You are going on a long trip You start on the road at mile post 0 Along the way there are n hotels, at mile posts a1 a2 an, where each ai is measured from the starting point The only places you are allowed to stop are at these hotels, but you can choose which of the hotels you stop at You must stop at the final hotel (at distance an), which is your destination You'd ideally like to travel 200 miles a day, but this may not be possible (depending on the spacing of the hotels) If you travel x miles during a day, the penalty for that day is (200 x)2 You want to plan your trip so as to minimize the total penalty that is, the sum, over all travel days, of the daily penalties Give an efficient algorithm that determines the optimal sequence of hotels at which to stop Here is the input file 66 83 99 104 109 164 263 266 276 306 337 343 418 432 462 489 558 590 620 672 719 741 752 823 919 977 994 1004 1086 1088 1117 1130 1219 1245 1289 1357 1436 1519 1525 1560 1597 1678 1703 1795 1885 1921 1976 2012 2046 2126 2209 2261 2355 2403 2478 2559 2605 2704 2758 2796 2859 2881 2957 2998 3076 3098 3188 3232 3260 3334 3427 3524 3596 3611 3646 3722 3764 3790 3863 3867 3932 3993 4001 4026 4094 4156 4199 4228 4271 4355 4386 4454 4551 4559 4578 4674 4735 4746 4833 4905 Your program should read in a file like the above and create a corresponding output file, HW1Output txt, that lists the mile posts of an optimal trip from the 0 mile post to the final mile post, along with the total penalty that has accumulated at each stop (It should look like this) Distance 0 Total Penalty 0 Distance 164 Total Penalty 1296 Distance 343 Total Penalty 1737 Distance 558 Total Penalty 1962 Distance 741 Total Penalty 2251 Distance 919 Total Penalty 2735 Distance 4735 Total Penalty 8639 Distance 4905 Total Penalty 9539 With one hundred or more stops to consider, it is impossible for the program to finish in a reasonable amount of time if it uses a straightforward brute force search that explicitly considers every possible combination of stops For this assignment, you are required to use a dynamic programming solution Your program (in Java) should be flexible enough to handle input files of various lengths (I would recommend using an ArrayList)

Question

You are going on a long trip  You start on the road at mile post 0  Along the way there are n hotels, at mile posts a1   a2     an, where each ai is measured from the starting point  The only places you are allowed to stop are at these hotels, but you can choose which of the hotels you stop at  You must stop at the final hotel (at distance an), which is your destination  You'd ideally like to travel 200 miles a day, but this may not be possible (depending on the spacing of the hotels)  If you travel x miles during a day, the penalty for that day is (200   x)2   You want to plan your trip so as to minimize the total penalty   that is, the sum, over all travel days, of the daily penalties  Give an efficient algorithm that determines the optimal sequence of hotels at which to stop  Here is the input file  66 83 99 104 109 164 263 266 276 306 337 343 418 432 462 489 558 590 620 672 719 741 752 823 919 977 994 1004 1086 1088 1117 1130 1219 1245 1289 1357 1436 1519 1525 1560 1597 1678 1703 1795 1885 1921 1976 2012 2046 2126 2209 2261 2355 2403 2478 2559 2605 2704 2758 2796 2859 2881 2957 2998 3076 3098 3188 3232 3260 3334 3427 3524 3596 3611 3646 3722 3764 3790 3863 3867 3932 3993 4001 4026 4094 4156 4199 4228 4271 4355 4386 4454 4551 4559 4578 4674 4735 4746 4833 4905 Your program should read in a file like the above and create a corresponding output file, HW1Output txt, that lists the mile posts of an optimal trip from the 0 mile post to the final mile post, along with the total penalty that has accumulated at each stop (It should look like this)  Distance  0 Total Penalty  0 Distance  164 Total Penalty  1296 Distance  343 Total Penalty  1737 Distance  558 Total Penalty  1962 Distance  741 Total Penalty  2251 Distance  919 Total Penalty  2735 Distance  4735 Total Penalty  8639 Distance  4905 Total Penalty  9539 With one hundred or more stops to consider, it is impossible for the program to finish in a reasonable amount of time if it uses a straightforward brute force search that explicitly considers every possible combination of stops  For this assignment, you are required to use a dynamic programming solution Your program (in Java) should be flexible enough to handle input files of various lengths (I would recommend using an ArrayList)

Accepted Answer

The Answer is in the image, click to view ...

Question

You are going on a long trip. You start on the road at mile post 0. Along the way there are n hotels, at mile

Step by Step Solution

Step: 1

Get Instant Access to Expert-Tailored Solutions

Step: 2

Step: 3

Ace Your Homework with AI