Statistics

Problem Statement for "PuckShot"

Problem Statement

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The left-handed Finnish hockey player Slaapi Shotti has a spectacular move where he fires the puck from the blue line, off the boards, and into the net. The relevant portion of an international hockey rink is shown below.

The rink is 3000 centimeters (cm) wide. The distance between the blue line and the goal line is 1733 cm. Centered on the goal line is the goal itself, which is 183 cm wide and marked with a goalpost at each end. When Slaapi shoots, the puck will travel in a straight line from a given point on the blue line, rebound symmetrically from the right border of the rink, and continue traveling in a straight line. We shall model the puck and the goalposts as infinitesimal points on the ice.

Positioned on the ice are up to nine players, whom we model as line segments that are 50 cm long and parallel to the blue line. Each player must stand on or below the goal line, at least one centimeter above the blue line, and at least one centimeter away from the sides. Players may overlap or coincide. In order for Slaapi to score a goal, the puck may not intersect a player's line segment at any point, including its endpoints. For the purposes of player position as well as puck rebound, you may ignore the curvature of the rink and assume that the boards are perfectly straight, forming a rectangle with the blue line and goal line.

Slaapi must shoot the puck from the point on the blue line whose distance from the left border of the rink is given by the int puckCoord. You are also given two int[]s, xCoords and yCoords. The distance in centimeters of the nth player's midpoint from the left border of the rink is given by the nth element of xCoords, and the distance of his midpoint from the blue line is given by the nth element of yCoords.

Calculate the angle, measured counterclockwise from the blue line, at which Slaapi must shoot the puck so that its point of intersection with the goal line is between the goalposts, inclusively, and as close as possible to the right goalpost. Return your answer in degrees as a double value with an absolute or relative error of 1.0e-9. Return -1.0 if Slaapi cannot score a goal in the prescribed manner. The input is guaranteed to be such that the rightmost gap through which Slaapi can score, if any, is at least 1.0e-6 cm wide at the goal line.

Definition

Class:
PuckShot
Method:
caromAngle
Parameters:
int, int[], int[]
Returns:
double
Method signature:
double caromAngle(int puckCoord, int[] xCoords, int[] yCoords)
(be sure your method is public)

Constraints

  • puckCoord is between 1 and 2999, inclusive
  • xCoords contains between one and nine elements, inclusive
  • yCoords contains the same number of elements as xCoords
  • each element of xCoords is between 26 and 2974, inclusive
  • each element of yCoords is between 1 and 1733, inclusive
  • the input is such that the rightmost gap through which Slaapi can score, if any, is at least 1.0e-6 cm wide at the goal line

Examples

  1. 2833

    {1500, 1580}

    {1730, 1730}

    Returns: 47.022170720170784

    Two players are positioned near the goal, one in the center and another by the right goalpost. Between them is a gap that lets Slaapi score a goal. He puts the puck as close to the right goalpost as possible.

  2. 2833

    {2690}

    {500}

    Returns: 44.88563731851585

    A single player not far from the blue line forces Slaapi to put the puck near the left goalpost.

  3. 2833

    {2690, 2676}

    {500, 500}

    Returns: -1.0

    Two players not far from the blue line are completely blocking Slaapi's shot.

  4. 2900

    {1500, 1580, 2200, 2600}

    {1730, 1730, 1000, 500}

    Returns: 46.79257639615244

  5. 55

    {1479, 1427, 2556, 2834, 2866, 2958, 2763, 2899, 2630}

    {1708, 1726, 487, 471, 121, 446, 473, 266, 380}

    Returns: 21.706043385046158

  6. 1809

    {1571}

    {1730}

    Returns: 33.18726534329994

    The player's right endpoint is exactly in the way of the right goalpost, so Slaapi must shoot to the left of the player.

