UVA 1347 Tour DP

DP

dp[i][j] 前i个点已经全部走过,落后的那个人在j号点

往i+1号点转移 既 dp[i+1][i]   or   dp[i+1][j]

Tour

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

Description

John Doe, a skilled pilot, enjoys traveling. While on vacation, he rents a small plane and starts visiting beautiful places. To save money, John must determine the shortest closed tour that connects his destinations. Each destination is represented by a point in the plane p_i = < x_i, y_i > . John uses the following strategy: he starts from the leftmost point, then he goes strictly left to right to the rightmost point, and then he goes strictly right back to the starting point. It is known that the points have distinct x -coordinates.

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

Input 

The program input is from a text file. 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 are correct.

Output 

For each set of data, your program should print the result to the standard output from the beginning of a line. The tour length, a floating-point number with two fractional digits, represents the result.

Note: An input/output sample is in the table below. Here there are two data sets. The first one contains 3 points specified by their x and y coordinates. The second point, for example, has the x coordinate 2, and the y coordinate 3. The result for each data set is the tour length, (6.47 for the first data set in the given example).

Sample Input 

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

Sample Output 

6.47
7.89

Source

Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Rare Topics :: Rare Problems ::  Bitonic TSP
Root :: AOAPC II: Beginning Algorithm Contests (Second Edition) (Rujia Liu) :: Chapter 9. Dynamic Programming ::  Examples
Root :: AOAPC I: Beginning Algorithm Contests -- Training Guide (Rujia Liu) :: Chapter 1. Algorithm Design :: Dynamic Programming ::  Exercises: Intermediate

Submit Status

/* ***********************************************
Author        :CKboss
Created Time  :2015年02月07日 星期六 22时23分20秒
File Name     :UVA1347.cpp
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;

const int maxn=1111;

int n;
struct point
{
	double x,y;
}pt[maxn];

double dist(int a,int b)
{
	double dx=fabs(pt[a].x-pt[b].x);
	double dy=fabs(pt[a].y-pt[b].y);
	return sqrt(dx*dx+dy*dy);
}

double dp[maxn][maxn];

int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);

	while(scanf("%d",&n)!=EOF)
	{
		for(int i=0;i<n;i++) scanf("%lf%lf",&pt[i].x,&pt[i].y);

		for(int i=0;i<maxn;i++)
			for(int j=0;j<maxn;j++)
				dp[i][j]=(1LL<<60);

		dp[0][0]=0; dp[1][0]=dist(1,0);
		for(int i=1;i<n;i++)
		{
			for(int j=0;j<i;j++)
			{
				dp[i+1][i]=min(dp[i+1][i],dp[i][j]+dist(j,i+1));
				dp[i+1][j]=min(dp[i+1][j],dp[i][j]+dist(i,i+1));
			}
		}

		double ans=1LL<<60;
		for(int i=0;i<n;i++)
			ans=min(ans,dp[n-1][i]+dist(i,n-1));

		printf("%.2lf\n",ans);
	}
    
    return 0;
}