i checked the answer and it's not off by much from my answer, but it is still an error. can someone check my coding to see what mistake caused me to get a value of 1319?
#include <iostream>
#include <vector>
using namespace std;
int main()
{
int k = 0;
int o = 0;
vector<int> n(1,0);
n[0] = 1;
while (k < 1001)
{
for (int l = 0; l < n.size(); l++)
n[l] = n[l] * 2;
for (int l = 0; l < n.size(); l++)
{
if (n[l] >= 1000000)
{
int m;
if (l == n.size() - 1)
n.resize(n.size() + 1);
m = n[l] / 1000000;
n[l] = n[l] % 1000000;
n[l+1] = n[l+1] + m;
}
}
k++;
}
for (int l = 0; l < n.size(); l++)
o = o + int (n[l]/1000000) + int ((n[l] % 1000000) / 100000) + int ((n[l] % 100000) / 10000) + int ((n[l] % 10000) / 1000) + int ((n[l] % 1000) / 100) + int ((n[l] % 100) / 10) + n[l] % 10;
cout << o;
cin >> k;
return 0;
}
Make it
while (k < 1000)
in the outer loop condition.
In the while loop, you start with a representation of 2^k in the vector with the value k has at entering the loop. So you are actually computing 2^1001 and not 2^1000.
Problem of solving this in c++ is datatype limit, "int" is not sufficient to calculate 2^1000.
I have solved a prototype for this i.e. sum of the digits of number 2^4.The power 2^4 is 16 and sum of digits id 7.
Hope the code guides u.
#include<iostream.h>
#include<conio.h>
void main()
{
int count=1;
int power=1;
int sum=0;
while(count<=4)
{ count++;
power=power*2;
}
cout<<"The power is"<<power<<"\t";
while(power!=0)
{
int digit=power%10;
sum=sum+digit;
power=power/10;
}
cout<<"The sum of digits is"<<sum;
getch();
}
Related
This is the code for function f(T,k) where
f(T,0)=∑(from i=1 to i≤len(T)) T[i], where len(T) is length of array T.
f(T,k)=∑(from i=1 to i≤len(T)) ∑(from j=i to j≤len(T)) f(T[i...j],k-1), for k>0, where len(T) is length
of array T and T[i...j] is sub-array of T with elements form the i-th to the j-th position (T[i],T[i+1],...,T[j])
It is a recursive function and I need to reduce the complexity, but I don't know how.
Can someone help me out?
This is the problem text:
1000000007 players participate in this game and the winner is decided by random selection. To make the selection random, the company has set strict rules for selecting that player. First they number the players with identification numbers from 0 to 1000000006. Then they choose array A with N elements and the number k. They then define the winner as the player who has the identification number f (A, k) mod (100000007)
#include <iostream>
#include <vector>
using namespace std;
int N,k,a;
vector<int>A;
int fja(vector<int>A,int k){
long long suma=0;
if(k==0){// If k==0 calculate the first said function
for(auto it=A.begin();it!=A.end();it++)suma=(suma+(*it))%(1000000007);//Moduo is there because suma is very big
return suma;
}else{//If k>0 calculate the second function
int duzina=A.size();//duzina is length of A (T)
for(int i=0;i<duzina;i++){//Going through the first and second sum of second function
for(int j=i;j<duzina;j++){
vector<int>b(A.begin()+i,A.begin()+j+1);//Creating new vector (array) to pass it into the new function call
suma=(suma+fja(b,k-1))%(1000000007);//Moduo is there because suma is very big
}
}
return suma;
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin>>N>>k; //Number of elements and k
for(int i=0;i<N;i++){
cin>>a;
A.push_back(a);//All the elements
}
cout<<fja(A,k);
}
I implemented non-recursive version, only loop-based, but it has O(k * n^4) so for biggest 10^5 values of N and k it will be too slow.
I provided recursive solution for reference, it can solve for N and k up to 10, my non-recursive solution can solve up to N and k of 100.
I'm sure some loops can be removed in my solution by algorithmic optimization. Still I could not figure out how to solve task for very large values of 10^5.
In current main() function N and k both are 10, for testing only, to leave only fast version you may change N and k from 10 to 100 and comment out f_ref() call. f_ref() is reference recursive function, f_fast() is my faster variant.
Try it online!