  7. 1

    {1831}

    {1629}

    Returns: 21.464425628113574

  8. 11

    {1668}

    {1693}

    Returns: 21.508782280926084

  9. 115

    {1504, 1430, 2568, 2477, 2767, 2507, 2645, 2684, 2838}

    {1732, 1720, 281, 228, 173, 472, 325, 225, 229}

    Returns: 21.980648511094003

  10. 2839

    {1472, 1550, 2905, 2692, 2687, 2688, 2854, 2798, 2950}

    {1705, 1701, 85, 174, 193, 263, 141, 448, 276}

    Returns: -1.0

  11. 655

    {1474, 1500, 2885, 2534, 2478, 2794, 2576, 2769, 2694}

    {1714, 1732, 391, 253, 392, 450, 186, 341, 326}

    Returns: 24.78288409190985

  12. 480

    {1514, 1509, 2600, 2675, 2878, 2782, 2584, 2873, 2722}

    {1699, 1688, 379, 119, 389, 283, 224, 102, 366}

    Returns: 23.803968594369593

  13. 1247

    {1545, 1503, 2615, 2504, 2886, 2721, 2497, 2579, 2926}

    {1647, 1678, 357, 83, 240, 446, 433, 211, 109}

    Returns: 28.729681693903068

  14. 2901

    {1486, 1447, 2627, 2797, 2908, 2827, 2713, 2647, 2500}

    {1698, 1659, 91, 186, 455, 280, 463, 93, 123}

    Returns: -1.0

  15. 37

    {1575, 1476, 2568, 2716, 2510, 2730, 2774, 2626, 2916}

    {1710, 1692, 142, 298, 292, 367, 99, 340, 156}

    Returns: 21.62493085310635

  16. 1669

    {1470, 1575, 2799, 2716, 2481, 2687, 2904, 2521, 2685}

    {1640, 1714, 435, 253, 301, 217, 139, 170, 108}

    Returns: 32.31733026762112

  17. 840

    {1528, 1472, 2953, 2854, 2918, 2849, 2643, 2663, 2852}

    {1649, 1725, 491, 284, 491, 343, 98, 243, 256}

    Returns: 25.902981728497977

  18. 1441

    {1580, 1494, 2834, 2658, 2650, 2486, 2648, 2891, 2649}

    {1729, 1649, 499, 229, 188, 141, 139, 259, 475}

    Returns: 29.923263658520504

  19. 1359

    {1464, 1500, 2765, 2961, 2705, 2896, 2866, 2650, 2720}

    {1685, 1732, 477, 286, 309, 214, 59, 260, 429}

    Returns: 29.609131167187037

  20. 72

    {1531, 1469, 2735, 2539, 2540, 2574, 2769, 2763, 2485}

    {1666, 1718, 174, 212, 134, 363, 162, 440, 380}

    Returns: 21.783183102247648

  21. 851

    {1551, 1516, 2841, 2763, 2565, 2493, 2857, 2512, 2550}

    {1731, 1658, 306, 244, 140, 393, 303, 461, 302}

    Returns: 25.972558302706005

  22. 2026

    {1494, 1475, 2841, 2540, 2959, 2718, 2930, 2580, 2862}

    {1700, 1703, 396, 460, 85, 249, 358, 392, 51}

    Returns: -1.0

  23. 2458

    {1501, 1585, 2568, 2612, 2671, 2928, 2861, 2769, 2531}

    {1720, 1687, 395, 219, 178, 423, 302, 456, 283}

    Returns: -1.0

  24. 950

    {1522, 1499, 2835, 2681, 2482, 2898, 2655, 2831, 2740}

    {1703, 1704, 441, 241, 232, 427, 93, 88, 91}

    Returns: 26.61472958617206

  25. 1411

    {1501, 1420, 2869, 2563, 2967, 2920, 2862, 2620, 2896}

    {1722, 1718, 133, 201, 260, 227, 144, 155, 479}

    Returns: 30.034287741826027

  26. 2861

    {1478, 1499, 2668, 2822, 2953, 2943, 2485, 2695, 2812}

    {1658, 1725, 293, 290, 177, 187, 292, 352, 220}

    Returns: 48.23641542085916

  27. 519

    {1521, 1545, 2570, 2750, 2963, 2728, 2944, 2883, 2534}

