Getting WA, created own test cases too but not getting approved answers - c++

Link of Question : https://www.codechef.com/JULY20B/problems/PTMSSNG
Question Statement
Chef has N axis-parallel rectangles in a 2D Cartesian coordinate system. These rectangles may intersect, but it is guaranteed that all their 4N vertices are pairwise distinct.
Unfortunately, Chef lost one vertex, and up until now, none of his fixes have worked (although putting an image of a point on a milk carton might not have been the greatest idea after all…). Therefore, he gave you the task of finding it! You are given the remaining 4N−1 points and you should find the missing one.
Can anyone suggest where I'm going wrong or update my code or share a few test cases.
#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#define ll long long
using namespace std;
int main()
{
int t;
cin >> t;
for (int i = 0; i < t; i++)
{
vector<pair<ll, ll>> v;
ll n, m, a;
bool checkx = false;
cin >> n;
m = 4 * n - 1;
ll x[m], y[m];
ll c, d;
a = (m - 1) / 2;
for (ll i = 0; i < m; i++)
{
cin >> x[i] >> y[i];
v.push_back(make_pair(x[i], y[i]));
}
sort(v.begin(), v.end());
for (ll i = a; i >= 1; --i)
{
if (v[2 * i].first != v[2 * i - 1].first)
{
c = v[2 * i].first;
checkx = true;
if ((2 * i) % 4 == 0 && i >= 2)
{
if (v[2 * i].second == v[2 * i + 1].second)
{
d = v[2 * i + 2].second;
}
else
{
d = v[2 * i + 1].second;
}
}
else
{
if (v[2 * i].second != v[2 * i - 1].second)
{
d = v[2 * i - 1].second;
}
else
{
d = v[2 * i - 2].second;
}
}
break;
}
}
if (checkx)
{
cout << c << " " << d;
}
else
{
if (v[0].second == v[1].second)
{
d = v[2].second;
}
else
{
d = v[1].second;
}
cout << v[0].first << " " << d;
}
cout << endl;
}
return 0;
}

You don't need to do such complex things. Just input your x and y vectors and xor every element of each vector. The final value will be the required answer.
LOGIC :
(a,b)------------------(c,b)
| |
| |
| |
| |
(a,d)------------------(c,d)
See by this figure, each variable (a, b, c, d) occurs even number of times. This "even thing" will also be true for the N rectangles. Hence, you have to find the values of x and y which are occurring odd number of times.
To find the odd one out in such cases, the best trick is to xor every element of the vector. This works because of these properties of xor : k xor k = 0 and k xor 0 = k.
CODE:
#include <functional>
#include <iostream>
#include <numeric>
#include <vector>
signed main() {
std::size_t t, n;
std::cin >> t;
while (t--) {
std::cin >> n;
n = 4 * n - 1;
std::vector<int> x(n), y(n);
for (std::size_t i = 0; i < n; ++i)
std::cin >> x.at(i) >> y.at(i);
std::cout << std::accumulate(x.begin(), x.end(), 0L, std::bit_xor<int>()) << ' '
<< std::accumulate(y.begin(), y.end(), 0L, std::bit_xor<int>()) << '\n';
}
return 0;
}

here is a test case that your code doesn't work:
1
2
1 1
1 4
4 6
6 1
9 6
9 3
4 3
the output of your code is (6,3),but it should be (6,4).
I guess you can check more cases where the rectangles intersects.

from functools import reduce
for _ in range(int(input())):
n=int(input())
li=[]
li1=[]
for i in range(4*n-1):
m,n=map(int,input().split())
li.append(m)
li1.append(n)
r =reduce(lambda x, y: x ^ y,li)
print(r,end=' ')
r =reduce(lambda x, y: x ^ y,li1)
print(r,end=' ')
print()

