{
  "id": 21587,
  "title": "full leak",
  "url": "/competitions/expedia-hotel-recommendations/discussion/21587",
  "author_name": "",
  "post_date": "2016-06-11T03:26:42.033Z",
  "votes": 4,
  "comment_count": 2,
  "views": 1014,
  "content": "<p>You can obtain almost full map of hotels and cities exactly to better than 3.2 meter accuracy, without\nneeding any extra data and just mantain arbitrary lat long up to some unknown rotation to the real \nworld lat long. \nObtain also the overlapping relations between the destinations because you can match the hotels by coords.\nEarth radius deducted from grid search: 3963.0000 miles (strange choice??)\nComputations was started initially from all the destinations who have \nmaximum ONE length of distance from any city. These are candidate for being &quot;single hotels&quot;\ntop 5 by number of cities pointed by:</p>\n\n<p>dest 43062 htmax= 1 ndist= 111 ncty= 111 nhit= 246</p>\n\n<p>dest 3789 htmax= 1 ndist= 137 ncty= 137 nhit= 287</p>\n\n<p>dest 3470 htmax= 1 ndist= 121 ncty= 121 nhit= 309</p>\n\n<p>dest 25174 htmax= 1 ndist= 146 ncty= 146 nhit= 310</p>\n\n<p>dest 9703 htmax= 1 ndist= 72 ncty= 72 nhit= 600</p>\n\n<p>dest 21063 htmax= 1 ndist= 213 ncty= 213 nhit= 617</p>\n\n<p>dest 33865 htmax= 1 ndist= 115 ncty= 115 nhit= 759</p>\n\n<p>dest 48752 htmax= 1 ndist= 279 ncty= 279 nhit= 826</p>\n\n<p>The destinations (single hotels) i started with were :</p>\n\n<p>h1=25174,</p>\n\n<p>h2=33865,</p>\n\n<p>h3=48752</p>\n\n<p>Then pick the cities c1,c2,c3 that have the following distance matrix  to the above 3\nhotels</p>\n\n<p>e(c1,h1)= 1371.0242 e(c1,h2)= 1680.7709 e(c1,h3)= 1022.7044</p>\n\n<p>e(c2,h1)=  710.2743 e(c2,h2)= 1767.2299 e(c2,h3)= 1446.413</p>\n\n<p>e(c3,h1)= 2140.0445 e(c3,h2)= 1084.3085 e(c3,h3)= 1768.1506</p>\n\n<p>(with e(a,b) i note the spherical distance on the sphere in miles)</p>\n\n<p>knowing radius R (you will do gridsearch later to the 3963 value)\nyou obtain a nonlinear system that has at most 16 full real solutions \n(and many more complex) for a 3x3 distance matrix\nbut there are 4 symmetries so there are at most 4 distinct full real solutions <br>\nbut usually only at most 2-3 converge to 100 decimals (i used mpfr).\nmatching with full tethraedrons to other city and hotels you select the correct \nbase solution with 3 further single hotels h4,h5,h6 which have each 3 distances \nwith c1,c2,c3 and six further cities c4,c5,c6,c7,c8,c9 which have each \n3 distances with h1,h2,h3\nso you obtain accurate to 4 decimals:</p>\n\n<p>e(c1,c2)= 803.595455 e(c1,c3)= 883.753673 e(c2,c3)= 1452.09340</p>\n\n<p>e(h1,h2)= 2441.36694 e(h1,h3)= 1561.38509 e(h2,h3)= 2697.01204</p>\n\n<p>choose h4 to have known</p>\n\n<p>e(c1,h4)  1375.3989</p>\n\n<p>e(c2,h4)   710.6864</p>\n\n<p>e(c3,h4)  2142.2537</p>\n\n<p>choose h5 to have known</p>\n\n<p>e(c1,h5)  1036.4751</p>\n\n<p>e(c2,h5)  1473.8628</p>\n\n<p>e(c3,h5)  1770.4498</p>\n\n<p>choose h6 to have known</p>\n\n<p>e(c1,h6)  1550.5012</p>\n\n<p>e(c2,h6)  1740.3875</p>\n\n<p>e(c3,h6)  2358.7705</p>\n\n<p>choose c4 to have known</p>\n\n<p>e(c4,h1)     