Polygon game (DP), game dp

Polygon game (DP), game dp
Description

A polygon game is a single player game.NPolygon composed of vertices. Each vertex is assigned an integer, and each edge is assigned an operator "+" or "*". All edges are sequentially rounded up from 1NId.

In step 2 of the game, delete an edge.

SubsequentN-Perform the following operations in Step 1:

(1) Select an edgeEAndETwo Connected verticesV1AndV2;

(2) Replacing edges with a new vertexEAnd the two vertices connected by E.V1AndV2. The VertexV1AndV2The integer through the edgeEThe result obtained from the operation on is assigned to a new vertex.

Finally, all edges are deleted and the game ends. The game score is the integer on the remaining vertices.

Problem: Calculate the highest score for a given polygon.W(-1, 231 <W<231 ).

Input

The first line is a separate integer.N(3 ≤N≤ 18), indicating the number of vertices of a polygon (also the number of edges ). NextNLine. Each line contains an operator ("+" or "*") and an integer.V[I] (-10 <V[I] <10), indicatingIOperators andINumber of vertices.

Output

The output has only one integer, indicating the highest score.W.

Sample Input

3
+ 2
* 3
+ 1

Sample Output

9

#include<string.h>#include<stdio.h>#include<iostream>#define MAX 102using namespace std;int v[MAX];char op[MAX];int n,minf,maxf;int m[MAX][MAX][2];void minMax(int i,int s,int j){    int e[5];    int a=m[i][s][0],        b=m[i][s][1],        r=(i+s-1)%n+1,        c=m[r][j-s][0],        d=m[r][j-s][1];    if(op[r]=='+')    {        minf=a+c;        maxf=b+d;    }    else    {        e[1]=a*c;        e[2]=a*d;        e[3]=b*c;        e[4]=b*d;        minf=e[1];        maxf=e[1];        for(int k=2; k<5; k++)        {            if(minf>e[k])                minf=e[k];            if(maxf<e[k])                maxf=e[k];        }    }}int polyMax(){    for(int i=1;i<=n;i++)        for(int j=2;j<=n;j++){            m[i][j][0]=1000000;            m[i][j][1]=-1000000;        }    for(int j=2; j<=n; j++)        for(int i=1; i<=n; i++)            for(int s=1; s<j; s++)            {                minMax(i,s,j);                if(m[i][j][0]>minf)                    m[i][j][0]=minf;                if(m[i][j][1]<maxf)                    m[i][j][1]=maxf;            }    int temp=m[1][n][1];    for(int i=2; i<=n;i++)        if(temp<m[i][n][1]) temp=m[i][n][1];    return temp;}int main(){    memset(m,0,sizeof(m));    cin >> n;    getchar();    for(int i=1;i<=n;i++)    {        cin >> op[i] >> v[i];        getchar();        m[i][1][0]=m[i][1][1]=v[i];    }    cout << polyMax() <<endl;    return 0;}