Task: | Kortit II |
Sender: | Pikaksi |
Submission time: | 2024-10-31 17:56:36 +0200 |
Language: | C++ (C++20) |
Status: | READY |
Result: | 100 |
group | verdict | score |
---|---|---|
#1 | ACCEPTED | 3 |
#2 | ACCEPTED | 5 |
#3 | ACCEPTED | 26 |
#4 | ACCEPTED | 28 |
#5 | ACCEPTED | 38 |
test | verdict | time | group | |
---|---|---|---|---|
#1 | ACCEPTED | 0.05 s | 1, 2, 3, 4, 5 | details |
#2 | ACCEPTED | 0.05 s | 2, 3, 4, 5 | details |
#3 | ACCEPTED | 0.05 s | 3, 4, 5 | details |
#4 | ACCEPTED | 0.05 s | 4, 5 | details |
#5 | ACCEPTED | 0.11 s | 5 | details |
#6 | ACCEPTED | 0.13 s | 5 | details |
Code
#include <bits/stdc++.h>using namespace std;typedef long long ll;const ll ansMod = 1000000007;const int cacheSize = 2002;ll aCache[cacheSize][cacheSize];ll binomCache[cacheSize][cacheSize];// a(n+1, r) = r*a(n, r) + (n+1-r)*a(n, r-1) + n*a(n-1, r-1)ll a(ll n, ll r){if (r >= n) {return 0;}if (n - 1 == r || r == 1) {return 1;}n -= 1;ll cacheAns = aCache[n][r];if (cacheAns != -1) {return cacheAns;}ll ans =((r * a(n, r)) % ansMod)+ (((n + 1 - r) * a(n, r - 1)) % ansMod)+ ((n * a(n - 1, r - 1)) % ansMod) % ansMod;aCache[n][r] = ans;return ans;}ll binomRecursive(ll n, ll k){if (k > n) {return 0;}if (k == 0 || k == n) {return 1;}ll cacheAns = binomCache[n][k];if (cacheAns != -1) {return cacheAns;}ll ans = ((binomRecursive(n - 1, k - 1) % ansMod) + (binomRecursive(n - 1, k) % ansMod)) % ansMod;binomCache[n][k] = ans;return ans;}ll factorial(ll a){if (a == 0) {return 1;}ll b = a;for (int i = 2; i < b; i++) {a = a * i % ansMod;}return a;}void SolveCase(int cards, int p1, int p2){int draws = cards - p1 - p2;string ans1;string ans2;if (p1 + p2 > cards) {cout << "0\n";return;}if ((p1 > 0 && p2 == 0) || (p2 > 0 && p1 == 0)) {cout << "0\n";return;}ll ans = binomRecursive(cards, draws);//cout << binomRecursive(cards, draws) << "\n";ans %= ansMod;ans *= ans;ans %= ansMod;ans *= factorial(draws);//cout << factorial(draws) << "\n";ans %= ansMod;ans *= factorial(p1 + p2);//cout << factorial(p1 + p2) << "\n";ans %= ansMod;if (p1 != 0 || p2 != 0) {ll bigger = max(p1, p2);ll smaller = min(p1, p2);ans *= a(bigger + smaller, smaller);}//cout << p1 << " " << p2 << " " << a(bigger + smaller, smaller) << "\n";ans %= ansMod;cout << ans << "\n";}int main(){ios_base::sync_with_stdio(0);cin.tie(0);for (int x = 0; x < cacheSize; x++) {for (int y = 0; y < cacheSize; y++) {aCache[x][y] = -1;binomCache[x][y] = -1;}}/*for (int i = 0; i < C; i++) {comparison[i] = i + 1;}int test[C];for (int i = 0; i < C; i++) {test[i] = 0;}testBruteForce(test);cout << globalCount << "\n";cout << playerWinCombinations(g_p1, g_p2) << "\n";return 0;*///SolveCase(9, 3, 5);//return 0;int n;cin >> n;vector<int> input1, input2, input3;for (int i = 0; i < n; i++) {int a, b, c;cin >> a >> b >> c;input1.push_back(a);input2.push_back(b);input3.push_back(c);}for (int i = 0; i < n; i++) {SolveCase(input1[i], input2[i], input3[i]);}}/*draw possibilities:cardsdrawslocation combinations of victories and draws:(draws)_cardsCombinations for draws not placement:draws!Combinations for victory positions in list:(victories)_p1Combinations for ordering p1 and p2 wins seperately wins:p1! * p2!current best: binom(c; d)*binom(c; d)*d!*binom(p1+p2;p1)*p1!*p2!*binom(p1+p2;p1)better:binom(c; d)*binom(c; d)*d!*(p1+p2)!