Statistics

Problem Statement for "NumericalSequence"

Problem Statement

A numerical sequence is called a palindrome if the reverse of the sequence is the same as the original. For example sequences {1, 2, 1}, {15, 78, 78, 15} and {112} are palindromes, but {1, 2, 2}, {15, 78, 87, 51} and {112, 2, 11} are not.

You will be given a int[] sequence. You can replace any two adjacent numbers with their sum. Your method should return a minimal number of such operations required to make the given sequence a palindrome.

Definition

Class:
NumericalSequence
Method:
makePalindrome
Parameters:
int[]
Returns:
int
Method signature:
int makePalindrome(int[] sequence)
(be sure your method is public)

Constraints

  • sequence will contain between 1 and 50 elements, inclusive.
  • Each element of sequence will be between 1 and 10000, inclusive.

Examples

  1. {15,78,78,15}

    Returns: 0

    The sequence is a palindrome already.

  2. {1,1,1,3}

    Returns: 2

    We should replace two ones with 2 and afterwards replace 2 and 1 with 3.

  3. {15,78,87,51}

    Returns: 3

  4. {3,23,21,23,42,39,63,76,13,13,13,32,12,42,26}

    Returns: 8

  5. {1}

    Returns: 0

  6. {10000}

    Returns: 0

  7. {10000,9999}

    Returns: 1

  8. {10000,9999,10000,9999}

    Returns: 2

  9. {1,1}

    Returns: 0

  10. {1,2,1}

    Returns: 0

  11. {1,2,2}

    Returns: 2

  12. {1,3,2}

    Returns: 2

  13. {1,2,3}

    Returns: 1

  14. {1,2,3,6}

    Returns: 2

  15. {2,2}

    Returns: 0

  16. {37,81,61,4,78,59,65,99,71,87,69,50,61,29,99,40,1,29,97,76,65,70,8,48,51,97,33,79,83,1,36,43,61,46,68,2,12,17,81,41,26,30,41,87,62,1,7,94,60,2574}

    Returns: 49

  17. {2574,37,81,61,4,78,59,65,99,71,87,69,50,61,29,99,40,1,29,97,76,65,70,8,48,51,97,33,79,83,1,36,43,61,46,68,2,12,17,81,41,26,30,41,87,62,1,7,94,60}

    Returns: 49

  18. {37,81,61,4,78,59,65,99,71,87,69,50,61,29,99,40,1,29,97,76,65,70,8,48,51,97,33,79,83,1,36,43,61,46,68,2,12,17,81,41,26,30,41,87,62,1,7,94,60,2575}

    Returns: 49

  19. {2575,37,81,61,4,78,59,65,99,71,87,69,50,61,29,99,40,1,29,97,76,65,70,8,48,51,97,33,79,83,1,36,43,61,46,68,2,12,17,81,41,26,30,41,87,62,1,7,94,60}

    Returns: 49

  20. {9999,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,9999,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,10000}

    Returns: 48

  21. {65,100,96,73,45,1,95}

    Returns: 6

  22. {69,41,10,18,31,66,32,7,33,67,15,1,45,81,34,81,83,23,45,54,41,26,19,1,79,26,53,76,74,81,95,24,59,21,89,1,79,29,25,19,29,61,85}

    Returns: 42

  23. {92,74,1,49,8,93,73,61,77,1,53,41,93,69,25,41,19,68,21}

    Returns: 18

  24. {1,65,49,57,29,97,9,55,55,59,39,75,89,26,13,96,19,13,97,81,43,97,57,83,53,29,88,94,86,25,35,73,55,47}

    Returns: 33

  25. {77,89,93,85,79,71,58,41,75,31,47,26,61,51,81,93,45,39,2,29,36,30,21,51,81}

    Returns: 24

  26. {97,88,21,45,76,47,79,26,91,33,67,53,51,37,70,13,41,11,76,97,63,27,45,3}

    Returns: 23

  27. {21,25,31,97,52,9,73,69,61,41,47,76,93,81,11,12,19,17,91,61,81,94,35,29,5,54,1,43,36,32,2,45,39}

    Returns: 32

  28. {44,27,33,1,15,39,25,21,61,16,29,15,45,55,95,15,49,34,60,83,71,96,5,27,33,21,25,77,27,21,93,15,96,66,76,55}