2.1402</p>\n\n<p>e(c4,h2)  2443.3882</p>\n\n<p>e(c4,h3)  1562.3011</p>\n\n<p>choose c5 to have known</p>\n\n<p>e(c5,h1)  340.5342</p>\n\n<p>e(c5,h2)  2108.4495</p>\n\n<p>e(c5,h3)  1626.4935</p>\n\n<p>choose c6 to have known</p>\n\n<p>e(c6,h1)  2450.4404</p>\n\n<p>e(c6,h2)   914.0866</p>\n\n<p>e(c6,h3)  2118.8973</p>\n\n<p>choose c7 to have known</p>\n\n<p>e(c7,h1)  2022.6995</p>\n\n<p>e(c7,h2)   627.9322</p>\n\n<p>e(c7,h3)  2653.9268</p>\n\n<p>choose c8 to have known</p>\n\n<p>e(c8,h1)   329.1878</p>\n\n<p>e(c8,h2)  2331.2786</p>\n\n<p>e(c8,h3)  1856.1279</p>\n\n<p>choose c9 to have known</p>\n\n<p>e(c9,h1)  2406.3413</p>\n\n<p>e(c9,h2)   161.6393</p>\n\n<p>e(c9,h3)  2764.0730</p>\n\n<p>Tetrahedron systems have only 2 solutions\nyou start with 3 known points and add one which has 3 distances known to them\nand then select the correct solution closest to be on the sphere\nSo you now have a solid base of 9 cities and 6 hotels </p>\n\n<p>Now its time to do the gridsearch for earth radius R by minimizing\nthe error of the extra 12 distances between the 6 hotels and 9 cities \nnot described above (c4-c9 known distances to h4-h6) and also minimizing\ntheir distance to the sphere.\nI just steped 0.0001 from 3950 to 3970 miles for a simple gridsearch.</p>\n\n<p>you can conquer the rest of the world\nby doing thetraedrons at first and even 2 distances at latest stage\nand selecting based on destination center.\nBut its nontrivial you will have to mantain a database of edges\n(&gt; 12 million) and some structuring so you don't do full \nexhaustive 3 edge search\nyou will get &gt; 2 million hotels (nonduplicated)\nWhy i am not in TOP 3?\noh, i started my code 3 days ago, and i just needed few more hours (after the deadline)\nWell that explains the 66% bookings from the problem\nonce you know the exact hotel from the booking and its exact cluster history</p>",
  "messages": [
    {
      "id": "123326",
      "postDate": "06/11/2016 03:26:42",
      "content": "<p>You can obtain almost full map of hotels and cities exactly to better than 3.2 meter accuracy, without\nneeding any extra data and just mantain arbitrary lat long up to some unknown rotation to the real \nworld lat long. \nObtain also the overlapping relations between the destinations because you can match the hotels by coords.\nEarth radius deducted from grid search: 3963.0000 miles (strange choice??)\nComputations was started initially from all the destinations who have \nmaximum ONE length of distance from any city. These are candidate for being &quot;single hotels&quot;\ntop 5 by number of cities pointed by:</p>\n\n<p>dest 43062 htmax= 1 ndist= 111 ncty= 111 nhit= 246</p>\n\n<p>dest 3789 htmax= 1 ndist= 137 ncty= 137 nhit= 287</p>\n\n<p>dest 3470 htmax= 1 ndist= 121 ncty= 121 nhit= 309</p>\n\n<p>dest 25174 htmax= 1 ndist= 146 ncty= 146 nhit= 310</p>\n\n<p>dest 9703 htmax= 1 ndist= 72 ncty= 72 nhit= 600</p>\n\n<p>dest 21063 htmax= 1 ndist= 213 ncty= 213 nhit= 617</p>\n\n<p>dest 33865 htmax= 1 ndist= 115 ncty= 115 nhit= 759</p>\n\n<p>dest 48752 htmax= 1 ndist= 279 ncty= 