*3361*//*const int g_p1 = 7;const int g_p2 = 4;const int C = g_p1 + g_p2;int comparison[C];int globalCount = 0;// T\left(n{,}k\right)=\sum_{j=0}^n\binom{-j-1}{-n-1}\cdot eulerian1(j{,}k)// T\left(n{,}k\right)=\sum_{u=0}^k(-1)^u\cdot\binom{n+1}{u}\cdot(k+1-u)^n// T\left(n{,}k\right)=\sum_{j=0}^n\left(\binom{-j-1}{-n-1}\cdot\sum_{u=0}^k\left((-1)^u\cdot\binom{j+1}{u}\cdot(k+1-u)^n\right)\right)ll factorial(ll a){if (a == 0) {return 1;}ll negative = 1;if (a < 0) {if (a & 1) {negative = -1;}a *= -1;}ll aCopy = a;for (ll i = 1; i < aCopy; i++) {a *= i;}return a * negative;}ll binomial(ll a, ll b){if (a < 0) {if (b >= 0) {return pow(-1, b) * binomial(b - a - 1, b);}return pow(-1, a - b) * binomial(-b - 1, a - b);}ll a1 = factorial(a);ll a2 = factorial(b);ll a3 = factorial(a - b);//cout << "binom a1 " << a1 << " a2 " << a2 << " a3 " << a3 << "\n";return a1 / (a2 * a3);}ll BinomialCoeffient(ll n, ll k){if (k > n)return 0;ll c = n;for (ll i = 1; i < k; i++){c *= n - i;c /= i + 1;}return c;}ll eulerian(ll n, ll k) {ll ans = 0;for (ll j = 0; j < k + 1; j++) {ll loopAns = pow(-1LL, j);loopAns *= BinomialCoeffient(n + 1, j) % ansMod;loopAns *= pow(k + 1 - j, n);ans += loopAns;}return ans;}ll playerWinCombinations(ll n, ll k){if (n < 2 || k < 2) {return 1;}n += k - 2;if (k > n) {ll temp = n;n = k;k = temp;}n += 2;ll ans = 0;for (ll j = 0; j < n + 1; j++) {ll E1 = eulerian(j, k);E1 *= binomial(-j - 1, -n - 1);ans += E1;ans %= ansMod;}return ans;}bool containsNumber(int numbersUsed[C], int number){for (int i = 0; i < C; i++) {if (numbersUsed[i] == number) {return true;}}return false;}void testBruteForce(int numbersUsed[C]){cout << "called with ";for (int i = 0; i < C; i++) {cout << numbersUsed[i];}cout << "\n";bool allUsed = true;for (int i = 0; i < C; i++) {if (numbersUsed[i] == 0) {allUsed = false;for (int newNum = 1; newNum < C + 1; newNum++) {if (comparison[i] != newNum && !containsNumber(numbersUsed, newNum)) {numbersUsed[i] = newNum;testBruteForce(numbersUsed);}}numbersUsed[i] = 0;break;}}if (!allUsed) {return;}int larger = 0, smaller = 0;for (int i = 0; i < C; i++) {if (numbersUsed[i] < comparison[i]) {smaller++;}else if (numbersUsed[i] > comparison[i]) {larger++;}}if (smaller == g_p1 && larger == g_p2) {globalCount++;}}*/
Test details
Test 1
Group: 1, 2, 3, 4, 5
Verdict: ACCEPTED
input |
---|
54 4 4 0 3 1 3 3 2 2 4 0 4 ... |
correct output |
---|
0 0 0 0 0 ... |
user output |
---|
0 0 0 0 0 ... |
Test 2
Group: 2, 3, 4, 5
Verdict: ACCEPTED
input |
---|
284 6 1 0 5 0 2 7 1 5 7 7 5 ... |
correct output |
---|
0 0 35280 0 36720 ... |
user output |
---|
0 0 35280 0 36720 ... |
Test 3
Group: 3, 4, 5
Verdict: ACCEPTED
input |
---|
841 19 3 12 19 19 13 19 7 13 20 11 15 ... |
correct output |
---|
40291066 0 0 0 0 ... |
user output |
---|
40291066 0 0 0 0 ... |
Test 4
Group: 4, 5
Verdict: ACCEPTED
input |
---|
1000 15 12 6 7 1 6 44 4 26 6 6 5 ... |
correct output |
---|
0 5040 494558320 0 340694548 ... |
user output |
---|
0 5040 494558320 0 340694548 ... |
Test 5
Group: 5
Verdict: ACCEPTED
input |
---|
1000 892 638 599 966 429 655 1353 576 1140 1403 381 910 ... |
correct output |
---|
0 0 0 249098285 0 ... |
user output |
---|
0 0 0 249098285 0 ... |
Test 6
Group: 5
Verdict: ACCEPTED
input |
---|
1000 2000 1107 508 2000 1372 249 2000 588 65 2000 1739 78 ... |
correct output |
---|
750840601 678722180 744501884 159164549 868115056 ... |
user output |
---|
750840601 678722180 744501884 159164549 868115056 ... |