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| github | https://github.com/JasonZhangCauc/JZOffer |
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- 剑指offer编程题（JAVA实现)——第35题：数组中的逆序对
- 题目描述
在数组中的两个数字，如果前面一个数字大于后面的数字，则这两个数字组成一个逆序对。
输入一个数组,求出这个数组中的逆序对的总数P。并将P对1000000007取模的结果输出。
即输出P%1000000007 - 输入描述:
题目保证输入的数组中没有的相同的数字 - 数据范围：
对于%50的数据,size<=10^4
对于%75的数据,size<=10^5
对于%100的数据,size<=2*10^5 - 示例1
输入
1,2,3,4,5,6,7,0
输出
7
public class Test35 {
//牛客网这道题的测试程序有问题，以至于这么写通不过
public static void main(String[] args) {
int[] array = { 1, 2, 3, 4, 5, 6, 7, 0 };
System.out.println(InversePairs(array));
int[] array2 = { 364, 637, 341, 406, 747, 995, 234, 971, 571, 219, 993, 407, 416, 366, 315, 301, 601, 650, 418,
355, 460, 505, 360, 965, 516, 648, 727, 667, 465, 849, 455, 181, 486, 149, 588, 233, 144, 174, 557, 67,
746, 550, 474, 162, 268, 142, 463, 221, 882, 576, 604, 739, 288, 569, 256, 936, 275, 401, 497, 82, 935,
983, 583, 523, 697, 478, 147, 795, 380, 973, 958, 115, 773, 870, 259, 655, 446, 863, 735, 784, 3, 671,
433, 630, 425, 930, 64, 266, 235, 187, 284, 665, 874, 80, 45, 848, 38, 811, 267, 575 };
int sysarray2 = InversePairs(array2);
System.out.println(sysarray2);// 2519
int[] array3 = { 627126, 415347, 850134, 371085, 279048, 705820, 453064, 944751, 92317, 58592, 167988, 284065,
992573, 78043, 190215, 104546, 607528, 391775, 701214, 849731, 231053, 603058, 975374, 199773, 479544,
143961, 206797, 325662, 90035, 69615, 429916, 717161, 484962, 796403, 604598, 280362, 502223, 57662,
741466, 594540, 632606, 909454, 394957, 625180, 503849, 585172, 729726, 627729, 976947, 947293, 477461,
724352, 66703, 452835, 440478, 62599, 596797, 163627, 388261, 203184, 233243, 334529, 436697, 234557,
647284, 41295, 514920, 665859, 615310, 256386, 776752, 247916, 682192, 171709, 389448, 186041, 273234,
635527, 813771, 766533, 582820, 807584, 490886, 649523, 260419, 447716, 228474, 373568, 611343, 616735,
576752, 844586, 467616, 529801, 595496, 631253, 571097, 110416, 297112, 186407, 883154, 73864, 950675,
81698, 245574, 340124, 267739, 35160, 975651, 597862, 801693, 74823, 921798, 292579, 240698, 182218,
256647, 469172, 72138, 867991, 602259, 165243, 228929, 69875, 695044, 824425, 701128, 782493, 451193,
998241, 485252, 334347, 588457, 435928, 416045, 350383, 292404, 200137, 385543, 268055, 314351, 187237,
859230, 236150, 996168, 99928, 934720, 252816, 569100, 523210, 120807, 171359, 688453, 866088, 757586,
383498, 206866, 458715, 682343, 658059, 973308, 167596, 508759, 78117, 603524, 441156, 428501, 412280,
157645, 814044, 196687, 471997, 1281, 55917, 224499, 997450, 155845, 159219, 250266, 241297, 682429,
887425, 412656, 887235, 269865, 686594, 787085, 476731, 661661, 469428, 134791, 634969, 637024, 643550,
229439, 756900, 601058, 657940, 169180, 758704, 471984, 365867, 230701, 473266, 421784, 455200, 470716,
93981, 130771, 237334, 335278, 329552, 641111, 264286, 733139, 910976, 950881, 520224, 904060, 612542,
989653, 38851, 763864, 143029, 198753, 993303, 899930, 799811, 651243, 585462, 558515, 639579, 951330,
305568, 112845, 889466, 277120, 99913, 499800, 924243, 853599, 835078, 770148, 11062, 615717, 503287,
922039, 82950, 23512, 826099, 695492, 529517, 381302, 975708, 672546, 96407, 485363, 88828, 896218,
652958, 674291, 971086, 292538, 141973, 276654, 921735, 547791, 70127, 21649, 47591, 994370, 391600,
399022, 764518, 402663, 14739, 267806, 841054, 97689, 807670, 183505, 309533, 337187, 564807, 801594,
