PKU 2137 - Cowties (DP)

题意

每个牛有几个适合的位置,选一个,让连起来的环形最短。

思路

今天又学到了一招,如果是环形的枚举起点会较简洁。

$dp[i][j] = dp[i-1][k] + Dis(i-1, k, i, j)$

代码

#include <stack>
#include <cstdio>
#include <list>
#include <cassert>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#include <string>
#include <map>
#include <cmath>
using namespace std;
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(arr, num) memset(arr, num, sizeof(arr))
#define PB push_back
#define X first
#define Y second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 100 + 10;
const int MOD = 9901;
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
int cases = 0;
typedef pair<int, int> pii;
 
vector<pii> G[MAXN];
double dp[MAXN][50];
 
double Dis(int a, int apos, int b, int bpos)
{
    int x = G[a][apos].X - G[b][bpos].X;
    int y = G[a][apos].Y - G[b][bpos].Y;
    return sqrt(x*x + y*y);
}
 
int main()
{
    //ROP;
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
    {
        int tmp;
        scanf("%d", &tmp);
        for (int j = 0; j < tmp; j++)
        {
            int a, b;
            scanf("%d%d", &a, &b);
            G[i].PB(MP(a, b));
        }
    }
    double ans = INF;
    for (int i = 0; i < 50; i++) dp[1][i] = INF;
    for (int st = 0; st < SZ(G[1]); st++)    //枚举起点
    {
        dp[1][st] = 0;
        for (int i = 2; i <= n; i++)
            for (int j = 0; j < SZ(G[i]); j++)
            {
                dp[i][j] = INF;
                for (int k = 0; k < SZ(G[i-1]); k++)
                    dp[i][j] = min(dp[i][j], dp[i-1][k] + Dis(i-1, k, i, j));
            }
        for (int i = 0; i < SZ(G[n]); i++)
            ans = min(ans, dp[n][i] + Dis(n, i, 1, st));
        dp[1][st] = INF;
    }
    printf("%d\n", (int)(ans*100));
    return 0;
}

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