Multiply numbers among themselves - c++

I want to build the following program:
The user has to insert a number between 100 and 999 (like 100 < i < 999) and the numbers have to be multiplied among themselves.
Example:
A Valid Input: 178
Corresponding Result: 1*7*8 = 72
I tried to achieve the first part i.e. checking for the number given as input to be within 100 and 999 in the two ways below, but my approach isn't said to be elegant:
#include <stdio.h>
int main()
{
char n[4];
scanf("%s", n);
printf("%d\n", (n[0]-'0')*(n[1]-'0')*(n[2]-'0'));
return 0;
}
or
#include<stdio.h>
int main()
{
int array[3];
scanf("%1d%1d%1d", &array[0],&array[1],&array[2]);
for ( int i=0; i<3; i++) {
printf("%d\n", array[i]);
}
return 0;
}
Are they any better ways to achieve the same?
I'm looking for a C++ solution.

You can impose std::cin as a conditional in a while:
int x;
while (std::cin >> x && x>=100 && x <=999)
\\ Do what you want
For multiplying the digits, simply extract each digit by getting its remainder when divided by 10, multiply that with the current product (set a variable, with inital value 1) then divide by 10 subsequently in a loop till you get the product of all digits. For example, create a function which returns the product of digits of a number:
int digitproduct(int x)
{ int product = 1;
while (x != 0)
{
product *= (n % 10);
x /= 10;
}
return product;
}
Call that inside the while:
int x;
while (std::cin >> x && x>=100 && x <=999)
{ cout<< digitproduct(x);
break;
}

People may say, your solution isn't elegant, because it does not easily scales if you may want to add more digest or remove some.
The first one will also have a buffer overflow as soon the user enters more than 4 characters!
But out of my option I like the second one quite much, because it shows a much better understanding of C than just reading the number via int n; std::cin >> n;, validating it, and then calculating the result.
But there is a small flaw as well, you need to check the return value of scanf in order to detect if a number has been successfully parsed or not.
int res = scanf("%1d%1d%1d", &array[0],&array[1],&array[2]);
if(res != 3) {
printf("Invalid number format. Expected a three digit number, but got %d", res);
return 0;
}

More elegant solution will be to obtain the number as an integer and then decompose it to the single digits with division and modulo operations.
This greatly increases the ability to validate the input number and knowing how to decompose the integer may be useful if the number is not given as a string, but from other parts of the program as a number.
Sample code:
#include <stdio.h>
int main() {
int number;
scanf("%d", &number);
if(number > 999 || number < 100) {
printf("Number not in range\n");
return -1;
}
printf("%d\n",
(number / 100) * // hundreds digit
(number / 10 % 10) * // tens digit
(number % 10) // units digit
);
return 0;
}

Related

Unable to have 100 factorial with C++ on output screen(displaying 0)

Well I am stuck on this problem for quite a while:
Question:
You are asked to calculate factorials of some small positive integers.
Input:
An integer t, 1<=t<=100, denoting the number of testcases, followed by t lines, each containing a single integer n, 1<=n<=100.
Output:
For each integer n given at input, display a line with the value of n!
//coded in c++
#include <bits/stdc++.h> //loadind up all the libraries at once.
using namespace std;
int main()
{ int T;
scanf("%d", &T);
//I am not doing "cin<<" cause "scanf" is faster than it
for (int i = 0; i < T; i++)
{
int N;
scanf("%d",&N);
long long int product = 1;
while (N >0){
product = product * N;
N--;
}
printf("%lld\n",product);
}
return 0;
}
I am able to get 10!,20! but unable to get 100! (factorial)
so the extreme case doesn't satisfy. Please help me to get a good data type for my variable as 100! a factorial has over than 100 digits. It is displaying 0 when I input 100 on the terminal.
P.S - This problem is from CodeChef website (FCTRL2).
A 64bit integer will overflow with 23!
Therefore you need to do it with digits and a vector.
This is a rather simple task. We can do it like we would do it on a piece of paper. We use a std::vector of digits to hold the number. Because the result will be already too big for an unsigned long long for 23!.
The answer will be exact.
With such an approach the calculation is simple. I do not even know what to explain further.
Please see the code:
#include <iostream>
#include <vector>
int main()
{
std::cout << "Calculate n! Enter n (max 10000): ";
if (unsigned int input{}; (std::cin >> input) && (input <= 10000)) {
// Here we store the resulting number as single digits
std::vector<unsigned int> result(3000, 0); // Magic number. Is big enough for 100000!
result.back() = 1; // Start calculation with 1 (from right to left)
// Multiply up to the given input value
for (unsigned int count = 2; count <= input; count++)
{
unsigned int sum{}, remainder{};
unsigned int i = result.size() - 1; // Calculate from right to left
while (i > 0)
{
// Simple multiplication like on a piece of paper
sum = result[i] * count + remainder;
result[i--] = sum % 10;
remainder = sum / 10;
}
}
// Show output. Supporess leading zeroes
bool showZeros{ false };
for (const unsigned int i : result) {
if ((i != 0) || showZeros) {
std::cout << i;
showZeros = true;
}
}
}
else std::cerr << "\nError: Wrong input.";
}
Using a bigint library will be much faster.
Developed and tested with Microsoft Visual Studio Community 2019, Version 16.8.2.
Additionally compiled and tested with clang11.0 and gcc10.2
Language: C++17