    {1725, 1730, 68, 242, 376, 161, 311, 149, 413}

    Returns: 24.015771472506188

  28. 678

    {1489, 1497, 2627, 2696, 2705, 2835, 2772, 2839, 2613}

    {1682, 1706, 122, 200, 291, 488, 340, 298, 452}

    Returns: 24.917177035275017

  29. 2849

    {1498, 1535, 2721, 2492, 2591, 2769, 2540, 2501, 2573}

    {1732, 1703, 115, 394, 249, 404, 287, 108, 264}

    Returns: -1.0

  30. 2859

    {1543, 1441, 2709, 2688, 2549, 2491, 2648, 2866, 2625}

    {1685, 1722, 144, 331, 250, 241, 172, 323, 206}

    Returns: 47.114293288225944

  31. 499

    {1508, 1535, 2932, 2946, 2850, 2809, 2526, 2505, 2873}

    {1732, 1669, 283, 215, 447, 136, 251, 419, 222}

    Returns: 23.906713436666493

  32. 2243

    {1425, 1540, 2688, 2575, 2584, 2785, 2649, 2723, 2823}

    {1686, 1656, 500, 161, 141, 171, 408, 380, 257}

    Returns: 36.45054739069765

  33. 858

    {1484, 1567, 2944, 2523, 2628, 2532, 2487, 2817, 2864}

    {1669, 1707, 98, 451, 391, 486, 84, 81, 125}

    Returns: 26.017015664393845

  34. 1438

    {1468, 1517, 2769, 2931, 2501, 2752, 2690, 2547, 2737}

    {1646, 1731, 186, 324, 399, 482, 162, 470, 308}

    Returns: 30.259435247307067

  35. 2128

    {1590, 1528, 2653, 2657, 2804, 2604, 2796, 2743, 2850}

    {1730, 1707, 219, 414, 178, 303, 168, 215, 213}

    Returns: 36.7704834376051

  36. 91

    {1460, 1412, 2926, 2874, 2553, 2769, 2734, 2921, 2665}

    {1722, 1699, 354, 449, 84, 51, 253, 110, 159}

    Returns: 21.870017567612067

  37. 1486

    {1537, 1476, 2751, 2682, 2784, 2510, 2781, 2704, 2742}

    {1676, 1649, 98, 430, 402, 165, 371, 93, 219}

    Returns: 30.66732440931191

  38. 838

    {1468, 1485, 2903, 2898, 2743, 2864, 2661, 2667, 2836}

    {1691, 1712, 364, 226, 412, 354, 312, 136, 185}

    Returns: 25.890368709532936

  39. 2810

    {1511, 1518, 2613, 2562, 2542, 2963, 2495, 2831, 2693}

    {1678, 1670, 367, 473, 302, 140, 292, 98, 453}

    Returns: -1.0

  40. 1098

    {1493, 1453, 2917, 2820, 2483, 2955, 2779, 2946, 2765}

    {1712, 1686, 239, 461, 397, 110, 358, 362, 477}

    Returns: 27.631422371236447

  41. 1140

    {1472, 1552, 2657, 2724, 2524, 2729, 2791, 2836, 2952}

    {1686, 1695, 470, 98, 101, 460, 500, 370, 255}

    Returns: 27.933100262427935

  42. 2762

    {1500, 1594, 2814, 2659, 2865, 2542, 2904, 2942, 2660}

    {1732, 1719, 342, 182, 71, 245, 401, 497, 470}

    Returns: 45.84550797561554

  43. 35

    {1460, 1525, 2541, 2757, 2949, 2957, 2921, 2746, 2581}

    {1644, 1725, 284, 447, 243, 422, 490, 284, 224}

    Returns: 21.61595396254762

  44. 2679

    {1450, 1545, 2701, 2657, 2681, 2672, 2476, 2530, 2790}

    {1687, 1690, 400, 140, 476, 250, 388, 223, 338}

    Returns: 45.05791629169531

  45. 2328

    {1431, 1526, 2475, 2586, 2647, 2910, 2803, 2714, 2817}

    {1720, 1680, 444, 333, 198, 391, 428, 235, 56}

    Returns: 39.79337934817982

  46. 152

    {1500, 1487, 2728, 2491, 2621, 2825, 2642, 2955, 2904}