    Returns: 35

  29. {3,25,93,45,33,21,81,69,29,55,29,37,91,21,5}

    Returns: 14

  30. {51,57,34,44,89,65,84}

    Returns: 6

  31. {10,40,1,3,32,14,1,1,1,1,3,1,17,73,7,3,11,27,2,2,2,14,38,7,2,13,36,1,1,1,1,14,36,2,1,1,1,4,81,55,36,91,90,54,58,56,50,98,50,50}

    Returns: 32

  32. {1,1,9,6,9,9,1,7,1,1,6,1,9,1,3,9,10,1,1,9,3}

    Returns: 18

  33. {6,9,2,2,5,6,5,1,1,2,6,10,3,4,3,1,9,7,1,3,9,3,9,4,1,9,7,9,8,5,5,1,9,9}

    Returns: 25

  34. {5,3,1,1,1,9}

    Returns: 2

  35. {1,5,3,2,9,3,7,7,1,6,9,8,4,6,4,1,3,1,7,4,1,10,9,8,1,1,6,6,1,2,5,5,1,9,1,9,9,1,4,3,1,5,7,8,7,9,1,9,7,1}

    Returns: 38

  36. {9,3,5,1,9,7,6,3,6,9,1,5,5,3,3,1,8,5,9,10,1,3,5,9,1,1,3,2,3,1,1,1,1,9,5,6,9,1,8,5,10,8,8,3,5,9}

    Returns: 31

  37. {9,6,7,3,1,7,9,1,2,7,1,6,7}

    Returns: 11

  38. {3,7,1,1,9,3,9,5}

    Returns: 7

  39. {1,4,5,1,1,7,1,1,8,3,1,3,5,9,9,1,3,1,1,1,1,6,1,3,3,8,4,4,1,1,1,9,9,1,6,1,1,9,1}

    Returns: 24

  40. {6,6,6,4,1,2,1,1,6,5,3,1,1,1,1,2,3,7,9,1,1,7,1,1}

    Returns: 19

  41. {3,3,2,7,1,5,1,7,5}

    Returns: 8

  42. {2812,274,2557,794,4931,607,2060,728,842,2599,682,4136,4686,1264,9934,11,7059,21,456,1575,1067,3523,293,671,2656,6117,2942,2291,599,52,6034,3703,4590,1170,659,223,1018,3219,978,1855,9934,2505,3445,4136,3281,842,9120,3116,2229,298}

    Returns: 26

  43. {7046,3740,9590,6414,2949,3555,3830,7536,4294,610,241,1080,288,6627,1183,3118,1912,6,11,726,39,1452,2740,3562,740,7014,782,396,2496,2138,7810,1345,874,4011,8,275,7536,1095,2666,69,2439,100,158,310,548,5546,3817,9590,3740,7046}

    Returns: 24

  44. {1080,949,124,156,1605,9990,3695,4064,2906,1335,5027,870,60,44,1558,9258,92,134,1402,1242,3048,743,862,2031,3610,5720,1032,436,1419,49,5720,3610,2893,479,264,5918,9258,1662,870,6362,3785,1086,328,1771,1254,2441,2417,1727,5846,3914}

    Returns: 22

  45. {7110,5246,224,7062,227,1531,3636,87,54,385,2278,5,4,4923,2017,131,1445,2090,272,792,2494,1738,793,1369,1754,13,9578,9578,157,1886,1093,5025,792,272,2090,349,1227,6949,354,1924,476,50,722,4672,7062,5099,100,234,37,7110}

    Returns: 22

  46. {9615,9002,8374,1589,280,2466,4785,9898,284,483,5451,600,730,338,1537,396,1668,626,417,1503,2083,1212,106,1884,4420,919,3501,509,271,985,225,3295,4610,1875,1289,41,5490,728,6047,991,2860,6842,2278,1226,6318,449,381,9002,5507,4108}

    Returns: 26

  47. {342,132,368,2705,943,5077,763,23,2499,2017,88,28,581,1390,1068,3066,1856,1366,1595,563,1729,3109,3120,4133,3239,420,5570,2552,1388,1610,5,15,601,3058,349,6904,6996,6288,2238,5,215,653,23,21,2017,2499,786,924,4153,4490}