finding the number of possible decodings of the given number(dynamic programming)

I am trying to solve a problem where every letter has a respective number such as a-1,b-2....z-26.
Now given a number, in how many ways can the number be decoded is the question. consider an example where 25114 can be decoded as 'BEAN',‘BEAAD’, ‘YAAD’, ‘YAN’, ‘YKD’ and ‘BEKD’. this could be decoded in 6 ways.
I have written code in c++ but I am getting the wrong answer. Please correct my code.
#include<bits/stdc++.h>
using namespace std;
int total = 0;
int arr[100001];
void func(int start,int end,int factor){
if(start==end)
return;
int j =start;
if(factor==2&&j==end-1)//if j is the last element and factor is 2,accessing j+1 element is illegual
return;
if(factor==2){
if((arr[j]*10+arr[j+1])>26)
return;
else{
total++;
func(start+2,end,1);
func(start+2,end,2);
}
}
else{//factor is 1
total++;
func(start+1,end,1);
func(start+1,end,2);
}
}
int main(){
int n;
cin>>n;
for(int i=0;i<n;i++){
int p;
cin>>p;
arr[i]=p;
}
func(0,n,1);
func(0,n,2);
cout<<total<<endl;
return 0;
}
essentially what my code is doing is that it fixes one number from the given array(using one digit or two digits from the the given array) and recurses until all the combinations are covered. for example considering the above case, I first choose '2' as my first digit and decode it as 'B'(factor = 1) and then choose '25' and decode it as 'E'(factor = 2).
**following are the input and output from the following code
input : 25114
expected output : 6
my output : 15
input : 3333333333(10 digits)
expected output : 1
my output : 10
Based on the original program from the question I suggest to count the encodings when you reach the end only (if(start==end)).
As func will always be called twice with factor=1 and factor=2, I can freely choose either condition for counting.
Here is the modified code:
#include<bits/stdc++.h>
using namespace std;
int total = 0;
int arr[100001];
void func(int start,int end,int factor){
if(start==end) {
if(factor == 1) total++; // count once when reaching the end
return;
}
int j =start;
if((factor==2) && (j==end-1))//if j is the last element and factor is 2,accessing j+1 element is illegal
return;
if(factor==2){
if((arr[j]*10+arr[j+1])>26)
return;
else{
//total++;
func(start+2,end,1);
func(start+2,end,2);
}
}
else{//factor is 1
//total++;
func(start+1,end,1);
func(start+1,end,2);
}
return;
}
int main(){
int n;
cin>>n;
for(int i=0;i<n;i++){
int p;
cin>>p;
arr[i]=p;
}
func(0,n,1);
func(0,n,2);
cout<<total<<endl;
return 0;
}
This calculates the expected results from the example input in the question.
$ echo 5 2 5 1 1 4|./program
6
$ echo 10 3 3 3 3 3 3 3 3 3 3|./program
1
There is room for improvement.
Instead of modifying a global variable I would return the number of combinations from func and add the values in the higher level.
I would also handle the distinction between 2-digit and 1-digit numbers in the called func instead of in the caller.
Something like this pseudo code:
int func(int start, int end)
{
if(remaining length is <2) {
// we reached the end, so this is one combination
return 1;
}
if(two-digit number is >26) {
// only a 1-digit number is possible, count remaining combinations
return func(start+1, end);
}
// both a 1-digit or 2-digit number is possible, add the remaining combinations for both cases
return func(start+1) + func(start+2);
}
Your question is tagged as "dynamic-programming", but it is anything but.
Instead, think about the state space and its boundary conditions:
The empty string has zero encodings;
A single digit has a single encoding;
An n-digit string has as many encodings as an (n-1)-digit substring plus as many encodings as an (n-2)-digit substring if the first two digits are <= 26.
Thus, we can walk the string from back to front and store the intermediate results for reuse:
uint64_t solve(std::vector<int>& digits) {
const int n = digits.size();
std::vector<int> encodings(n+1);
encodings[n] = 1;
for (int i = n-1; i >= 0; i--) {
bool two_digits_fit = (i < n - 1) && (digits[i] * 10 + digits[i+1]) <= 26; // What if digits[i] == 0?
encodings[i] = encodings[i+1] + (two_digits_fit ? encodings[i+2] : 0);
}
return encodings[0];
}

