ZOJ 2581 Tour

Tour

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Time Limit: 2 Seconds    Memory Limit: 65536 KB

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John Doe, a skilled pilot, enjoys traveling. While on vacation,he rents a small plane and starts visiting beautiful places. Tosave money, John must determine the shortest closed tour thatconnects his destinations. Each destination is represented by apoint in the plane pi = . John uses the following strategy: hestarts from the leftmost point, then he goes strictly left to rightto the rightmost point, and then he goes strictly right back to thestarting point. It is known that the points have distinctx-coordinates.

Write a program that, given a set of n points in the plane,computes the shortest closed tour that connects the oints accordingto John's strategy.

Input

Each data set in the file stands for a particular set of points.For each set of points the data set contains the number of points,and the point coordinates in ascending order of the x coordinate.White spaces can occur freely in input. The input data arecorrect.

Output

For each set of data, your program should print the result tothe standard output from the beginning of a line. The tour length,a floating-point number with two fractional digits, represents theresult. An input/output sample is in the table below. Here thereare two data sets. The first one contains 3 points specified bytheir x and y coordinates. The second point, for example, has the xcoordinate 2, and the y coordinate 3. The result for each data setis the tour length, (6.47 for the first data set in the givenexample).

Sample Input

3
1 1
2 3
3 1
4
1 1
2 3
3 1
4 2

Sample Output

6.47
7.89

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Source: Southeastern Europe 2005
源码：


解题报告：
首先需理解题意：从最左边一个点一直走到最右边一个点且严格按照从左到右的顺序，再从最右一个点一直走到最最左一个点且严格按照从右到左的顺序。
这是一个欧几里得旅行商问题，
dp[i][j]  表示从1到i再从j到1的距离和
建立递推关系：
    dp[i+1][j]=min(dp[i+1][j],dp[i][j]+dist[i][i+1]); 添加一个i+1先刷新dp[i+1][j]的值
    dp[i+1][i]=min(dp[i+1][i],dp[i][j]+dist[j][i+1]); 要么将i+1与i连，要么将i+1和j连 
最后再从j中挑出一个最大的连接j和n