][2] =82; dreieck[9][7] =16; dreieck[13][1 ]=66;
dreieck[4][3] =47; dreieck[9][8] =94; dreieck[13][2 ]=4 ;
dreieck[4][4] =65; dreieck[9][9] =29; dreieck[13][3 ]=68;
dreieck[5][0] =19; dreieck[10][0]=53; dreieck[13][4 ]=89;
dreieck[5][1] =1 ; dreieck[10][1]=71; dreieck[13][5 ]=53;
dreieck[5][2] =23; dreieck[10][2]=44; dreieck[13][6 ]=67;
dreieck[5][3] =75; dreieck[10][3]=65; dreieck[13][7 ]=30;
dreieck[5][4] =3 ; dreieck[10][4]=25; dreieck[13][8 ]=73;
dreieck[5][5] =34; dreieck[10][5]=43; dreieck[13][9 ]=16;
dreieck[6][0] =88; dreieck[10][6]=91; dreieck[13][10]=69;
dreieck[6][1] =2 ; dreieck[10][7]=52; dreieck[13][11]=87;
dreieck[6][2] =77; dreieck[10][8]=97; dreieck[13][12]=40;
dreieck[6][3] =73; dreieck[10][9]=51; dreieck[13][13]=31;
dreieck[6][4] =7 ; dreieck[10][10]=14; dreieck[14][0]=04;
dreieck[6][5] =63; dreieck[11][0]=70; dreieck[14][1 ]=62;
dreieck[6][5] =67; dreieck[11][1 ]=11; dreieck[14][2 ]=98;
dreieck[7][0] =99; dreieck[11][2 ]=33; dreieck[14][3 ]=27;
dreieck[7][1] =65; dreieck[11][3 ]=28; dreieck[14][4 ]=23;
dreieck[7][2] =4 ; dreieck[11][4 ]=77; dreieck[14][5 ]=9 ;
dreieck[7][3] =28; dreieck[11][5 ]=73; dreieck[14][6 ]=70;
dreieck[7][4] =6 ; dreieck[11][6 ]=17; dreieck[14][7 ]=98;
dreieck[7][5] =16; dreieck[11][7 ]=78; dreieck[14][8 ]=73;
dreieck[7][6] =70; dreieck[11][8 ]=39; dreieck[14][9 ]=93;
dreieck[7][7] =92; dreieck[11][9 ]=68; dreieck[14][10]=38;
dreieck[8][0] =41; dreieck[11][10]=17; dreieck[14][11]=53;
dreieck[8][1] =41; dreieck[11][11]=57; dreieck[14][12]=60;
dreieck[8][2] =26; dreieck[12][0]=91; dreieck[14][13]=4 ;
dreieck[8][3] =56; dreieck[12][1 ]=71; dreieck[14][14]=23;
int b[dim][dim];
for (int i=0;i<dim;i++)
for (int j=0;j<dim;j++)
b[i][j]=0;
b[0][0]=dreieck[0][0];
for (int zeile=1;zeile<dim;zeile++)
{
b[zeile][0]=b[zeile-1][0] + dreieck[zeile][0];
b[zeile][zeile]=b[zeile-1][zeile-1] + dreieck[zeile][zeile];
for (int spalte=1;spalte<zeile;spalte++)
{
if (b[zeile-1][spalte]>b[zeile-1][spalte-1])
b[zeile][spalte]=b[zeile-1][spalte]+dreieck[zeile][spalte];
else
b[zeile][spalte]=b[zeile-1][spalte-1]+dreieck[zeile][spalte];
}
}
int max =0;
for (int j=0;j<dim;j++)
if (b[dim-1][j]>max)
max = b[dim-1][j];
cout << max << endl;
}
int anzahltage(int month, int year) {
switch (month)
{
case 1: case 3: case 5: case 7: case 8: case 10: case 12:
return 31;
case 4: case 6: case 9: case 11:
return 30;
}
//Schaltjahr
if (year%4==0 and year%100!=0 and year%400 == 0)
return 29;
//kein Schaltjahr
return 28;
}
void Problem19() {
int tag = 2, sonntage=0;
for (int year=1901;year<2001;year++)
for (int month=1;month<=12;month++)
{
tag += anzahltage(month, year);
if (tag%7 == 0)
sonntage ++;
}
cout << sonntage << endl;
}