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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#290352 | #6558. Allergen Testing | akshaykhandelwal | TL | 0ms | 0kb | C++20 | 2.9kb | 2023-12-24 21:20:53 | 2023-12-24 21:20:54 |
answer
#include<bits/stdc++.h>
using namespace std;
// matrix multiplication
vector<vector<__int128>> matmul(vector<vector<__int128>> &a, vector<vector<__int128>> &b){
int n = (int)a.size(), m = (int)a[0].size(), l = (int)b[0].size();
vector<vector<__int128>> ret(n, vector<__int128>());
for (int i = 0; i < n; i++){
for (int j = 0; j < l; j++){
__int128 ths = 0;
for (int k = 0; k < m; k++){
ths += a[i][k] * b[k][j];
}
ret[i].push_back(ths);
}
}
return ret;
}
vector<vector<__int128>> matexp(vector<vector<__int128>> &mat, long long k){
int n = (int)mat.size();
if (k == 0){
vector<vector<__int128>> id(n, vector<__int128>());
for (int i = 0; i < n; i++){
for (int j = 0; j < n; j++){
id[i].push_back(0);
}
id[i][i] = 1;
}
return id;
}
else if (k%2){
vector<vector<__int128>> w = matexp(mat, k - 1);
return matmul(w, mat);
}
else{
vector<vector<__int128>> w = matexp(mat, k/2);
return matmul(w, w);
}
}
int main(){
ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
long long x = 60, d = 300000;
vector<vector<__int128>> dp(x + 1, vector<__int128>(d + 1, 0));
vector<vector<__int128>> c(x + 1, vector<__int128>(x + 1, 0));
c[0][0] = 1;
for (int i = 0; i <= d; i++) dp[0][i] = 1;
long long p = 1;
for (int i = 1; i <= x; i++) {
c[i][0] = 1;
for (int j = 1; j <= x; j++) {
c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
}
p *= 2;
dp[i][1] = p;
for (int j = 2; j <= d; j++) {
for (int y = 0; y <= i; y++) {
dp[i][j] += dp[i - y][j - 1] * c[i][y];
}
}
}
int t;
cin >> t;
while (t--) {
long long n, dd;
cin >> n >> dd;
if (n == 1) {
cout << 0 << '\n';
continue;
}
if (dd <= d) {
for (long long i = 1; i <= x; i++) {
if (dp[i][dd] >= n) {
cout << i << '\n';
break;
}
}
}
else {
vector<vector<__int128>> v = {{1}, {2}, {4}, {8}};
vector<vector<__int128>> mat = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}};
mat = matexp(mat, dd - 1);
v = matmul(mat, v);
if (v[1][0] >= n) {
cout << 1 << '\n';
continue;
}
if (v[2][0] >= n) {
cout << 2 << '\n';
continue;
}
if (v[3][0] >= n) {
cout << 3 << '\n';
continue;
}
cout << 4 << '\n';
}
}
return 0;
}
Details
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Test #1:
score: 0
Time Limit Exceeded
input:
1 4 1