uva10201-dp

题意：

租了一俩车从城市A到城市B，开始有100L油，油箱总共可以装200L油，行驶1KM要1L油，路上有加油站，离A有不同的距离，每升油价格不同。

问，到城市B油箱还有100L油，最少的花费是多少。

dp[i][j] 表示在站点 i 有油 j 时的最小花费。那么

dp[i][j] = min(dp[i-1][j+d[i]],dp[i][j]),d[i] 表示 i-1到i的距离。

dp[i][j]有俩个来源，一个是从dp[i-1][j+d[i]]，dp[i][j]表示在站点i加油到j 的花费。

import java.io.ByteArrayInputStream;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class Main
{
    static Scanner scanner;

    final static int G = 110;
    // final static int G = 8;
    final static int T = 206;
    // final static int N = 5;
    // dij表示在i站点gas是j的时候最小花费
    static int[][] dp = new int[G][T];
    static int dis;
    static int[] sd = new int[G];
    static int[] sp = new int[G];
    static int[] disSum = new int[G];
    static int gt;
    static int INF = Integer.MAX_VALUE;
    static int maxDis = -1;
    static int tt = 1;

    public static void main(String[] args) throws FileNotFoundException
    {
         scanner = new Scanner(System.in);
        //scanner = new Scanner(new File("/Users/caicai/in"));
        String str = scanner.nextLine();
        int val = Integer.valueOf(str);
        // empty line
        tt = 1;
        while (val-- != 0)
        {
            gt = 1;
            maxDis=-1;
            dis = scanner.nextInt();
            sd[0] = 0;
            sp[0] = 0;
            int preDis = 0;
            str = scanner.nextLine();
            while (scanner.hasNextLine())
            {
                // split
                str = scanner.nextLine();
                if (str.isEmpty())
                {
                    break;
                }
                ByteArrayInputStream si = new ByteArrayInputStream(str.getBytes());
                Scanner scanner2 = new Scanner(si);
                int diss = scanner2.nextInt();
                int price = scanner2.nextInt();
                scanner2.close();
                if (diss > dis) continue;
                sd[gt] = diss - preDis;
                preDis = diss;
                sp[gt] = price;
                ++gt;
                if (diss > maxDis) maxDis = diss;
            }
            // dp
            dp();

        }
    }

    static void init()
    {
        for (int i = 0; i < G; i++)
        {
            for (int j = 0; j < T; j++)
            {
                if (i == 0 || j == 0) dp[i][j] = INF - 1;
                else
                    dp[i][j] = INF;
            }
        }

    }

    static void dp()
    {
        init();
        if (sd[1] > 100)
        {
            if (tt != 1) System.out.println();
            System.out.println("Impossible");
            ++tt;
            return;
        }
        dp[1][100 - sd[1]] = 0;
        // 多余的gas
        int h = 100 - sd[1];
        for (int i = h; i >= 0; i--)
        {
            dp[1][i] = (h - i) * -1 * sp[1];
        }
        for (int i = 1; i < gt; i++)
        {
            for (int j = 0; j <= 200; j++)
            {
                // 当前的站点gas是j
                int diss = sd[i];
                if (diss + j > 200 || dp[i - 1][diss + j] == INF)
                {
                    continue;
                }
                dp[i][j] = Math.min(dp[i - 1][diss + j], dp[i][j]);
                for (int k = j + 1; k <= 200; k++)
                {
                    // 当前站点加到k气要的钱
                    int curPrice = sp[i] * (k - j) + dp[i][j];
                    dp[i][k] = Math.min(dp[i][k], curPrice);
//                    if (diss + k > 200) continue;
//                    int preCurPrice = dp[i - 1][diss + k];
//                    dp[i][k] = Math.min(dp[i][k], preCurPrice);
                }
            }
        }
        // check val
        int half = 100;
        // 检查最后一个站点
        int lastDis = dis - maxDis;
        int gas = lastDis + half;
        if (gas > 200 || dp[gt - 1][gas] == INF)
        {
            if (tt != 1) System.out.println();
            System.out.println("Impossible");
            ++tt;
            return;
        }
        else
        {
            if (tt != 1) System.out.println();
            ++tt;
            System.out.println(dp[gt - 1][gas]);
        }
    }

}