Related

The next prime number

Among the given input of two numbers, check if the second number is exactly the next prime number of the first number. If so return "YES" else "NO".
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
int nextPrime(int x){
int y =x;
for(int i=2; i <=sqrt(y); i++){
if(y%i == 0){
y = y+2;
nextPrime(y);
return (y);
}
}
return y;
}
int main()
{
int n,m, x(0);
cin >> n >> m;
x = n+2;
if(n = 2 && m == 3){
cout << "YES\n";
exit(0);
}
nextPrime(x) == m ? cout << "YES\n" : cout << "NO\n";
return 0;
}
Where is my code running wrong? It only returns true if next number is either +2 or +4.
Maybe it has something to do with return statement.
I can tell you two things you are doing wrong:
Enter 2 4 and you will check 4, 6, 8, 10, 12, 14, 16, 18, ... for primality forever.
The other thing is
y = y+2;
nextPrime(y);
return (y);
should just be
return nextPrime(y + 2);
Beyond that your loop is highly inefficient:
for(int i=2; i <=sqrt(y); i++){
Handle even numbers as special case and then use
for(int i=3; i * i <= y; i += 2){
Using a different primality test would also be faster. For example Miller-Rabin primality test:
#include <iostream>
#include <cstdint>
#include <array>
#include <ranges>
#include <cassert>
#include <bitset>
#include <bit>
// square and multiply algorithm for a^d mod n
uint32_t pow_n(uint32_t a, uint32_t d, uint32_t n) {
if (d == 0) __builtin_unreachable();
unsigned shift = std::countl_zero(d) + 1;
uint32_t t = a;
int32_t m = d << shift;
for (unsigned i = 32 - shift; i > 0; --i) {
t = ((uint64_t)t * t) % n;
if (m < 0) t = ((uint64_t)t * a) % n;
m <<= 1;
}
return t;
}
bool test(uint32_t n, unsigned s, uint32_t d, uint32_t a) {
uint32_t x = pow_n(a, d, n);
//std::cout << " x = " << x << std::endl;
if (x == 1 || x == n - 1) return true;
for (unsigned i = 1; i < s; ++i) {
x = ((uint64_t)x * x) % n;
if (x == n - 1) return true;
}
return false;
}
bool is_prime(uint32_t n) {
static const std::array witnesses{2u, 3u, 5u, 7u, 11u};
static const std::array bounds{
2'047u, 1'373'653u, 25'326'001u, 3'215'031'751u, UINT_MAX
};
static_assert(witnesses.size() == bounds.size());
if (n == 2) return true; // 2 is prime
if (n % 2 == 0) return false; // other even numbers are not
if (n <= witnesses.back()) { // I know the first few primes
return (std::ranges::find(witnesses, n) != std::end(witnesses));
}
// write n = 2^s * d + 1 with d odd
unsigned s = 0;
uint32_t d = n - 1;
while (d % 2 == 0) {
++s;
d /= 2;
}
// test widtnesses until the bounds say it's a sure thing
auto it = bounds.cbegin();
for (auto a : witnesses) {
//std::cout << a << " ";
if (!test(n, s, d, a)) return false;
if (n < *it++) return true;
}
return true;
}
And yes, that is an awful lot of code but it runs very few times.
Something to do with the return statement
I would say so
y = y+2;
nextPrime(y);
return (y);
can be replaced with
return nextPrime(y + 2);
Your version calls nextPrime but fails to do anything with the return value, instead it just returns y.
It would be more usual to code the nextPrime function with another loop, instead of writing a recursive function.