279 nhit= 826</p>\n\n<p>The destinations (single hotels) i started with were :</p>\n\n<p>h1=25174,</p>\n\n<p>h2=33865,</p>\n\n<p>h3=48752</p>\n\n<p>Then pick the cities c1,c2,c3 that have the following distance matrix  to the above 3\nhotels</p>\n\n<p>e(c1,h1)= 1371.0242 e(c1,h2)= 1680.7709 e(c1,h3)= 1022.7044</p>\n\n<p>e(c2,h1)=  710.2743 e(c2,h2)= 1767.2299 e(c2,h3)= 1446.413</p>\n\n<p>e(c3,h1)= 2140.0445 e(c3,h2)= 1084.3085 e(c3,h3)= 1768.1506</p>\n\n<p>(with e(a,b) i note the spherical distance on the sphere in miles)</p>\n\n<p>knowing radius R (you will do gridsearch later to the 3963 value)\nyou obtain a nonlinear system that has at most 16 full real solutions \n(and many more complex) for a 3x3 distance matrix\nbut there are 4 symmetries so there are at most 4 distinct full real solutions <br>\nbut usually only at most 2-3 converge to 100 decimals (i used mpfr).\nmatching with full tethraedrons to other city and hotels you select the correct \nbase solution with 3 further single hotels h4,h5,h6 which have each 3 distances \nwith c1,c2,c3 and six further cities c4,c5,c6,c7,c8,c9 which have each \n3 distances with h1,h2,h3\nso you obtain accurate to 4 decimals:</p>\n\n<p>e(c1,c2)= 803.595455 e(c1,c3)= 883.753673 e(c2,c3)= 1452.09340</p>\n\n<p>e(h1,h2)= 2441.36694 e(h1,h3)= 1561.38509 e(h2,h3)= 2697.01204</p>\n\n<p>choose h4 to have known</p>\n\n<p>e(c1,h4)  1375.3989</p>\n\n<p>e(c2,h4)   710.6864</p>\n\n<p>e(c3,h4)  2142.2537</p>\n\n<p>choose h5 to have known</p>\n\n<p>e(c1,h5)  1036.4751</p>\n\n<p>e(c2,h5)  1473.8628</p>\n\n<p>e(c3,h5)  1770.4498</p>\n\n<p>choose h6 to have known</p>\n\n<p>e(c1,h6)  1550.5012</p>\n\n<p>e(c2,h6)  1740.3875</p>\n\n<p>e(c3,h6)  2358.7705</p>\n\n<p>choose c4 to have known</p>\n\n<p>e(c4,h1)     2.1402</p>\n\n<p>e(c4,h2)  2443.3882</p>\n\n<p>e(c4,h3)  1562.3011</p>\n\n<p>choose c5 to have known</p>\n\n<p>e(c5,h1)  340.5342</p>\n\n<p>e(c5,h2)  2108.4495</p>\n\n<p>e(c5,h3)  1626.4935</p>\n\n<p>choose c6 to have known</p>\n\n<p>e(c6,h1)  2450.4404</p>\n\n<p>e(c6,h2)   914.0866</p>\n\n<p>e(c6,h3)  2118.8973</p>\n\n<p>choose c7 to have known</p>\n\n<p>e(c7,h1)  2022.6995</p>\n\n<p>e(c7,h2)   627.9322</p>\n\n<p>e(c7,h3)  2653.9268</p>\n\n<p>choose c8 to have known</p>\n\n<p>e(c8,h1)   329.1878</p>\n\n<p>e(c8,h2)  2331.2786</p>\n\n<p>e(c8,h3)  1856.1279</p>\n\n<p>choose c9 to have known</p>\n\n<p>e(c9,h1)  2406.3413</p>\n\n<p>e(c9,h2)   161.6393</p>\n\n<p>e(c9,h3)  2764.0730</p>\n\n<p>Tetrahedron systems have only 2 solutions\nyou start with 3 known points and add one which has 3 distances known to them\nand then select the correct solution closest to be on the sphere\nSo you now have a solid base of 9 cities and 6 hotels </p>\n\n<p>Now its time to do the gridsearch for earth radius R by minimizing\nthe error of the extra 12 distances between the 6 hotels and 9 cities \nnot described above (c4-c9 known distances to h4-h6) and also minimizing\ntheir distance to the sphere.\nI just steped 0.0001 from 3950 to 3970 miles for a simple gridsearch.