[HihoCoder]#1360 : 凸多边形

华电北风吹
天津大学认知计算与应用重点实验室
2016-08-14

题目链接：
http://hihocoder.com/problemset/problem/1360

题目分析：
动态规划，思路参考Floyd解决所有节点对的最短路径类型的动态规划。

参考代码：

#include 
#include 
#include 
#include 
using namespace std;

#define Length 105

struct Point
{
    int x, y;
};
int N, M;
Point point[Length];
double tringleSize[Length][Length][Length], state[Length][Length][Length];

double CalculateTringle(int i, int j, int k)
{
    return 0.5*(point[i].x * point[j].y + point[j].x * point[k].y + point[k].x * point[i].y - point[i].x * point[k].y - point[j].x * point[i].y - point[k].x * point[j].y);
}

int main()
{
    cin >> N >> M;
    for (int i = 0; i < N; i++)
    {
        cin >> point[i].x >> point[i].y;
    }
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            for (int k = 0; k < N; k++)
            {
                tringleSize[i][j][k] = abs(CalculateTringle(i, j, k));
            }
        }
    }
    memset(state, 0, sizeof(state));
    for (int k = 3; k <= M; k++)
    {
        for (int i = 0; i < N; i++)
        {
            for (int j = i + 1; j != i; j = (j + 1) % N)
            {
                for (int u = i + 1; u != j; u = (u + 1) % N)
                {
                    state[i][j][k] = max(state[i][j][k], state[i][u][k - 1] + tringleSize[u][j][i]);
                }
            }
        }
    }
    double result = 0;
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
        {
            result = max(result, state[i][j][M]);
        }
    }
    cout << fixed << setprecision(2) << result << endl;
    return 0;
}