文章目錄

• T1：Sequence
• • title
  • solution
• T2：Bamboo Partition
• • title
  • solution
  • code

T1：Sequence

title

傳送

solution

一眼就是很裸的矩陣加速
$?\frac{p}{l}?$分塊矩陣加速就可以了
$$?\begin{array}{c}B\\ A\\ 1\end{array}?\times ?\begin{array}{ccc}D& C& ?\frac{p}{l}?\\ 0& 1& 0\\ 0& 0& 1\end{array}?$$
這道題唯一算得上是坑的應該是$n,p$的大小，當$p/l==0$直接矩陣加速到底即可，注意$r$不能超過$n$
## code

#include <cstdio> #include <cstring> #include <iostream> using namespace std; #define ll long long #define mod 1000000007 struct Matrix {ll c[5][5];void init() {memset( c, 0, sizeof( c ) );}Matrix operator * ( const Matrix &a ) {Matrix ans;ans.init();for( int i = 1;i <= 3;i ++ )for( int j = 1;j <= 3;j ++ )for( int k = 1; k <= 3;k ++ )ans.c[i][j] = ( ans.c[i][j] + c[i][k] * a.c[k][j] ) % mod;return ans;} }V; ll T, A, B, C, D, P, n; ll ans1, ans2;Matrix qkpow( Matrix a, int b ) {Matrix ans;ans.init();for( int i = 1;i <= 3;i ++ ) ans.c[i][i] = 1;while( b ) {if( b & 1 ) ans = ans * a;a = a * a;b >>= 1;}return ans; }signed main() {scanf( "%lld", &T );while( T -- ) {scanf( "%lld %lld %lld %lld %lld %lld", &A, &B, &C, &D, &P, &n );if( n == 1 ) { printf( "%lld\n", A ); continue; }if( n == 2 ) { printf( "%lld\n", B ); continue; }ans1 = B, ans2 = A;for( int l = 3, r;l <= n;l = r + 1 ) {if( P / l == 0 ) {V.init();V.c[1][1] = D, V.c[1][2] = C;V.c[2][1] = V.c[3][3] = 1;V = qkpow( V, n - l + 1 );ans1 = ( V.c[1][1] * ans1 % mod + V.c[1][2] * ans2 % mod + V.c[1][3] ) % mod;ans2 = ( V.c[2][1] * ans1 % mod + V.c[2][2] * ans2 % mod + V.c[2][3] ) % mod;break;}r = min( n, P / ( P / l ) );V.init();V.c[1][1] = D, V.c[1][2] = C, V.c[1][3] = P / l;V.c[2][1] = V.c[3][3] = 1;V = qkpow( V, r - l + 1 );ll newans1 = ( V.c[1][1] * ans1 % mod + V.c[1][2] * ans2 % mod + V.c[1][3] ) % mod;ll newans2 = ( V.c[2][1] * ans1 % mod + V.c[2][2] * ans2 % mod + V.c[2][3] ) % mod;ans1 = newans1, ans2 = newans2;}printf( "%lld\n", ans1 );} return 0; }

T2：Bamboo Partition

title

傳送門

solution

$$\sum _{i=1}^{n}d?((a_i?1)\%d+1)\le k$$
$$=\sum _{i=1}^{n}d?\sum _{i=1}^n(a_i?1??\frac{a_i?1}{d}??d+1)\le k$$
$$=n?d?\sum _{i=1}^n{a}_i+\sum _{i=1}^n?\frac{a_i?1}{d}??d\le k$$
$$d(n+\sum _{i=1}^n?\frac{a_i?1}{d}??d)\le k+\sum _{i=1}^n{a}_i$$
$?\frac{a_i?1}{d}?$有根號的取值，我們直接分塊即可

code

#include <cstdio> #include <iostream> using namespace std; #define N 105 #define int long long int n, k, Max, ans; int a[N];signed main() {scanf( "%lld %lld", &n, &k );for( int i = 1;i <= n;i ++ ) scanf( "%lld", &a[i] ), k += a[i], Max = max( Max, a[i] - 1 );for( int l = 1, r, sum;l <= Max;l = r + 1 ) {r = Max, sum = 0;for( int i = 1;i <= n;i ++ )if( a[i] - 1 >= l ) {sum += ( a[i] - 1 ) / l;r = min( r, ( a[i] - 1 ) / ( ( a[i] - 1 ) / l ) );}if( l <= k / ( sum + n ) ) ans = max( ans, min( k / ( sum + n ), r ) );}if( Max < k / n ) ans = max( ans, k / n );printf( "%lld", ans );return 0; }

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