</p>\n\n<p>you can conquer the rest of the world\nby doing thetraedrons at first and even 2 distances at latest stage\nand selecting based on destination center.\nBut its nontrivial you will have to mantain a database of edges\n(&gt; 12 million) and some structuring so you don't do full \nexhaustive 3 edge search\nyou will get &gt; 2 million hotels (nonduplicated)\nWhy i am not in TOP 3?\noh, i started my code 3 days ago, and i just needed few more hours (after the deadline)\nWell that explains the 66% bookings from the problem\nonce you know the exact hotel from the booking and its exact cluster history</p>",
      "rawMarkdown": "You can obtain almost full map of hotels and cities exactly to better than 3.2 meter accuracy, without\r\nneeding any extra data and just mantain arbitrary lat long up to some unknown rotation to the real \r\nworld lat long. \r\nObtain also the overlapping relations between the destinations because you can match the hotels by coords.\r\nEarth radius deducted from grid search: 3963.0000 miles (strange choice??)\r\nComputations was started initially from all the destinations who have \r\nmaximum ONE length of distance from any city. These are candidate for being \"single hotels\"\r\ntop 5 by number of cities pointed by:\r\n\r\ndest 43062 htmax= 1 ndist= 111 ncty= 111 nhit= 246\r\n\r\ndest 3789 htmax= 1 ndist= 137 ncty= 137 nhit= 287\r\n\r\ndest 3470 htmax= 1 ndist= 121 ncty= 121 nhit= 309\r\n\r\ndest 25174 htmax= 1 ndist= 146 ncty= 146 nhit= 310\r\n\r\ndest 9703 htmax= 1 ndist= 72 ncty= 72 nhit= 600\r\n\r\ndest 21063 htmax= 1 ndist= 213 ncty= 213 nhit= 617\r\n\r\ndest 33865 htmax= 1 ndist= 115 ncty= 115 nhit= 759\r\n\r\ndest 48752 htmax= 1 ndist= 279 ncty= 279 nhit= 826\r\n\r\n\r\nThe destinations (single hotels) i started with were :\r\n\r\nh1=25174,\r\n\r\nh2=33865,\r\n\r\nh3=48752\r\n\r\nThen pick the cities c1,c2,c3 that have the following distance matrix  to the above 3\r\nhotels\r\n\r\ne(c1,h1)= 1371.0242 e(c1,h2)= 1680.7709 e(c1,h3)= 1022.7044\r\n\r\ne(c2,h1)=  710.2743 e(c2,h2)= 1767.2299 e(c2,h3)= 1446.413\r\n\r\ne(c3,h1)= 2140.0445 e(c3,h2)= 1084.3085 e(c3,h3)= 1768.1506\r\n\r\n(with e(a,b) i note the spherical distance on the sphere in miles)\r\n\r\nknowing radius R (you will do gridsearch later to the 3963 value)\r\nyou obtain a nonlinear system that has at most 16 full real solutions \r\n(and many more complex) for a 3x3 distance matrix\r\nbut there are 4 symmetries so there are at most 4 distinct full real solutions  \r\nbut usually only at most 2-3 converge to 100 decimals (i used mpfr).\r\nmatching with full tethraedrons to other city and hotels you select the correct \r\nbase solution with 3 further single hotels h4,h5,h6 which have each 3 distances \r\nwith c1,c2,c3 and six further cities c4,c5,c6,c7,c8,c9 which have each \r\n3 distances with h1,h2,h3\r\nso you obtain accurate to 4 decimals:\r\n\r\ne(c1,c2)= 803.595455 e(c1,c3)= 883.753673 e(c2,c3)= 1452.09340\r\n\r\ne(h1,h2)= 2441.36694 e(h1,h3)= 1561.38509 e(h2,h3)= 2697.01204\r\n\r\nchoose h4 to have known\r\n\r\ne(c1,h4)  1375.3989\r\n\r\ne(c2,h4)   710.6864\r\n\r\ne(c3,h4)  2142.2537\r\n\r\nchoose