#include <cstdint>
#include <vector>
#include <iostream>
typedef uint32_t u32;
typedef int64_t i64;
typedef uint64_t u64;
enum { mod = 100000007 };
i64 f_ref(std::vector<i64> const & T, size_t begin, size_t end, size_t k) {
i64 sum = 0;
if (k == 0)
for (size_t i = begin; i < end; ++i)
sum = (sum + T[i]) % mod;
else
for (size_t i = begin; i < end; ++i)
for (size_t j = i; j < end; ++j)
sum = (sum + f_ref(T, i, j + 1, k - 1)) % mod;
return sum;
}
i64 f_fast(std::vector<i64> const & T, size_t k) {
size_t N = T.size();
std::vector<std::vector<i64>> mc, mn;
for (size_t n = 1; n <= N; ++n) {
mc.resize(mc.size() + 1);
for (size_t j = 0; j < n; ++j)
mc.back().push_back(((n + (n - 2 * j)) * (j + 1) / 2) % mod);
}
for (size_t ik = 0; ik + 1 < k; ++ik) {
mn.clear();
mn.resize(N);
for (size_t n = 1; n <= N; ++n) {
mn[n - 1].resize(n);
for (size_t i = 0; i < n; ++i)
for (size_t j = i; j < n; ++j)
for (size_t l = 0; l <= j - i; ++l)
mn[n - 1][i + l] = (mn[n - 1][i + l] + mc[j - i][l]) % mod;
}
mc = mn;
}
i64 sum = 0;
for (size_t i = 0; i < N; ++i)
sum = (sum + mc.back()[i] * (T[i] % mod)) % mod;
return sum;
}
int main() {
std::vector<i64> a;
for (size_t i = 0; i < 10; ++i)
a.push_back(i + 1);
size_t k = 10;
std::cout << f_ref(a, 0, a.size(), k) << " " << f_fast(a, k) << std::endl;
return 0;
}
Output for N = 10 and k = 10:
78689325 78689325
Output for N = 100 and k = 100:
37190121
Given m integer from 1 to m, for each 1 <=i <= m find the smallest prime x that i % x = 0 and the biggest number y which is a power of x such that i % y = 0
My main approach is :
I use Eratos agorithm to find x for every single m like this :
I use set for more convenient track
#include<bits/stdc++.h>
using namespace std;
set<int> s;
void Eratos() {
while(!s.empty()) {
int prime = *s.begin();
s.erase(prime);
X[prime] = prime;
for(int j = prime * 2; j <= L ; j++) {
if(s.count(j)) {
int P = j / prime;
if( P % prime == 0) Y[j] = Y[P]*prime;
else Y[j] = prime;
}
}
}
signed main() {
for(int i = 2; i<= m; i++) s.insert(i);
Eratos();
for(int i = 1; i <= m; i++) cout << X[m] << " " << Y[m] ;
}
with X[m] is the number x corresponding to m and same as Y[m]
But it seems not really quick and optimal solution. And the memory request for this is so big and when m is 1000000. I get MLE. So is there an function that can help to solve this problem please. Thank you so much.
Instead of simply marking a number prime/not-prime in the original Sieve of Eratosthenes, save the corresponding smallest prime factor which divides that number.
Once that's done, the biggest power of the smallest prime of a number would mean to simply check how many times that smallest prime appears in the prime factorization of that number which is what the nested for loop does in the following code:
#include <iostream>
#include <vector>
using namespace std;
void SoE(vector<int>& sieve)
{
for (int i = 2; i < sieve.size(); i += 2)
sieve[i] = 2;
for (int i = 3; i < sieve.size(); i += 2)
if (sieve[i] == 0)
for (int j = i; j < sieve.size(); j += i)
if(sieve[j] == 0)
sieve[j] = i;
}
int main()
{
int m;
cin >> m;
vector<int> sieve(m + 1, 0);
SoE(sieve);
for (int i = 2; i < sieve.size(); ++i)
{
int x, y;
x = y = sieve[i];
for (int j = i; sieve[j / x] == x; j /= x)
y *= x;
cout << x << ' ' << y << endl;
}
}
I didn't get what you're trying to do but I understand that you're trying to use Sieve of Eratosthenes to find prime numbers. Well, what you probably need is a bitset, it's like a boolean array but uses bits instead of bytes which means it uses less memory. Here's what I did:
#include <iostream>
#include <vector>
#include <bits/stdc++.h>
#include <cmath>
using namespace std;
vector<int> primes;
int main()
{
const int m = 1e7;
bitset<m> bs;
int limit = (int) sqrt (m);
for (int i = 2; i < limit; i++) {
if (!bs[i]) {
for (int j = i * i; j < m; j += i)
bs[j] = 1;
}
}
for (int i = 2; i < m; i++) {
if (!bs[i]) {
primes.push_back (i);
}
}
return 0;
}
#include <iostream>
#include <math.h>
using namespace std;
int fact(int number)
{
unsigned long long int p = 1;
if (number == 0) {
return p;
}
for (int i = 1; number >= i; i++) {
p = p * i;
}
return p;
}
int main()
{
long long int a, x, sum = 0, result;
int n ;
cin >> a;
cin >> x;
cin >> n;
for (int k = 0; n >= k; k++) {
result = fact(n) / (fact(k) * fact(n - k));
sum = sum + (result * pow(x, k) * pow(a, n - k));
}
cout << sum;
return 0;
}
I want to calculate this series
So I considered the long long int sum, but the sum number sometimes gets too big. What can I do to save the sum number without using library?