    {1732, 1731, 143, 336, 324, 266, 208, 165, 298}

    Returns: 22.15330349945802

  47. 1031

    {1501, 1535, 2857, 2678, 2560, 2779, 2967, 2598, 2557}

    {1724, 1655, 70, 376, 282, 272, 261, 127, 381}

    Returns: 27.162423084690076

  48. 55

    {1479, 1427, 2530, 2808, 2840, 2932, 2737, 2873, 2604}

    {1708, 1726, 487, 471, 121, 446, 473, 266, 380}

    Returns: 21.706043385046158

  49. 2628

    {1548, 1485, 2725, 2519, 2813, 2883, 2620, 2836, 2647}

    {1667, 1645, 204, 125, 347, 407, 391, 169, 357}

    Returns: 44.22544934160531

  50. 1891

    {1543, 1518, 2662, 2944, 2757, 2493, 2962, 2557, 2769}

    {1697, 1698, 214, 155, 206, 53, 479, 444, 382}

    Returns: 32.722652216820116

  51. 1919

    {1498, 1589, 2876, 2731, 2672, 2763, 2539, 2749, 2884}

    {1689, 1710, 100, 140, 319, 387, 230, 426, 313}

    Returns: 34.842691883211046

  52. 623

    {1588, 1496, 2567, 2691, 2867, 2635, 2511, 2958, 2523}

    {1691, 1676, 76, 160, 345, 450, 205, 498, 83}

    Returns: 24.59828302183631

  53. 665

    {1472, 1538, 2610, 2951, 2756, 2634, 2967, 2847, 2671}

    {1710, 1716, 238, 463, 318, 128, 425, 241, 52}

    Returns: 24.84110535733005

  54. 1693

    {1455, 1442, 2579, 2944, 2740, 2667, 2932, 2580, 2797}

    {1678, 1651, 407, 63, 183, 194, 377, 494, 352}

    Returns: 32.54553768877361

  55. 2199

    {1504, 1466, 2655, 2722, 2795, 2887, 2614, 2762, 2886}

    {1643, 1683, 271, 245, 485, 420, 326, 487, 315}

    Returns: 36.53508316908163

  56. 943

    {1541, 1494, 2652, 2799, 2813, 2807, 2539, 2849, 2964}

    {1683, 1730, 96, 200, 420, 118, 158, 164, 463}

    Returns: 26.56835772021335

  57. 1129

    {1479, 1539, 2598, 2741, 2955, 2587, 2604, 2641, 2913}

    {1699, 1698, 114, 209, 207, 270, 375, 492, 97}

    Returns: 27.85350529829538

  58. 2767

    {1521, 1469, 2707, 2651, 2923, 2511, 2778, 2734, 2852}

    {1716, 1721, 450, 223, 302, 221, 410, 52, 74}

    Returns: -1.0

  59. 1709

    {1594, 1491, 2612, 2904, 2519, 2795, 2618, 2954, 2677}

    {1706, 1703, 69, 293, 370, 233, 151, 462, 306}

    Returns: 32.699275562952415

  60. 2841

    {1514, 1438, 2672, 2719, 2773, 2673, 2828, 2510, 2945}

    {1694, 1703, 324, 235, 249, 140, 406, 262, 256}

    Returns: 46.96696076023582

  61. 393

    {1497, 1562, 2678, 2611, 2690, 2518, 2482, 2656, 2633}

    {1696, 1689, 364, 240, 448, 363, 485, 51, 491}

    Returns: 23.343947654891466

  62. 811

    {1426, 1480, 2580, 2554, 2691, 2485, 2941, 2693, 2573}

    {1680, 1725, 104, 288, 379, 310, 317, 314, 236}

    Returns: 25.72120594463378

  63. 1336

    {1472, 1509, 2554, 2552, 2813, 2900, 2827, 2704, 2901}

    {1699, 1722, 205, 335, 162, 389, 495, 201, 301}

    Returns: 29.42455449702296

  64. 1334

    {1527, 1513, 2509, 2505, 2873, 2893, 2707, 2857, 2585}

    {1654, 1671, 338, 75, 303, 485, 254, 281, 496}

    Returns: 29.408603323726766

  65. 1646

    {1479, 1468, 2762, 2547, 2878, 2485, 2615, 2597, 2808}