h5 to have known\r\n\r\ne(c1,h5)  1036.4751\r\n\r\ne(c2,h5)  1473.8628\r\n\r\ne(c3,h5)  1770.4498\r\n\r\nchoose h6 to have known\r\n\r\ne(c1,h6)  1550.5012\r\n\r\ne(c2,h6)  1740.3875\r\n\r\ne(c3,h6)  2358.7705\r\n\r\nchoose c4 to have known\r\n\r\ne(c4,h1)     2.1402\r\n\r\ne(c4,h2)  2443.3882\r\n\r\ne(c4,h3)  1562.3011\r\n\r\nchoose c5 to have known\r\n\r\ne(c5,h1)  340.5342\r\n\r\ne(c5,h2)  2108.4495\r\n\r\ne(c5,h3)  1626.4935\r\n\r\nchoose c6 to have known\r\n\r\ne(c6,h1)  2450.4404\r\n\r\ne(c6,h2)   914.0866\r\n\r\ne(c6,h3)  2118.8973\r\n\r\nchoose c7 to have known\r\n\r\ne(c7,h1)  2022.6995\r\n\r\ne(c7,h2)   627.9322\r\n\r\ne(c7,h3)  2653.9268\r\n\r\nchoose c8 to have known\r\n\r\ne(c8,h1)   329.1878\r\n\r\ne(c8,h2)  2331.2786\r\n\r\ne(c8,h3)  1856.1279\r\n\r\nchoose c9 to have known\r\n\r\ne(c9,h1)  2406.3413\r\n\r\ne(c9,h2)   161.6393\r\n\r\ne(c9,h3)  2764.0730\r\n\r\nTetrahedron systems have only 2 solutions\r\nyou start with 3 known points and add one which has 3 distances known to them\r\nand then select the correct solution closest to be on the sphere\r\nSo you now have a solid base of 9 cities and 6 hotels \r\n\r\nNow its time to do the gridsearch for earth radius R by minimizing\r\nthe error of the extra 12 distances between the 6 hotels and 9 cities \r\nnot described above (c4-c9 known distances to h4-h6) and also minimizing\r\ntheir distance to the sphere.\r\nI just steped 0.0001 from 3950 to 3970 miles for a simple gridsearch.\r\n\r\nyou can conquer the rest of the world\r\nby doing thetraedrons at first and even 2 distances at latest stage\r\nand selecting based on destination center.\r\nBut its nontrivial you will have to mantain a database of edges\r\n(> 12 million) and some structuring so you don't do full \r\nexhaustive 3 edge search\r\nyou will get > 2 million hotels (nonduplicated)\r\nWhy i am not in TOP 3?\r\noh, i started my code 3 days ago, and i just needed few more hours (after the deadline)\r\nWell that explains the 66% bookings from the problem\r\nonce you know the exact hotel from the booking and its exact cluster history",
      "votes": null
    },
    {
      "id": "123491",
      "postDate": "06/12/2016 07:36:53",
      "content": "<p>Nice! I too was trying to create a map using a different method, but spherical distances threw me and I too ran out of time. My great circles would end up witn NaN distances and figuring out how to move a city to match a distance to a hotel in long/lat was just impossible with the time I had left.</p>\n\n<p>Thanks for sharing!</p>",
      "rawMarkdown": "Nice! I too was trying to create a map using a different method, but spherical distances threw me and I too ran out of time. My great circles would end up witn NaN distances and figuring out how to move a city to match a distance to a hotel in long/lat was just impossible with the time I had left.\r\n\r\nThanks for sharing!",
      "votes": null
    },
    {
      "id": "123513",
      "postDate": "06/12/2016 12:18:04",
      "content": "<p>The leaderboard should be open again for late submissions. Did you resubmit -- and how did your method do? </p>",