9733, 661214, 803309, 614914, 73784, 456268, 805557, 44870, 265158, 947530, 837877, 703245, 11673,
908004, 241246, 59265, 418726, 632847, 974639, 183245, 35510, 505730, 967403, 392916, 603419, 775073,
576421, 429304, 112260, 141228, 747250, 638345, 318794, 550560, 769611, 392578, 523180, 575168, 953801,
304690, 39050, 308030, 7935, 50724, 216034, 249182, 626341, 151112, 882029, 600980, 334357, 433891,
106710, 818112, 826807, 226481, 593185, 919580, 172137, 221797, 60808, 919388, 376495, 895954, 986300,
146106, 804884, 509480, 237627, 275037, 814170, 276677, 583067, 338457, 327401, 315453, 587639, 953742,
466566, 986020, 71074, 317275, 936263, 694136, 135388, 763070, 920617, 728573, 682650, 92755, 466723,
259810, 528495, 843218, 672116, 514795, 505676, 477001, 24275, 259655, 752038, 354797, 536333, 335106,
693254, 380086, 166911, 797246, 850181, 633477, 783266, 921255, 950753, 719530, 615392, 86141, 998952,
52361, 331066, 197955, 661468, 797789, 974117, 189963, 157359, 646234, 704758, 179388, 639587, 245385,
439043, 907977, 116534, 491728, 759435, 809789, 871815, 926347, 123387, 721996, 559824, 423005, 159603,
510577, 142535, 774995, 113070, 657840, 343709, 444137, 372147, 5177, 758278, 346264, 195141, 915638,
508850, 416251, 611378, 664789, 661637, 50421, 572767, 294523, 58502, 332202, 620664, 930317, 258549,
744051, 652313, 818374, 167057, 811916, 845303, 825944, 103264, 474726, 483784, 446973, 918863, 855931,
968502, 677141, 718548, 163643, 109131, 743750, 96247, 720509, 408540, 274236, 287283, 981307, 568759,
862137, 313509, 189424, 792454, 88411, 933475, 961119, 423137, 616884, 773035, 268440, 442829, 392651,
743166, 442965, 839624, 178381, 815249, 324479, 371875, 533797, 488122, 481006, 793899, 100721, 717868,
202439, 374957, 521503, 183746, 943717, 383640, 13608, 133141, 692446, 618371, 582968, 653565, 41508,
716205, 942952, 826300, 159034, 335604, 85819, 118351, 691580, 780552, 933600, 16059, 152427, 983749,
20534, 149786, 777649, 121255, 384006, 980088, 496213, 421861, 680187, 956282, 321853, 210147, 605775,
14299, 828518, 188743, 667864, 386378, 904948, 610816, 212678, 580334, 462772, 814849, 698686, 154353,
595402, 148638, 170412, 747829, 132388, 190946, 897615, 910037, 828554, 797973, 406477, 324767, 219834,
603016, 281049, 541687, 813163, 886824, 555986, 158033, 591919, 740202, 60763, 13220, 867371, 789794,
109906, 330143, 604643, 324944, 484496, 200045, 473583, 171261, 464227, 605971, 878559, 878194, 32360,
707113, 676168, 438837, 31880, 896002, 41854, 829281, 954042, 371369, 232457, 510028, 45755, 340729,
766583, 106518, 353949, 633954, 896312, 463855, 964097, 17308, 788800, 448594, 733705, 262383, 619855,
714284, 384706, 498414, 592479, 417066, 721880, 784999, 855903, 753760, 197353, 414109, 99394, 151395,
301831, 848203, 177776, 347586, 188932, 944359, 970456, 542881, 578313, 383121, 523089, 58762, 400429,
828241, 507356, 134134, 606976, 643563, 848419, 991682, 658330, 957250, 408748, 380210, 258601, 781003,
650322, 455954, 195113, 266068, 123702, 13296, 114272, 301478, 360882, 303204, 762189, 331338, 846086,
856854, 714459, 885527, 915616, 631240, 713768, 939325, 281727, 837096, 99240, 646498, 828778, 757570,
603748, 753878, 654132, 862349, 534881, 304455, 834655, 246346, 86875, 958357, 259642, 201147, 776187,
136876, 504352, 538376, 984567, 866790, 911582, 699026, 268669, 343551, 846619, 982437, 282876, 128346,
819533, 382116, 774844, 164663, 656039, 894944, 918541, 826523, 273645, 969774, 647330, 108300, 732473,