    Returns: 26

  48. {1841,8082,714,2144,4028,2705,99,40,328,99,988,120,146,4180,4420,3,2,33,109,9148,1124,3790,33,16,66,37,1436,1507,1490,580,1722,5299,1588,3790,631,392,101,9295,5513,688,2399,138,128,988,335,231,9591,8082,989,852}

    Returns: 26

  49. {7674,1022,250,5381,9802,3710,2994,128,578,6705,4399,2359,2599,2431,5362,3398,1678,1108,164,268,350,689,471,7359,2264,1092,4003,1778,1165,483,1302,4920,3840,744,759,928,1865,734,6758,6705,572,84,23,27,6704,1597,8205,6653,4268,3406}

    Returns: 24

  50. {5336,448,335,526,5004,1394,8630,2038,594,1693,6385,4831,234,1744,4423,1884,83,2085,3289,2582,9045,9045,4005,1866,1758,326,54,30,1092,716,44,15,17,4423,1744,1449,163,3453,3488,3713,877,2632,7611,647,294,78,1394,5865,2958,2826}

    Returns: 24

  51. {7073,755,7328,5694,277,5412,9642,9610,1,4,1805,1445,901,9750,432,2206,3328,3857,49,601,650,475,6710,1955,683,9750,417,1788,47,94,706,786,318,9610,777,4316,798,3751,864,3095,1730,1115,357,1472,2750,5639,164,423,1102,7828}

    Returns: 26

  52. {4674,9767,6172,4635,2114,2111,2213,7618,9050,4010,1994,235,1692,440,1252,95,12,128,1905,84,3,2,3953,4,45,8,9050,5181,669,1768,1700,351,162,591,99,1421,1312,178,624,4635,2914,3258,3848,150,1201,3680,888,2586,241,1847}

    Returns: 24

  53. {6562,8090,3460,8438,5998,3366,2274,4430,2644,3760,3188,572,1812,534,129,169,1976,1298,760,396,1225,905,88,13,43,332,1711,326,997,5123,582,145,52,96,476,7464,375,94,29,2615,845,2068,5086,643,293,5816,498,191,33,24}

    Returns: 30

  54. {730,7560,1370,8168,7662,9776,6905,750,8810,5810,3767,6160,7104,7104,2621,591,2891,57,961,1877,272,657,1968,1705,309,298,1530,1258,7552,393,357,4728,2177,2095,2442,993,3302,944,2658,4777,227,4314,3854,1258,21,91,4337,2046,1177,730}

    Returns: 24

  55. {529,6135,616,3230,4330,3780,4420,9106,5039,1334,917,1302,1325,34,19,60,48,3903,226,1370,1701,1906,4420,202,292,1457,1722,55,21,20,11,4330,1747,463,667,226,52,75,575,33,8,101,6034,26,401,47,34,8,13}

    Returns: 31

  56. {2826,5792,1827,924,4626,4670,3296,7366,2337,4568,301,67,41,20,32,3296,1635,1940,205,807,73,10,4626,845,64,9,1,5,156,1066,316,218,10,47,7,7,930,677,771,1384,742,274,832,66,73,43,1728,357,298,443}

    Returns: 34

  57. {3080,6957,9706,6490,4501,7018,3990,7794,1534,4796,217,624,623,3431,177,62,58,262,2202,3621,528,667,1278,3223,445,5953,44,26,15,3,4,2791,2712,2853,84,342,4,218,702,264,1361,3924,365,364,239,355,30,39,16,3080}{1,19,157,194,242,2078,5058,1,1,4,133,144,970,778,4645,1014,3,2,1,3,5,28,216,119,111,62,33,35,354,5,199,1528,1592,371,2146,894,934,12,120,212,706,7110,7110,1038,1840,6325,488,6437,1253,7749}

    Returns: 34

  58. {483,2828,381,553,1203,3918,202,1611,5,186,408,107,638,5,127,3157,3875,1291,240,93,37,36,521,1109,5964,2105,1288,383,83,452,734,70,5382,4890,4,790,3204,696,226,944,1816,3682,3998,4890,7104,3393,7760,9440,2210,9568}

    Returns: 32

  59. {158,34,151,295,1062,1326,1755,2170,488,717,20,11,8,13,49,82,302,761,2040,2,14,8,26,364,201,819,1339,1,2,4,1,2,192,4409,44,7,397,878,480,58,2286,671,3701,4372,4150,4611,1339,1434,3286,8156}