      "rawMarkdown": "The leaderboard should be open again for late submissions. Did you resubmit -- and how did your method do?",
      "votes": null
    }
  ],
  "comments": [
    {
      "id": 123491,
      "author_name": "mfagerlund",
      "author_url": "",
      "post_date": "06/12/2016 07:36:53",
      "content": "<p>Nice! I too was trying to create a map using a different method, but spherical distances threw me and I too ran out of time. My great circles would end up witn NaN distances and figuring out how to move a city to match a distance to a hotel in long/lat was just impossible with the time I had left.</p>\n\n<p>Thanks for sharing!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 123513,
      "author_name": "knitcode",
      "author_url": "",
      "post_date": "06/12/2016 12:18:04",
      "content": "<p>The leaderboard should be open again for late submissions. Did you resubmit -- and how did your method do? </p>",
      "votes": null,
      "replies": []
    }
  ],
  "raw_markdown_by_id": {
    "123326": "You can obtain almost full map of hotels and cities exactly to better than 3.2 meter accuracy, without\r\nneeding any extra data and just mantain arbitrary lat long up to some unknown rotation to the real \r\nworld lat long. \r\nObtain also the overlapping relations between the destinations because you can match the hotels by coords.\r\nEarth radius deducted from grid search: 3963.0000 miles (strange choice??)\r\nComputations was started initially from all the destinations who have \r\nmaximum ONE length of distance from any city. These are candidate for being \"single hotels\"\r\ntop 5 by number of cities pointed by:\r\n\r\ndest 43062 htmax= 1 ndist= 111 ncty= 111 nhit= 246\r\n\r\ndest 3789 htmax= 1 ndist= 137 ncty= 137 nhit= 287\r\n\r\ndest 3470 htmax= 1 ndist= 121 ncty= 121 nhit= 309\r\n\r\ndest 25174 htmax= 1 ndist= 146 ncty= 146 nhit= 310\r\n\r\ndest 9703 htmax= 1 ndist= 72 ncty= 72 nhit= 600\r\n\r\ndest 21063 htmax= 1 ndist= 213 ncty= 213 nhit= 617\r\n\r\ndest 33865 htmax= 1 ndist= 115 ncty= 115 nhit= 759\r\n\r\ndest 48752 htmax= 1 ndist= 279 ncty= 279 nhit= 826\r\n\r\n\r\nThe destinations (single hotels) i started with were :\r\n\r\nh1=25174,\r\n\r\nh2=33865,\r\n\r\nh3=48752\r\n\r\nThen pick the cities c1,c2,c3 that have the following distance matrix  to the above 3\r\nhotels\r\n\r\ne(c1,h1)= 1371.0242 e(c1,h2)= 1680.7709 e(c1,h3)= 1022.7044\r\n\r\ne(c2,h1)=  710.2743 e(c2,h2)= 1767.2299 e(c2,h3)= 1446.413\r\n\r\ne(c3,h1)= 2140.0445 e(c3,h2)= 1084.3085 e(c3,h3)= 1768.1506\r\n\r\n(with e(a,b) i note the spherical distance on the sphere in miles)\r\n\r\nknowing radius R (you will do gridsearch later to the 3963 value)\r\nyou obtain a nonlinear system that has at most 16 full real solutions \r\n(and many more complex) for a 3x3 distance matrix\r\nbut there are 4 symmetries so there are at most 4 distinct full real solutions  \r\nbut usually only at most 2-3 converge to 100 decimals (i used mpfr).