【SGU】116. Index of super-prime 完全背包

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题目分析：好久没写背包题了，本题只要预处理出超级素数，然后做完全背包，同时记录路径即可。

代码如下：

#include <map>#include <vector>#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>using namespace std ;typedef long long LL ;#define rep( i , a , b ) for ( int i = ( a ) ; i <  ( b ) ; ++ i )#define For( i , a , b ) for ( int i = ( a ) ; i <= ( b ) ; ++ i )#define rev( i , a , b ) for ( int i = ( a ) ; i >= ( b ) ; -- i )#define clr( a , x ) memset ( a , x , sizeof a )#define mid ( ( l + r ) >> 1 )const int MAXN = 10005 ;const int INF = 0x3f3f3f3f ;bool prime[MAXN] ;int super_prime[MAXN] , top ;int dp[MAXN] ;int pre[MAXN] ;int a[MAXN] ;int n ;void get_prime () {int cnt = 0 ;top = 0 ;clr ( prime , 1 ) ;prime[1] = 0 ;for ( int i = 2 ; i < MAXN ; ++ i ) {if ( prime[i] ) {++ cnt ;if ( prime[cnt] ) super_prime[top ++] = i ;for ( int j = i * i ; j < MAXN ; j += i ) {prime[j] = 0 ;}}}}void solve () {clr ( dp , INF ) ;dp[0] = 0 ;rep ( i , 0 , top ) {int cost = super_prime[i] ;For ( j , cost , n ) if ( dp[j] > dp[j - cost] + 1 ) {dp[j] = dp[j - cost] + 1 ;pre[j] = j - cost ;}}if ( dp[n] == INF ) printf ( "0\n" ) ;else {int cnt = 0 , x = n ;printf ( "%d\n" , dp[n] ) ;while ( x ) {a[cnt ++] = x - pre[x] ;x = pre[x] ;}sort ( a , a + cnt ) ;rev ( i , cnt - 1 , 0 ) printf ( "%d%c" , a[i] , i ? ' ' : '\n' ) ;}}int main () {get_prime () ;while ( ~scanf ( "%d" , &n ) ) solve () ;return 0 ;}

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