标签:style blog io ar for 2014 sp log on
题目:从1~n去若干个数字,使得他们的最小公倍数不小于M的有多少种。
分析:dp,数论,搜索。其实就是一个背包类似物。(貌似离散化dp写起来很简洁)
由于每个素数因子的个数有限(不超过20个)直接打表(dfs)计算出所有的最小公倍数;
然后DP更行最小公倍数即可;
这个题目要做一些优化(囧,TLE一次):
首先,二分查找,找到要更新的公倍数对应的位置;再次,就是把结果打表,然后每次求和即可。
说明:在比赛进行了2:30小时之后,我们终于A掉了第一道题,随即我终于找到了这个题的bug并将它A了;
原来是二分的上界 写成了36863.。。囧少写了一个WA半天。(2011-09-19 01:02)。
#include <stdio.h> #include <stdlib.h> #include <math.h> long long Lcm[ 42 ]; long long Pri[ 12 ] = {2,3,5,7,11,13,17,19,23,29,31,37}; long long Num[ 12 ] = {5,3,2,1,1,1,1,1,1,1,1,1}; long long Sav[ 36880 ]; long long Count = 0; long long F[ 42 ][ 36880 ]; long long gcd( long long a, long long b ) { return a%b?gcd( b, a%b ):b; } long long lcm( long long a, long long b ) { return a/gcd( a, b )*b; } void dfs( int s, long long v ) { if ( s == 12 ) Sav[ Count ++ ] = v; else for ( int i = 0 ; i <= Num[ s ] ; ++ i ) { long long save = 1LL; for ( int j = 0 ; j < i ; ++ j ) save *= Pri[ s ]; dfs( s+1, v*save ); } } int cmp( const void* a, const void* b ) { long long *p = (long long *)a; long long *q = (long long *)b; if ( *p < *q ) return -1; else return 1; } int search( long long V ) { int m,l = 1,h = 36864; while ( l < h ) { m = (l+h+1)>>1; if ( Sav[ m ] > V ) h = m-1; else l = m; } return h; } int main() { Lcm[ 1 ] = 1; for ( int i = 2 ; i <= 40 ; ++ i ) Lcm[ i ] = lcm( Lcm[ i-1 ], i ); Count = 0LL; dfs( 0, 1LL ); qsort( Sav, Count+1, sizeof( long long ), cmp ); for ( int i = 1 ; i <= 40 ; ++ i ) for ( int j = 0 ; j <= Count ; ++ j ) F[ i ][ j ] = 0LL; for ( int i = 1 ; i <= 40 ; ++ i ) { for ( int j = 1 ; j <= Count ; ++ j ) F[ i ][ j ] = F[ i-1 ][ j ]; for ( int j = 1 ; j <= Count ; ++ j ) F[ i ][ search( lcm( Sav[ j ], i ) ) ] += F[ i-1 ][ j ]; F[ i ][ i ] += 1LL; } long long T,N,M; while ( ~scanf("%I64d",&T) ) for ( int t = 1 ; t <= T ; ++ t ) { scanf("%I64d%I64d",&N,&M); int V = search( Lcm[ N ] ); long long sum = 0LL; for ( int i = 1 ; i <= V ; ++ i ) if ( Sav[ i ] >= M ) sum += F[ N ][ i ]; printf("Case #%d: %I64d\n",t,sum); } return 0; }
标签:style blog io ar for 2014 sp log on
原文地址:http://blog.csdn.net/mobius_strip/article/details/39429937