First of all I would suggest to use binomial theorem -- what you are computing is just pow(x+a, n)
If you want to do this through series, do not compute the binomial coefficient using factorials but something like this
int bin_coeff(int n, int k){
int lim = k > n/2 ? k : n - k;
int sum = 1;
for (int i = n; i > lim; i--){
sum *= i;
}
for (int i = 2; i < (n - lim + 1); i++){
sum /= i;
}
return sum;
}
I was assigned a "project" where I should create a C++ program to find the largest possible sum of two sub sequences. The user inputs N (array length), K (length of each sub sequence) and N numbers representing the array. The two sub sequences can touch but can't override each other e.g. 1 5 20 20 20 15 10 1 1 1 should output 90 ((5+20+20)+(20+15_10)) and not 115 ((20+20+20)+(20+20+15)).
My code until now is:
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
int main()
{
int N, K, MaxN;
cin >> N;
cin >> K;
int Pi[N];
MaxN = N - K + 1;
int Word[MaxN];
int MaxSum;
for(int nn=0; nn<N; nn++) {
cin >> Pi[nn];
}
for(int y=0;y<MaxN;y++) {
Word[y] = 0;
}
for(int j=0; j<MaxN; j++) {
for(int l=0; l<K; l++) {
Word[j] = Word[j] + Pi[j+l];
}
}
sort(Word, Word + MaxN);
MaxSum = Word[MaxN-2] + Word[MaxN-1];
cout << MaxSum;
return 0;
}
Which is correct only in the case where the 2 sub sequences don't interfere with each other e.g. in an array such as 2 4 15 12 10 1 1 20 4 10 which outputs 71.
Thank you all in advance.
This is solution:
precalculate prefixes and suffixes
iterate end of the first subarray
iterate begin of the second subarray, but start from the end of first sub. ar. + 1
we have sum of numbers on interval from 0 to *end* = prefix[end], but we are interested only in interval [end - k, k], so simply subtract prefix[end] - prefix[end - k - 1]
[0 .. end-k-1, end-k .. end]
The same approach for the second subarray: sum2 = suffix[begin] - suffix[begin + i + 1]
then compare with the previous answer
So we just brute-force all possible sub-arrays which not intersect and find the max their sum
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
int main()
{
int N,K,MaxN;
cin >> N;
cin >> K;
int Pi[N];
MaxN=N-K+1;
int Word[MaxN];
int MaxSum;
for(int nn=0;nn<N;nn++){
cin >> Pi[nn];
}
int prefix[N];
int sufix[N];
for (int i = 0; i < N; i++) {
prefix[i] = sufix[i] = 0;
}
for (int i = 0; i < N; i++) {
if (i == 0)
prefix[i] = Pi[i];
else
prefix[i] = Pi[i] + prefix[i - 1];
}
for (int i = N - 1; i >= 0; i--) {
if (i == N - 1)
sufix[i] = Pi[i];
else
sufix[i] = Pi[i] + sufix[i + 1];
}
int ans = 0;
for (int i = K - 1; i < MaxN; i++) {
for (int j = i + 1; j < MaxN; j++) {
int x = prefix[i] - (i - K >= 0 ? prefix[i - K] : 0);
int y = sufix[j] - (j + K < N ? sufix[j + K] : 0);
ans = max(ans, x + y);
}
}
cout << ans;
return 0;
}
I'm trying to make a parallel version of "Harmonic Progression Sum" problem using opemMP.