    {1729, 1697, 399, 400, 482, 271, 329, 307, 247}

    Returns: 32.101295117355

  66. 1309

    {1415, 1499, 2556, 2742, 2593, 2864, 2911, 2838, 2934}

    {1684, 1730, 470, 239, 474, 407, 114, 88, 104}

    Returns: 29.21053511716169

  67. 1664

    {1537, 1527, 2819, 2488, 2874, 2550, 2620, 2793, 2600}

    {1698, 1671, 257, 294, 281, 91, 432, 294, 461}

    Returns: 32.27014579240081

  68. 1461

    {1500, 1519, 2486, 2518, 2709, 2558, 2596, 2514, 2891}

    {1732, 1654, 364, 378, 283, 493, 434, 412, 159}

    Returns: 30.453650337044166

  69. 2215

    {1548, 1503, 2498, 2713, 2914, 2825, 2525, 2960, 2657}

    {1660, 1709, 425, 155, 292, 167, 321, 55, 356}

    Returns: 37.31873142401753

  70. 1819

    {1413, 1503, 2506, 2941, 2556, 2691, 2505, 2930, 2935}

    {1714, 1730, 206, 469, 387, 252, 121, 295, 131}

    Returns: 33.79206711472079

  71. 2699

    {1434, 1483, 2947, 2742, 2552, 2652, 2645, 2715, 2685}

    {1723, 1729, 355, 124, 75, 82, 324, 498, 322}

    Returns: 43.12723573636204

  72. 1797

    {1477, 1502, 2731, 2595, 2843, 2564, 2665, 2936, 2527}

    {1680, 1673, 282, 284, 312, 241, 77, 233, 380}

    Returns: 33.56838294203687

  73. 2404

    {1448, 1450, 2773, 2544, 2532, 2685, 2726, 2496, 2689}

    {1653, 1707, 205, 73, 273, 184, 398, 444, 240}

    Returns: -1.0

  74. 579

    {1510, 1447, 2527, 2572, 2540, 2894, 2715, 2737, 2877}

    {1714, 1665, 176, 152, 153, 472, 293, 55, 391}

    Returns: 24.3486301778553

  75. 2703

    {1439, 1449, 2753, 2558, 2533, 2827, 2967, 2598, 2655}

    {1708, 1694, 171, 355, 255, 234, 199, 470, 467}

    Returns: 45.4582231624032

  76. 2360

    {1550, 1427, 2560, 2825, 2648, 2825, 2663, 2651, 2693}

    {1731, 1711, 192, 281, 239, 113, 66, 411, 214}

    Returns: -1.0

  77. 845

    {1543, 1439, 2540, 2773, 2583, 2726, 2759, 2584, 2501}

    {1699, 1684, 415, 328, 443, 349, 323, 337, 362}

    Returns: 25.93456438043377

  78. 112

    {1546, 1499, 2861, 2795, 2831, 2573, 2612, 2773, 2917}

    {1676, 1732, 336, 63, 105, 185, 478, 76, 60}

    Returns: 21.96676149838636

  79. 2708

    {1511, 1538, 2690, 2616, 2598, 2537, 2887, 2643, 2706}

    {1709, 1687, 211, 342, 337, 342, 426, 166, 253}

    Returns: 44.73226466129779

  80. 2818

    {1530, 1481, 2664, 2491, 2951, 2774, 2837, 2759, 2532}

    {1698, 1702, 225, 370, 258, 241, 438, 376, 255}

    Returns: 44.59886924109083

  81. 2494

    {1528, 1450, 2487, 2506, 2822, 2587, 2516, 2730, 2787}

    {1689, 1684, 275, 99, 169, 259, 494, 370, 135}

    Returns: 42.15130536538905

  82. 879

    {1477, 1514, 2959, 2658, 2688, 2573, 2777, 2764, 2915}

    {1730, 1728, 247, 409, 206, 203, 173, 335, 158}

    Returns: 26.15124103849317

  83. 1293

    {1572, 1483, 2873, 2705, 2880, 2873, 2636, 2965, 2479}

    {1681, 1724, 95, 176, 61, 393, 285, 304, 454}

    Returns: 29.085043625440115

  84. 2357

    {1545, 1507, 2614, 2767, 2926, 2930, 2880, 2600, 2649}

    {1677, 1672, 415, 64, 195, 405, 267, 277, 344}