734206, 66658, 508467, 935353, 359197, 161696, 956057, 413926, 146263, 339199, 325508, 361641, 607868,
669059, 208260, 106657, 468287, 336606, 442542, 366756, 627802, 607205, 539147, 522746, 42098, 365670,
796391, 528225, 13001, 421044, 777050, 747207, 4054, 285517, 198912, 363251, 447213, 154970, 777177,
593476, 494169, 619038, 471470, 102038, 804449, 679730, 208695, 272737, 532689, 651238, 160491, 774795,
694992, 199590, 333246, 60662, 512333, 861471, 590015, 933377, 638521, 337222, 937431, 440390, 536135,
300683, 887604, 691105, 594212, 997432, 701626, 213250, 468902, 320016, 17700, 664985, 528712, 806789,
197674, 696302, 962634, 874517, 987449, 173978, 74107, 320695, 234640, 102793, 182166, 824656, 36170,
337039, 678230, 489954, 777430, 214365, 790637, 181386, 421822, 901201, 178818, 639801, 114452, 164073,
959817, 648504, 829058, 4881, 971645, 543084, 217535, 934279, 417601, 204985, 108257, 8061, 525680,
859249, 110854, 224199, 200257, 663376, 561238, 878488, 153330, 855020, 609205, 460319, 36406, 547380,
361521, 731577, 187181, 992325, 895650, 146998, 157181, 241060, 668232, 128826, 784144, 885767, 579457,
718097, 90752, 687714, 726158, 132785, 63315, 353364, 873336, 263573, 533093, 950926, 142061, 686423,
805947, 267618, 663095, 842353, 814998, 540968, 573930, 518531, 49645, 985932, 665530, 206826, 226992,
850114, 852004, 527488, 735881, 431461, 245586, 342986, 488096, 475771, 698842, 357813, 349107, 962415,
890906, 300033, 620828, 93681, 622332, 404799, 273128, 464686, 219797, 814096, 554968, 738329, 863741,
540901, 920211, 586919, 284245, 770325, 438923, 811734, 22558, 870384, 573672, 365544, 505911, 578120,
841315, 721106, 935933, 706774, 683521, 343191, 523160, 820702, 436873, 145492, 225501, 710001, 126530,
961650, 40450, 681499, 216331, 904191, 738752, 136542, 7463, 22997, 423219, 446386, 834731, 445778,
833123, 924755, 811322, 339034, 502876, 168990, 576492, 438809, 392116, 260014, 782001, 431628, 597068,
735226, 93473, 338921, 445227, 220003, 300571, 2029, 417854, 516903, 906221, 156606, 169797, 430036,
179604, 593017, 876422, 530687, 38795, 709545, 455443, 366469, 564932, 958319, 535459, 141424, 913480,
443928, 917790, 211833, 875556, 31210, 947059, 969029, 886483, 908639, 705385, 187055, 910668, 123239,
220310, 333241, 796198, 906459, 763277, 492154, 15828, 156052, 22841, 570975, 381949, 994636, 937445,
463233, 469307, 989256, 121010, 899140, 433184, 555152, 110973, 308741, 586363, 58033, 794122, 472846 };
System.out.println(InversePairs(array3));
}
public static int InversePairs(int[] array) {
double tmp = InversePairsHelper(array);
double length = array.length - 1;
return (int) ((length / 2.0 * length + length / 2.0) - tmp) % 1000000007;
}
public static int InversePairsHelper(int[] array) {
if (array == null || array.length < 2) {
return 0;
}
return mergeSort(array, 0, array.length - 1);
}
public static int mergeSort(int[] arr, int l, int r) {
if (l == r) {
return 0;
}
int mid = l + ((r - l) >> 1);
return mergeSort(arr, l, mid) + mergeSort(arr, mid + 1, r) + merge(arr, l, mid, r);
}
public static int merge(int[] arr, int l, int m, int r) {
int[] help = new int[r - l + 1];
int i = 0;
int p1 = l;
int p2 = m + 1;
int res = 0;
while (p1 <= m && p2 <= r) {
// res += arr[p1] < arr[p2] ? (r - p2 + 1) * arr[p1] : 0;
res += arr[p1] < arr[p2] ? (r - p2 + 1) * 1 : 0;
help[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];
}
while (p1 <= m) {