Count of binary numbers from 1 to n

I want to find the number of numbers between 1 and n that are valid numbers in base two (binary).
1 ≤ n ≤ 10^9
For example, suppose n is equal to 101.
Input: n = 101
In this case, the answer is 5
Output: 1, 10, 11, 100, 101 -> 5
Another example
Input: n = 13
Output: 1, 10, 11 -> 3
Here is my code...
#include <iostream>
using namespace std;
int main()
{
int n, c = 0;
cin >> n;
for (int i = 1; i <= n; ++i)
{
int temp = i;
bool flag = true;
while(temp != 0) {
int rem = temp % 10;
if (rem > 1)
{
flag = false;
break;
}
temp /= 10;
}
if (flag)
{
c++;
}
}
cout << c;
return 0;
}
But I want more speed.
(With only one loop or maybe without any loop)
Thanks in advance!
The highest binary number that will fit in a d-digit number d1 d2 ... dn is
b1 b2 ... bn where
bi = 0 if di = 0, and
bi = 1 otherwise.
A trivial implementation using std::to_string:
int max_binary(int input) {
int res = 0;
auto x = std::to_string(input);
for (char di : x) {
int bi = x == '0' ? 0 : 1;
res = 2 * res + bi;
}
return res;
}
Details:
In each step, if the digit was one, then we add 2 to the power of the number of digits we have.
If the number was greater than 1, then all cases are possible for that number of digits, and we can also count that digit itself and change the answer altogether (-1 is because we do not want to calculate the 0).
#include <iostream>
using namespace std;
int main()
{
long long int n, res = 0, power = 1;
cin >> n;
while(n != 0) {
int rem = n % 10;
if (rem == 1) {
res += power;
} else if (rem > 1) {
res = 2 * power - 1;
}
n /= 10;
power *= 2;
}
cout << res;
return 0;
}

greatest divisor of a number and prime factors relation

Question is as follows :
Given two numbers n and k. For each number in the interval [1, n], your task is to calculate its largest divisor that is not divisible by k. Print the sum of all these divisors.
Note: k is always a prime number.
t=3*10^5,1<=n<=10^9, 2<=k<=10^9
My approach toward the question:
for every i in range 1 to n, the required divisors is i itself,only when that i is not a multiple of k.
If that i is multiple of k, then we have to find the greatest divisor of a number and match with k. If it does not match, then this divisor is my answer. otherwise, 2nd largest divisor is my answer.
for example,take n=10 and k=2, required divisors for every i in range 1 to 10 is 1, 1, 3, 1, 5, 3, 7, 1, 9, 5. sum of these divisors are 36. So ans=36.
My code,which works for a few test cases and failed for some.
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
ll div2(ll n, ll k) {
if (n % k != 0 || n == 1) {
return n;
}
else {
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
ll aa = n / i;
if (aa % k != 0) {
return aa;
}
}
}
}
return 1;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
ll n, k;
cin >> n >> k;
ll sum = 0, pp;
for (pp = 1; pp <= n; pp++) {
//cout << div2(pp, k);
sum = sum + div2(pp, k);
}
cout << sum << '\n';
}
}
Can someone help me where I am doing wrong or suggest me some faster logic to do this question as some of my test cases is showing TIME LIMIT EXCEED
after looking every possible explanation , i modify my code as follows:
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
ll n, i;
ll k, sum;
cin >> n >> k;
sum = (n * (n + 1)) / 2;
for (i = k; i <= n; i = i + k) {
ll dmax = i / k;
while (dmax % k == 0) {
dmax = dmax / k;
}
sum = (sum - i) + dmax;
}
cout << sum << '\n';
}
}
But still it is giving TIME LIMIT EXCEED for 3 test cases. Someone please help.
Like others already said, look at the constraints: t=3*10^5,1<=n<=10^9, 2<=k<=10^9.
If your test has a complexity O(n), which computing the sum via a loop has, you'll end up doing a t * n ~ 10^14. That's too much.
This challenge is a math one. You'll need to use two facts:
as you already saw, if i = j * k^s with j%k != 0, the largest divisor is j;
sum_{i=1}^t i = (t * (t+1)) / 2
We start with
S = sum(range(1, n)) = n * (n+1) / 2
then for all number of the form k * x we added too much, let's correct:
S = S - sum(k*x for x in range(1, n/k)) + sum(x for x in range(1, n/k))
= S - (k - 1) * (n/k) * (n/k + 1) / 2
continue for number of the form k^2 * x ... then k^p * x until the sum is empty...
Ok, people start writing code, so here's a small Python function:
def so61867604(n, k):
S = (n * (n+1)) // 2
k_pow = k
while k_pow <= n:
up = n // k_pow
S = S - (k - 1) * (up * (up + 1)) // 2
k_pow *= k
return S
and in action here https://repl.it/repls/OlivedrabKeyProjections
In itself this is more of a mathematical problem:
If cur = [1..n], as you have already noticed, the largest divisor = dmax = cur is, if cur % k != 0, otherwise dmax must be < cur. From k we know that it is at most divisible into other prime numbers... Since we want to make sure that dmax is not divisible by k we can do this with a while loop... whereby this is certainly also more elegantly possible (since dmax must be a prime number again due to the prime factorization).
So this should look like this (without guarantee just typed down - maybe I missed something in my thinking):
#include <iostream>
int main() {
unsigned long long n = 10;
unsigned long long k = 2;
for (auto cur_n = decltype(n){1}; cur_n <= n; cur_n++)
{
if (cur_n % k != 0) {
std::cout << "Largest divisor for " << cur_n << ": " << cur_n << " (SELF)" << std::endl;
} else {
unsigned long long dmax= cur_n/k;
while (dmax%k == 0)
dmax= dmax/k;
std::cout << "Largest divisor for " << cur_n << ": " << dmax<< std::endl;
}
}
}
I wonder if something like this is what One Lyner means.
(Note, this code has two errors in it, which are described in the comments, as well as can be elucidated by One Lyner's new code.)
C++ code:
#include <vector>
#include <iostream>
using namespace std;
#define ll long long int
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
ll n;
ll k, _k, result;
vector<ll> powers;
cin >> n >> k;
result = n * (n + 1) / 2;
_k = k;
while (_k <= n) {
powers.push_back(_k);
_k = _k * k;
}
for (ll p : powers) {
ll num_js = n / p;
result -= num_js * (num_js + 1) / 2 * (p - 1);
int i = 0;
while (p * powers[i] <= n) {
result += powers[i] * (p - 1);
i = i + 1;
}
}
cout << result << '\n';
}
}