But the output are differents each other depending on the inputs. (Parallel and Sequential)
Program:
#include "stdafx.h"
#include <iostream>
#include <sstream>
#include <omp.h>
#include <time.h>
#define d 10 //Numbers of Digits (Example: 5 => 0,xxxxx)
#define n 1000 //Value of N (Example: 5 => 1/1 + 1/2 + 1/3 + 1/4 + 1/5)
using namespace std;
void HPSSeguencial(char* output) {
long unsigned int digits[d + 11];
for (int digit = 0; digit < d + 11; ++digit)
digits[digit] = 0;
for (int i = 1; i <= n; ++i) {
long unsigned int remainder = 1;
for (long unsigned int digit = 0; digit < d + 11 && remainder; ++digit) {
long unsigned int div = remainder / i;
long unsigned int mod = remainder % i;
digits[digit] += div;
remainder = mod * 10;
}
}
for (int i = d + 11 - 1; i > 0; --i) {
digits[i - 1] += digits[i] / 10;
digits[i] %= 10;
}
if (digits[d + 1] >= 5) {
++digits[d];
}
for (int i = d; i > 0; --i) {
digits[i - 1] += digits[i] / 10;
digits[i] %= 10;
}
stringstream stringstreamA;
stringstreamA << digits[0] << ",";
for (int i = 1; i <= d; ++i) {
stringstreamA << digits[i];
}
string stringA = stringstreamA.str();
stringA.copy(output, stringA.size());
}
void HPSParallel(char* output) {
long unsigned int digits[d + 11];
for (int digit = 0; digit < d + 11; ++digit)
digits[digit] = 0;
int i;
long unsigned int digit;
long unsigned int remainder;
#pragma omp parallel for private(i, remainder, digit)
for (i = 1; i <= n; ++i) {
remainder = 1;
for (digit = 0; digit < d + 11 && remainder; ++digit) {
long unsigned int div = remainder / i;
long unsigned int mod = remainder % i;
digits[digit] += div;
remainder = mod * 10;
}
}
for (int i = d + 11 - 1; i > 0; --i) {
digits[i - 1] += digits[i] / 10;
digits[i] %= 10;
}
if (digits[d + 1] >= 5) {
++digits[d];
}
for (int i = d; i > 0; --i) {
digits[i - 1] += digits[i] / 10;
digits[i] %= 10;
}
stringstream stringstreamA;
stringstreamA << digits[0] << ",";
for (int i = 1; i <= d; ++i) {
stringstreamA << digits[i];
}
string stringA = stringstreamA.str();
stringA.copy(output, stringA.size());
}
int main() {
//Sequential Method
cout << "Sequential Method: " << endl;
char outputSeguencial[d + 10];
HPSSeguencial(outputSeguencial);
cout << outputSeguencial << endl;
//Cleaning vector
string stringA = "";
stringA.copy(outputSeguencial, stringA.size());
//Parallel Method
cout << "Parallel Method: " << endl;
char outputParallel[d + 10];
HPSParallel(outputParallel);
cout << outputParallel << endl;
system("PAUSE");
return 0;
}
Examples:
Input:
#define d 10
#define n 1000
Output:
Sequential Method:
7,4854708606╠╠╠╠╠╠╠╠╠╠╠╠
Parallel Method:
6,6631705861╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠ÇJ^
Input:
#define d 12
#define n 7
Output:
Sequential Method:
2,592857142857╠╠╠╠╠╠╠╠╠╠╠╠╠╠ÀÂ♂ü─¨#
Parallel Method:
2,592857142857╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠╠ÇJJ
Regards
Pastecode
http://pastecode.org/index.php/view/62768285
Your threads step on each other's toes when updating the digits array. Hence some additions are lost, and you get bogus results (different results in different runs, almost certainly).
You must synchronise the writes to digits, e.g. with an atomic (or critical) section:
// ... <snip>
#pragma omp parallel for private(i, remainder, digit)
for (i = 1; i <= n; ++i) {
remainder = 1;
for (digit = 0; digit < d + 11 && remainder; ++digit) {
long unsigned int div = remainder / i;
long unsigned int mod = remainder % i;
#pragma omp atomic // <- HERE, could also be #pragma omp critical
digits[digit] += div;
remainder = mod * 10;
}
}
// <snip> ...
so that only one thread at a time can update the array. For a task like this, that would probably nullify any gains of splitting the task in several threads, though.
As Daniel Fischer pointed out, you have a write conflict, but you can avoid it more elegantly than with an omp critical section, e.g. by giving each thread it's own copy of digits and aggregating them all at the end of the loop.