Prime numbers between two given integers

This is my code for finding prime numbers between two integers. It compiles alright but giving a runtime error SIGXFSZ on codechef.
#include <bits/stdc++.h>
using namespace std;
int main() {
long long n,m;
int t;
cin>>t;
while(t--)
{
cin>>m>>n;
for(long long j=m;j<=n;j++)
for(long long i=2;i<=sqrt(j);i++)
if(j%i==0)
break;
else cout<<j<<"\n";
cout<<"\n";
}
return 0;
}
Seems that you are wrong on logic.
According to my understanding, you are supposed to print the prime numbers between two numbers.
But your code has logical errors.
1) Code doesn't consider 2 and 3 as prime numbers.
Say, m = 1, n = 10. For j = 2, 3, the inner loop won't execute even for the single time. Hence, the output won't be shown to be user.
2) else cout<<j<<"\n"; statement is placed incorrectly as it will lead to prime numbers getting printed multiple times and some composite numbers also.
Example:
For j = 11, this code will print 11 twice (for i = 2, 3).
For j = 15, this code will print 15 once (for i = 2) though it is a composite number.
You've underexplained your problem and underwritten your code. Your program takes two separate inputs: first, the number of trials to perform; second, two numbers indicating the start and stop of an individual trial.
Your code logic is incorrect and incomplete. If you were to use braces consistently, this might be clear. The innermost loop needs to fail on non- prime but only it's failure to break signals a prime, so there can't be one unless the loop completes. The location where you declare a prime is incorrect. To properly deal with this situation requires some sort of flag variable or other fix to emulate labelled loops:
int main() {
int trials;
cin >> trials;
while (trials--)
{
long long start, stop;
cin >> start >> stop;
for (long long number = start; number <= stop; number++)
{
if (number < 2 || (number % 2 == 0 && number != 2))
{
continue;
}
bool prime = true;
for (long long odd = 3; odd * odd <= number; odd += 2)
{
if (number % odd == 0)
{
prime = false;
break;
}
}
if (prime)
{
cout << number << "\n";
}
}
}
return 0;
}
The code takes the approach that it's simplest to deal with even numbers and two as a special case and focus on looping over the odd numbers.
This is basically "exceeded file size", which means that the output file is having size larger than the allowed size.
Please do check the output file size of your program.

basic nestled loop calculate prime numbers between 1 - 239, inclusive

I am working on a program in which I must print out the number of primes, including 1 and 239, from 1 - 239 ( I know one and or two may not be prime numbers, but we will consider them as such for this program) It must be a pretty simple program because we have only gone over some basics. So far my code is as such, which seems like decent logical flow to me, but doesnt produce output.
#include <iostream>
using namespace std;
int main()
{
int x;
int n = 1;
int y = 1;
int i = 0;
while (n<=239)
{x = n % y;
if (x = 0)
i++;
if (y < n)
y++;
n++;
while (i == 2)
cout << n;
}
return 0;
}
The way I want this to work is to take n, as long as n is 239 or less, and preform modulus division with every number from 1 leading up to n. Every time a number y goes evenly into n, a counter will be increased by 1. if the counter is equal to 2, then the number is prime and we print it to the screen. Any help would be so greatly appreciated. Thanks
std::cout << std::to_string(2) << std::endl;
for (unsigned int i = 3; i<240; i += 2) {
unsigned int j = 3;
int sq = sqrt(i);
for (; j <= sq; j += 2) if (!(i%j)) break;
if (j>sq) std::cout << std::to_string(i) << std::endl;
}
first of all, the prime definition: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
so you can skip all the even numbers (and hence ... i+=2).
Moreover no point to try to divide for a number greater than sqrt(i), because then it will have a divisor less than sqrt(i) and the code finds that and move to the next number.
Considering only odd numbers, means that we can skip even numbers as divisors (hence ... j+=2).
In your code there are clearly beginner errors, like (x = 0) instead of x==0. but also the logic doesn't convince. I agree with #NathanOliver, you need to learn to use a debugger to find all the errors. For the rest, good luck with the studies.
lets start with common errors:
first you want to take input from user using cin
cin>>n; // write it before starting your while loop
then,
if (x = 0)
should be:
if (x == 0)
change your second while loop to:
while (i == 2){
cout << n;
i++;
}