How can I print out the perimeter and the number of right-angled triangle with a given range?

The question need the user input two value, P and Q. The program then will output the number of right angle integer triangle as well as its perimeter from P to Q.
For example:
Input:
154 180
Output:
154 1
156 1
160 1
168 3
176 1
180 3
I think i need to find out the Pythagorean Triples in the P-Q range, but how to count the " number of right-angled triangle " ?
Here are my code :
#include <iostream>
#include <math.h>
using namespace std;
int main() {
int P, Q, a, b, c, i = 0;
cin >> P >> Q;
for ( a = P; a <= Q; ++a)
{
for ( b = a; b <= Q; ++b)
{
for ( c = b; b <= Q; ++c)
{
if ((pow(a, 2) + pow(b, 2)) == pow(c, 2) && a + b + c <= Q)
{
i +=1;
cout << a + b + c << " " << i << endl;
}
}
}
}
return 0;
}
Super Thanks !!
We can count the right angle integer triangles with a specific perimeter by std::map which has the perimeters as keys and the number of triangles as values:
std::map<int, int> triangle_map;
Next, using the symmetry of triangles of exchanging a and b with flipping, we can restrict our finding search into the case of a<=b.
But if a==b then c=sqrt(2)*a which is not an integer when a is an integer.
Therefore the following double-loop search would well work for us and can find all the target triangles:
const int Qmax_a = (Q-1)/2; // 1 is the minimum value of c.
for (int a = 1; a <= Qmax_a; ++a)
{
const int a_sqr = a*a;
for (int b = a+1; b <= Q-a-1; ++b)
{
const int two_side_sqr = a_sqr + b*b;
// possible candidate
const int c = static_cast<int>(std::round(std::sqrt(two_side_sqr)));
const int perimeter = (a+b+c);
if((c*c == two_side_sqr) && (P <= perimeter) && (perimeter <= Q)){
triangle_map[perimeter] += 1;
}
}
}
Finally, we can get the desired output from the resulted map:
DEMO
for(const auto& p : triangle_map){
std::cout << p.first << "," << p.second << std::endl;
}