    Returns: 40.18937659495279

  85. 2965

    {1461, 1479, 2748, 2572, 2905, 2961, 2779, 2727, 2806}

    {1724, 1701, 340, 322, 191, 321, 232, 334, 199}

    Returns: -1.0

  86. 1310

    {1499, 1507, 2619, 2880, 2832, 2599, 2693, 2552, 2537}

    {1696, 1698, 63, 344, 444, 450, 117, 361, 298}

    Returns: 29.218411128774186

  87. 2820

    {1442, 1503, 2678, 2523, 2586, 2886, 2652, 2957, 2726}

    {1705, 1719, 276, 258, 266, 418, 355, 315, 222}

    Returns: 47.49105008761407

  88. 2199

    {1558, 1524, 2766, 2751, 2621, 2682, 2721, 2872, 2804}

    {1725, 1721, 476, 314, 164, 252, 432, 150, 233}

    Returns: 38.108521290089946

  89. 347

    {1531, 1502, 2688, 2565, 2874, 2719, 2499, 2596, 2944}

    {1724, 1724, 473, 498, 66, 189, 111, 172, 104}

    Returns: 23.107440730927863

  90. 1423

    {1459, 1498, 2784, 2663, 2901, 2650, 2750, 2869, 2656}

    {1715, 1718, 274, 94, 163, 237, 66, 140, 425}

    Returns: 30.13397728369089

  91. 199

    {1531, 1441, 2732, 2906, 2823, 2952, 2831, 2785, 2617}

    {1723, 1673, 143, 490, 74, 316, 62, 207, 403}

    Returns: 22.37636975893011

  92. 1642

    {1478, 1521, 2801, 2842, 2782, 2847, 2478, 2703, 2931}

    {1685, 1728, 480, 296, 221, 165, 313, 308, 289}

    Returns: 32.06398685211629

  93. 2969

    {1554, 1524, 2966, 2506, 2943, 2849, 2548, 2884, 2659}

    {1649, 1713, 100, 192, 182, 491, 125, 196, 415}

    Returns: -1.0

  94. 490

    {1492, 1441, 2637, 2542, 2539, 2698, 2603, 2661, 2921}

    {1730, 1655, 330, 415, 151, 401, 142, 151, 197}

    Returns: 23.857940942631842

  95. 74

    {1484, 1571, 2663, 2939, 2761, 2849, 2720, 2537, 2938}

    {1724, 1678, 75, 482, 322, 135, 254, 315, 183}

    Returns: 21.792292668875902

  96. 1013

    {1505, 1455, 2763, 2539, 2532, 2518, 2952, 2475, 2528}

    {1721, 1653, 429, 447, 349, 129, 211, 242, 96}

    Returns: 27.03892029424609

  97. 2474

    {1433, 1483, 2672, 2624, 2504, 2555, 2886, 2659, 2956}

    {1716, 1700, 110, 199, 195, 319, 326, 500, 427}

    Returns: -1.0

  98. 2038

    {1473, 1531, 2549, 2640, 2818, 2603, 2754, 2905, 2527}

    {1682, 1665, 96, 185, 106, 249, 53, 68, 364}

    Returns: 35.3050273265593

  99. 654

    {1463, 1409, 2526, 2913, 2790, 2624, 2685, 2703, 2690}

    {1723, 1719, 80, 193, 104, 321, 209, 405, 265}

    Returns: 24.77707602455017

  100. 2483

    {1416, 1486, 2802, 2958, 2945, 2546, 2519, 2747, 2891}

    {1730, 1673, 340, 212, 202, 442, 155, 264, 212}

    Returns: 41.98803448278311

  101. 2334

    {1459,1396,1509,1559,1609}

    {1717,1727,1717,1717,1717}

    Returns: 37.569832573137546

  102. 1

    {26}

    {1}

    Returns: -1.0

  103. 1000

    {1400,1450,1500,1550,1600}

    {1733,1733,1733,1733,1733}

    Returns: -1.0

  104. 55

    { 1479, 1427, 2556, 2834, 2866, 2958, 2763, 2899, 2630 }

    { 1708, 1726, 487, 471, 121, 446, 473, 266, 380 }

    Returns: 21.706043385046158

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