\r\nmatching with full tethraedrons to other city and hotels you select the correct \r\nbase solution with 3 further single hotels h4,h5,h6 which have each 3 distances \r\nwith c1,c2,c3 and six further cities c4,c5,c6,c7,c8,c9 which have each \r\n3 distances with h1,h2,h3\r\nso you obtain accurate to 4 decimals:\r\n\r\ne(c1,c2)= 803.595455 e(c1,c3)= 883.753673 e(c2,c3)= 1452.09340\r\n\r\ne(h1,h2)= 2441.36694 e(h1,h3)= 1561.38509 e(h2,h3)= 2697.01204\r\n\r\nchoose h4 to have known\r\n\r\ne(c1,h4)  1375.3989\r\n\r\ne(c2,h4)   710.6864\r\n\r\ne(c3,h4)  2142.2537\r\n\r\nchoose h5 to have known\r\n\r\ne(c1,h5)  1036.4751\r\n\r\ne(c2,h5)  1473.8628\r\n\r\ne(c3,h5)  1770.4498\r\n\r\nchoose h6 to have known\r\n\r\ne(c1,h6)  1550.5012\r\n\r\ne(c2,h6)  1740.3875\r\n\r\ne(c3,h6)  2358.7705\r\n\r\nchoose c4 to have known\r\n\r\ne(c4,h1)     2.1402\r\n\r\ne(c4,h2)  2443.3882\r\n\r\ne(c4,h3)  1562.3011\r\n\r\nchoose c5 to have known\r\n\r\ne(c5,h1)  340.5342\r\n\r\ne(c5,h2)  2108.4495\r\n\r\ne(c5,h3)  1626.4935\r\n\r\nchoose c6 to have known\r\n\r\ne(c6,h1)  2450.4404\r\n\r\ne(c6,h2)   914.0866\r\n\r\ne(c6,h3)  2118.8973\r\n\r\nchoose c7 to have known\r\n\r\ne(c7,h1)  2022.6995\r\n\r\ne(c7,h2)   627.9322\r\n\r\ne(c7,h3)  2653.9268\r\n\r\nchoose c8 to have known\r\n\r\ne(c8,h1)   329.1878\r\n\r\ne(c8,h2)  2331.2786\r\n\r\ne(c8,h3)  1856.1279\r\n\r\nchoose c9 to have known\r\n\r\ne(c9,h1)  2406.3413\r\n\r\ne(c9,h2)   161.6393\r\n\r\ne(c9,h3)  2764.0730\r\n\r\nTetrahedron systems have only 2 solutions\r\nyou start with 3 known points and add one which has 3 distances known to them\r\nand then select the correct solution closest to be on the sphere\r\nSo you now have a solid base of 9 cities and 6 hotels \r\n\r\nNow its time to do the gridsearch for earth radius R by minimizing\r\nthe error of the extra 12 distances between the 6 hotels and 9 cities \r\nnot described above (c4-c9 known distances to h4-h6) and also minimizing\r\ntheir distance to the sphere.\r\nI just steped 0.0001 from 3950 to 3970 miles for a simple gridsearch.\r\n\r\nyou can conquer the rest of the world\r\nby doing thetraedrons at first and even 2 distances at latest stage\r\nand selecting based on destination center.\r\nBut its nontrivial you will have to mantain a database of edges\r\n(> 12 million) and some structuring so you don't do full \r\nexhaustive 3 edge search\r\nyou will get > 2 million hotels (nonduplicated)\r\nWhy i am not in TOP 3?\r\noh, i started my code 3 days ago, and i just needed few more hours (after the deadline)\r\nWell that explains the 66% bookings from the problem\r\nonce you know the exact hotel from the booking and its exact cluster history",
    "123491": "Nice! I too was trying to create a map using a different method, but spherical distances threw me and I too ran out of time. My great circles would end up witn NaN distances and figuring out how to move a city to match a distance to a hotel in long/lat was just impossible with the time I had left.\r\n\r\nThanks for sharing!",
    "123513": "The leaderboard should be open again for late submissions. Did you resubmit -- and how did your method do?"
  },
  "source": "meta"
}