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The Sum of Sub-matrices
Description
Seen draw a big 3*n matrix , whose entries Ai,j are all integer numbers ( 1 <= i <= 3, 1 <= j <= n ). Now he selects k sub-matrices( each Aij only belong one sub-matrices ), hoping to find the largest sum of sub-matrices’ elements.
Input
There are multiple test cases.
For each test case, the first line contains an integer n, k (1 <= n <= 100, 1 <= k <= 5, 3 * n >= k). The next three lines with n integers each gives the elements of the matrix ( | Ai,j | <= 10000).
Output
Sample Input
Sample Output
求3*n的矩阵里面的 k个子矩阵的最大和。
对列进行状态压缩
#include <iostream> #include <cstdio> #include <cstring> #include <string> #include <cmath> #include <vector> #include <queue> #include <map> #include <set> #include <stack> #include <algorithm> using namespace std; typedef long long LL; typedef pair<int,int> pii; const int mod = 1e9+7; const int N = 105 ; const int M = 13; #define X first #define Y second int st1[M] = { 0 , 1 , 2 , 4 , 3 , 5 , 6 , 7 , 8 , 16 , 12 , 17 , 32 }; int st2[M] = { 0 , 1 , 2 , 4 , 3 , 5 , 6 , 7 , 3 , 6 , 7 , 7 , 7 }; int num[M] = { 0 , 1 , 1 , 1 , 2 , 2 , 2 , 3 , 1 , 1 , 2 , 2 , 1 }; int A[3][N] , dp[N][6][M] , n , k ; int Sum( int colum , int st ) { int res = 0 ; for( int i = 0 ; i < 3 ; ++i ) if( st&(1<<i) )res += A[i][colum]; return res ; } void Run() { memset( dp , 0x80 , sizeof dp ) ; dp[0][0][0] = 0; for( int i = 0 ; i < 3 ; ++i ) for( int j = 1 ; j <= n ; ++j ) cin >> A[i][j]; for( int i = 1 ; i <= n ; ++i ) { for( int cs = 0 ; cs < M ; ++cs ) { for( int ps = 0 ; ps < M ; ++ps ) { int w = Sum(i,st2[cs]); for( int k1 = 0 ; k1 <= k ; ++k1 ) { int low = num[cs] , up = num[cs] ; for( int z = 0 ; z < 6 ; ++z ) if( st1[cs] & st1[ps] &(1<<z) ) low--; for( int k2 = low ; k1 + k2 <= k && k2 <= up ; ++k2 ){ dp[i][k1+k2][cs] = max( dp[i][k1+k2][cs] , dp[i-1][k1][ps] + w ); } } } } } cout << *max_element( dp[n][k] , dp[n][k]+M ) << endl ; } int main(){ #ifdef LOCAL freopen("in.txt","r",stdin); #endif // LOCAL ios::sync_with_stdio(false); while( cin >> n >> k )Run(); }
FZU 2060 The Sum of Sub-matrices(状态压缩DP)
标签:des style blog http ar io color os sp
原文地址:http://www.cnblogs.com/hlmark/p/4168443.html