This is a simple problem about string. Now a string S contains only ‘0’-‘9’. ?? wants to select a subsequence from this string. And makes this subsequence score maximum. The subsequence’s score is calculated as follows:
Score= Value – Total_Cost
The calculation of the Cost is as follows:
If the number of characters x in the subsequence is kx, And the two coefficients are ax,bx,The cost of character x calculated as follows:
$$ \left\{\begin{matrix}
cost[x]=0,kx=0\\ cost[x]=ax*(kx-1)+bx,kx\ne0
\end{matrix}\right.$$
$$TotalCost=\sum_{i=0}^{9}cost[i]$$
The calculation of the Value is as follows:
Value=0;
for(int i=1;i<=length(substr);++i){
for(int j=1;j<=length(substr);++j){
if(i!=j)
Value+=w[id[i]][id[j]];
}
}
id[i] is the position of the subsequence’s ith character in the original string,for example,if the original string is “13579”,and the subsubquence is “159”,then the array id ={1,3,5}. The w is a weight matrix.
The first line contains an integer T, denoting the number of the test cases.
For each test case, the first line contains one integers n, the length of a string.
Next line contains the string S.
Next ten lines,each line contains ai,bi,denote the char i’s(0-9) coefficients
Next is a n*n matrix w.
Limits:
T<=20,
0<=n<=100
0<=ai<=bi<=1000
0<=w[i][j]<=50
Each test output one line “Case #x: y” , where x is the case number ,staring from 1. y is the Maximum score.