Find the sum of digits of a sequence of integers

I made up my mind to write a little piece of code that gets two integers, lets say M and N ( M <= N ) and sum the digits of all the integers between them, inclusive. So for example if M = 1 and N = 9, DigitSum will equal to 45. If M = 10 and N = 11 the sum will be (1 + 0 (10) + 1 + 1 (11) = 3).
Here is my code so far (Done the for loop instead of the return):
#include <iostream>
#include <vector>
using namespace std;
// the partial digits sums digitSum[i] = the sum of the digits between 0 and i
int digitSum[] = {0, 1, 3, 6, 10, 15, 21, 28, 36, 45};
int pow_of_ten[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
// the sums of all the digits in the numbers from 1 to (10^(i) - 1) where i is the index in the array
long subsums[] = {0, 45, 20 * 45, 300 * 45, 4000 * 45, 50000 * 45, 600000 * 45, 7000000 * 45, 80000000 * 45,
900000000 * 45};
//Calculates the sum of all digits between 0 and M inclusive
long Digit_Sum(int M) {
if (M < 10) {
return digitSum[M];
}
long result = 0;
int same = M;
int counter = 0;
int lastdigit = 0;
while (same > 0) {
if (same < 10) {
lastdigit = same;
break;
}
same /= 10;
counter ++;
}
for(;counter >= 0; counter --) {
result += (subsums[counter] + M % pow_of_ten[counter] + 1) * lastdigit;
result += digitSum[lastdigit - 1] * pow_of_ten[counter];
if (counter == 0) {
break;
}
lastdigit = (M / pow_of_ten[counter - 1]) % 10;
}
return result;
}
int main() {
int M;
int N;
vector<long> sums;
while (true) {
cin >> M >> N;
if (M == 0 && N == 0) {
break;
}
sums.push_back(Digit_Sum(N) - Digit_Sum(M - 1));
}
for (vector<long>::iterator it = sums.begin(); it != sums.end(); ++it) {
cout << *it << endl;
}
}
For most cases this works well but an Online judge says it is wrong. I looked at other solutions that work but no one hard-coded the values in arrays the way I did. May this cause a partial problem, any ideas?
You can easily just create a for-loop to greatly simplify this code.
There is no need to go through all that effort.
for (Initialization Action, Boolean Expression, Update_Action)
Re deletion below: sorry, I have a bit influenza and mizread N as M. :(
I think a main error is M-1 in
sums.push_back(Digit_Sum(N) - Digit_Sum(M - 1));
Also noting that <when corrected that formula will only work for single-digit numbers. My comment earlier about using a simple formula was based on misunderstanding your problem description, in view of that formula and your examples. Both indicated single digit numbers only.
However, the complexity of the code appears unreasonably high. Consider this, assuming non-negative integers as input, and assuming m is always less than or equal to n:
#include <iostream>
#include <stdexcept>
using namespace std;
bool throwX() { throw std::runtime_error( "Ouch." ); }
auto main() -> int
{
for( ;; )
{
int m, n;
cin >> m >> n || throwX();
if( m == 0 && n == 0 ) { break; }
int sum = 0;
for( int i = m; i <= n; ++i )
{
for( int v = i; v != 0; v /= 10 )
{
sum += v % 10;
}
}
cout << sum << endl;
}
}
It needs not be more complicated than that.
Tested and working to spec, sans console input:
#include <iostream>
#include <string>
using namespace std;
void sum_a_to_b(const int & a, const int & b)
{
if (a <= b && a >= 0)
{
long long sum = 0;
for (int i = a; i <= b; i++)
{
sum += i;
}
cout << "Sum of digits from " << a << " through " << b << " is " << sum << ".\n";
}
}
int main()
{
sum_a_to_b(5, 6);
sum_a_to_b(1, 9);
}