| Task: | Kertoma |
| Sender: | chaotic |
| Submission time: | 2022-11-01 18:29:20 +0200 |
| Language: | C++ (C++17) |
| Status: | READY |
| Result: | 100 |
| group | verdict | score |
|---|---|---|
| #1 | ACCEPTED | 22 |
| #2 | ACCEPTED | 24 |
| #3 | ACCEPTED | 54 |
| test | verdict | time | group | |
|---|---|---|---|---|
| #1 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #2 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #3 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #4 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #5 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #6 | ACCEPTED | 0.00 s | 1, 2, 3 | details |
| #7 | ACCEPTED | 0.00 s | 2, 3 | details |
| #8 | ACCEPTED | 0.00 s | 2, 3 | details |
| #9 | ACCEPTED | 0.00 s | 2, 3 | details |
| #10 | ACCEPTED | 0.00 s | 2, 3 | details |
| #11 | ACCEPTED | 0.00 s | 3 | details |
| #12 | ACCEPTED | 0.00 s | 3 | details |
| #13 | ACCEPTED | 0.00 s | 3 | details |
| #14 | ACCEPTED | 0.00 s | 3 | details |
| #15 | ACCEPTED | 0.00 s | 3 | details |
| #16 | ACCEPTED | 0.00 s | 3 | details |
Code
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iostream>
#include <numeric>
#include <vector>
/*
* Kertoman x! lukujen määrä kasvaa ainakin yhdellä, kun x>10
* Tiedetään lukujen k määrä
* floor(log_10(x!) = k - 1
* log_10(x!) = ln(gamma(x))/ln(10)
* Joten ln(gamma(x)) = (k-1)*ln(10)
* Tämä voidaan ratkaista esim. sekanttimenetelmällä
*/
int main() {
std::vector<int> nums;
nums.reserve(10);
for (int i = 0; i < 10; ++i) {
int v;
std::cin >> v;
nums.push_back(v);
}
int k = std::accumulate(nums.begin(), nums.end(), 0);
double result;
if (k > 4) {
// Ratkaistaan yhtälö ln(gamma(x)) = (k-1)*ln(10) x:n suhteen
auto f = [k](double x) { return std::lgamma(x) - (k - 1) * std::log(10); };
// Sekanttimenetelmällä
double error = 0;
double x_n1 = 5;
double x_n2 = 20;
for (int i = 0; i < 100; ++i) {
double x_n = x_n1 - f(x_n1) * (x_n1 - x_n2) / (f(x_n1) - f(x_n2));
assert(x_n > 0);
x_n2 = x_n1;
x_n1 = x_n;
error = x_n1 - x_n2;
if (std::abs(error) < 0.01) break;
}
result = x_n1;
} else {
if (k == 4) result = 7;
if (k == 3) { result = nums[1] == 1 ? 5 : 6; }
if (k == 2) result = 4;
if (k == 1) { result = nums[2] == 1 ? 2 : 3; }
}
std::cout << std::floor(result);
}
Test details
Test 1
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 0 0 1 0 0 0 0 0 0 0 |
| correct output |
|---|
| 2 |
| user output |
|---|
| 2 |
Test 2
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 0 0 0 0 0 0 1 0 0 0 |
| correct output |
|---|
| 3 |
| user output |
|---|
| 3 |
Test 3
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 0 0 1 0 1 0 0 0 0 0 |
| correct output |
|---|
| 4 |
| user output |
|---|
| 4 |
Test 4
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 2 0 1 1 0 0 1 0 2 0 |
| correct output |
|---|
| 10 |
| user output |
|---|
| 10 |
Test 5
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 9 3 1 1 2 2 3 1 6 1 |
| correct output |
|---|
| 27 |
| user output |
|---|
| 27 |
Test 6
Group: 1, 2, 3
Verdict: ACCEPTED
| input |
|---|
| 10 4 3 4 3 2 2 4 3 7 |
| correct output |
|---|
| 36 |
| user output |
|---|
| 36 |
Test 7
Group: 2, 3
Verdict: ACCEPTED
| input |
|---|
| 71 53 36 30 25 29 42 24 34 29 |
| correct output |
|---|
| 199 |
| user output |
|---|
| 199 |
Test 8
Group: 2, 3
Verdict: ACCEPTED
| input |
|---|
| 71 33 46 38 27 45 36 21 35 35 |
| correct output |
|---|
| 205 |
| user output |
|---|
| 205 |
Test 9
Group: 2, 3
Verdict: ACCEPTED
| input |
|---|
| 93 38 35 26 43 54 38 25 41 34 |
| correct output |
|---|
| 222 |
| user output |
|---|
| 222 |
Test 10
Group: 2, 3
Verdict: ACCEPTED
| input |
|---|
| 100 33 33 45 36 43 38 54 56 36 |
| correct output |
|---|
| 242 |
| user output |
|---|
| 242 |
Test 11
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 3419 1797 1845 1849 1879 1791 ... |
| correct output |
|---|
| 5959 |
| user output |
|---|
| 5959 |
Test 12
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 4776 2695 2709 2781 2616 2753 ... |
| correct output |
|---|
| 8391 |
| user output |
|---|
| 8391 |
Test 13
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 20097 12282 12229 12214 12406 ... |
| correct output |
|---|
| 32001 |
| user output |
|---|
| 32001 |
Test 14
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 47934 29918 29878 29713 29984 ... |
| correct output |
|---|
| 71718 |
| user output |
|---|
| 71718 |
Test 15
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 84691 54156 54277 54533 54296 ... |
| correct output |
|---|
| 123123 |
| user output |
|---|
| 123123 |
Test 16
Group: 3
Verdict: ACCEPTED
| input |
|---|
| 99098 63339 63878 64182 63904 ... |
| correct output |
|---|
| 142663 |
| user output |
|---|
| 142663 |