    Returns: 36

  60. {3874,776,2610,9,1,69,756,2,1,30,140,327,284,106,6935,275,3549,1656,14,393,54,311,4257,2931,927,362,1222,298,27,79,80,99,4970,1,1,1,1,1,1,16,1492,1514,5255,2809,7960,5480,6935,890,835,7260}

    Returns: 32

  61. {9600,7312,2,1,1,4,44,33,64,59,71,62,641,2407,5775,14,7693,1127,1,1,1,2,2,47,4,1019,926,38,860,987,1539,534,2346,1,3,6,4,76,130,2073,1082,3650,7025,6304,2003,8834,8956,208,7312,9600}

    Returns: 34

  62. {20,25,85,25,9,57,43,44,75,18,47,57,27,16,27,88,36,21,16,41,11,65,41,93,50,47,3,17,56,15,3,84,64,76,67,31,4,5,35,45,10,96,97,21,33,23,63,99,53,2084}

    Returns: 48

  63. {2084,20,25,85,25,9,57,43,44,75,18,47,57,27,16,27,88,36,21,16,41,11,65,41,93,50,47,3,17,56,15,3,84,64,76,67,31,4,5,35,45,10,96,97,21,33,23,63,99,53}

    Returns: 48

  64. {20,25,85,25,9,57,43,44,75,18,47,57,27,16,27,88,36,21,16,41,11,65,41,93,50,47,3,17,56,15,3,84,64,76,67,31,4,5,35,45,10,96,97,21,33,23,63,99,53,2085}

    Returns: 49

  65. {2085,20,25,85,25,9,57,43,44,75,18,47,57,27,16,27,88,36,21,16,41,11,65,41,93,50,47,3,17,56,15,3,84,64,76,67,31,4,5,35,45,10,96,97,21,33,23,63,99,53}

    Returns: 49

  66. {3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 13, 32, 12, 42, 26 }

    Returns: 39

  67. {15, 78, 87, 51 }

    Returns: 3

  68. {2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    Returns: 1

  69. {3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26 }

    Returns: 8

  70. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    Returns: 4

  71. {3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 3, 23, 21, 23, 42, 39, 63, 76, 13, 13, 13, 32, 12, 42, 26, 4, 5, 6, 7, 8 }

    Returns: 47

  72. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7 }

    Returns: 43

  73. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 12, 13, 14, 15, 16, 17, 18, 19, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 12, 13, 14, 15, 16, 17, 18, 19, 1 }

    Returns: 40

  74. {3, 233, 13, 32, 12, 42, 26 }

    Returns: 6

  75. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    Returns: 49

  76. {15, 78, 87, 51, 121, 121, 12, 12, 1232, 34, 23, 12, 12, 12, 12, 123, 3, 23, 12, 1, 3, 2, 3, 3, 1, 1, 23, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 12, 34, 234, 34, 234, 4, 34, 3, 4 }

    Returns: 45

  77. {2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2 }

    Returns: 6

  78. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 5, 6, 8, 9, 5, 6, 8, 9, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

    Returns: 41

  79. {15, 78, 87, 51, 121, 121, 12, 12, 1232, 34, 23, 12, 12, 12, 12, 123, 3, 23, 12, 1, 3, 2, 3, 3, 1, 1, 23, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 12, 34, 234, 34, 234, 4, 34, 3, 4, 34, 234, 324, 234 }

    Returns: 49

  80. {1 }

    Returns: 0

  81. {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

    Returns: 0

  82. {1, 7, 12, 16, 21, 26, 31, 36, 41, 46, 50, 55, 56, 80, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 151, 156, 161, 170, 175, 182, 187, 192, 200, 208, 212, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 280, 290 }

    Returns: 49

  83. {21, 31, 8, 112, 4, 1, 852, 3, 86, 3, 42, 3, 8, 12, 45, 1, 85, 3, 86, 3, 21, 31, 8, 112, 4, 1, 852, 3, 86, 3, 42, 3, 8, 12, 45, 1, 85, 3, 86, 3, 7, 88, 5, 2, 3, 4, 5, 7, 8, 9 }

    Returns: 49

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