Find Largest Prime Factor - Complexity of Code

I tried a code on a coding website to find the largest prime factor of a number and it's exceeding the time limit for the last test case where probably they are using a large prime number. Can you please help me to reduce the complexity of the following code?
int main()
{
long n;
long int lar, fact;
long int sqroot;
int flag;
cin >> n;
lar=2, fact=2;
sqroot = sqrt(n);
flag = 0;
while(n>1)
{
if((fact > sqroot) && (flag == 0)) //Checking only upto Square Root
{
cout << n << endl;
break;
}
if(n%fact == 0)
{
flag = 1;
lar = fact;
while(n%fact == 0)
n = n/fact;
}
fact++;
}
if(flag == 1) //Don't display if loop fact reached squareroot value
cout << lar << endl;
}
Here I've also taken care of the loop checking till Square Root value. Still, how can I reduce its complexity further?
You can speed things up (if not reduce the complexity) by supplying a hard-coded list of the first N primes to use for the initial values of fact, since using composite values of fact are a waste of time. After that, avoid the obviously composite values of fact (like even numbers).
You can reduce the number of tests by skipping even numbers larger than 2, and stopping sooner if you have found smaller factors. Here is a simpler and faster version:
int main() {
unsigned long long n, lar, fact, sqroot;
cin >> n;
lar = 0;
while (n && n % 2 == 0) {
lar = 2;
n /= 2;
}
fact = 3;
sqroot = sqrt(n);
while (fact <= sqroot) {
if (n % fact == 0) {
lar = fact;
do { n /= fact; } while (n % fact == 0);
sqroot = sqrt(n);
}
fact += 2;
}
if (lar < n)
lar = n;
cout << lar << endl;
return 0;
}
I am not sure how large the input numbers may become, using the larger type unsigned long long for these computations will get you farther than long. Using a precomputed array of primes would help further, but not by a large factor.
The better result I've obtained is using the function below (lpf5()). It's based on the primality() function (below) that uses the formulas 6k+1, 6k-1 to individuate prime numbers. All prime numbers >= 5 may be expressed in one of the forms p=k*6+1 or p=k*6-1 with k>0 (but not all the numbers having such a forms are primes). Developing these formulas we can see a sequence like the following:
k=1 5,7
k=2 11,13
k=3 17,19
k=4 23,25*
k=5 29,31
.
.
.
k=10 59,61
k=11 65*,67
k=12 71,73
...
5,7,11,13,17,19,23,25,29,31,...,59,61,65,67,71,73,...
We observe that the difference between the terms is alternatively 2 and 4. Such a results may be obtained also using simple math. Is obvious that the difference between k*6+1 and k*6-1 is 2. It's simple to note that the difference between k*6+1 and (k+1)*6-1 is 4.
The function primality(x) returns x when x is prime (or 0 - take care) and the first divisor occurs when x is not prime.
I think you may obtain a better result inlining the primality() function inside the lpf5() function.
I've also tried to insert a table with some primes (from 1 to 383 - the primes in the first 128 results of the indicated formulas) inside the primality function, but the speed difference is unappreciable.
Here the code:
#include <stdio.h>
#include <math.h>
typedef long long unsigned int uint64;
uint64 lpf5(uint64 x);
uint64 primality(uint64 x);
uint64 lpf5(uint64 x)
{
uint64 x_=x;
while ( (x_=primality(x))!=x)
x=x/x_;
return x;
}
uint64 primality(uint64 x)
{
uint64 div=7,f=2,q;
if (x<4 || x==5)
return x;
if (!(x&1))
return 2;
if (!(x%3))
return 3;
if (!(x%5))
return 5;
q=sqrt(x);
while(div<=q) {
if (!(x%div)) {
return div;
}
f=6-f;
div+=f;
}
return x;
}
int main(void) {
uint64 x,k;
do {
printf("Input long int: ");
if (scanf("%llu",&x)<1)
break;
printf("Largest Prime Factor: %llu\n",lpf5(x));
} while(x!=0);
return 0;
}