help[i++] = arr[p1++];
}
while (p2 <= r) {
help[i++] = arr[p2++];
}
for (i = 0; i < help.length; i++) {
arr[l + i] = help[i];
}
return res;
}
}
/**
* 其他方法
public static int InversePairs(int [] array) {
if(array==null||array.length==0)
{
return 0;
}
int[] copy = new int[array.length];
for(int i=0;i<array.length;i++)
{
copy[i] = array[i];
}
int count = InversePairsCore(array,copy,0,array.length-1);//数值过大求余
return count;
}
private static int InversePairsCore(int[] array,int[] copy,int low,int high)
{
if(low==high)
{
return 0;
}
int mid = (low+high)>>1;
int leftCount = InversePairsCore(array,copy,low,mid)%1000000007;
int rightCount = InversePairsCore(array,copy,mid+1,high)%1000000007;
int count = 0;
int i=mid;
int j=high;
int locCopy = high;
while(i>=low&&j>mid)
{
if(array[i]>array[j])
{
count += j-mid;
copy[locCopy--] = array[i--];
if(count>=1000000007)//数值过大求余
{
count%=1000000007;
}
}
else
{
copy[locCopy--] = array[j--];
}
}
for(;i>=low;i--)
{
copy[locCopy--]=array[i];
}
for(;j>mid;j--)
{
copy[locCopy--]=array[j];
}
for(int s=low;s<=high;s++)
{
array[s] = copy[s];
}
return (leftCount+rightCount+count)%1000000007;
}
public static void main (String[] args) throws java.lang.Exception
{
int[] array={1,2,3,4,5,6,7,0};
System.out.println(InversePairs(array));
int[] array2 = {364,637,341,406,747,995,234,971,571,219,993,407,416,366,315,301,601,650,418,355,460,505,360,965,516,648,727,667,465,849,455,181,486,149,588,233,144,174,557,67,746,550,474,162,268,142,463,221,882,576,604,739,288,569,256,936,275,401,497,82,935,983,583,523,697,478,147,795,380,973,958,115,773,870,259,655,446,863,735,784,3,671,433,630,425,930,64,266,235,187,284,665,874,80,45,848,38,811,267,575};
System.out.println(InversePairs(array2));
int [] array3 = {627126,415347,850134,371085,279048,705820,453064,944751,92317,58592,167988,284065,992573,78043,190215,104546,607528,391775,701214,849731,231053,603058,975374,199773,479544,143961,206797,325662,90035,69615,429916,717161,484962,796403,604598,280362,502223,57662,741466,594540,632606,909454,394957,625180,503849,585172,729726,627729,976947,947293,477461,724352,66703,452835,440478,62599,596797,163627,388261,203184,233243,334529,436697,234557,647284,41295,514920,665859,615310,256386,776752,247916,682192,171709,389448,186041,273234,635527,813771,766533,582820,807584,490886,649523,260419,447716,228474,373568,611343,616735,576752,844586,467616,529801,595496,631253,571097,110416,297112,186407,883154,73864,950675,81698,245574,340124,267739,35160,975651,597862,801693,74823,921798,292579,240698,182218,256647,469172,72138,867991,602259,165243,228929,69875,695044,824425,701128,782493,451193,998241,485252,334347,588457,435928,416045,350383,292404,200137,385543,268055,314351,187237,859230,236150,996168,99928,934720,252816,569100,523210,120807,171359,688453,866088,757586,383498,206866,458715,682343,658059,973308,167596,508759,78117,603524,441156,428501,412280,157645,814044,196687,471997,1281,55917,224499,997450,155845,159219,250266,241297,682429,887425,412656,887235,269865,686594,787085,476731,661661,469428,134791,634969,637024,643550,229439,756900,601058,657940,169180,758704,471984,365867,230701,473266,421784,455200,470716,93981,130771,237334,335278,329552,641111,264286,733139,910976,950881,520224,904060,612542,989653,38851,763864,143029,198753,993303,899930,799811,651243,585462,558515,639579,951330,305568,112845,889466,277120,99913,499800,924243,853599,835078,770148,11062,615717,503287,922039,82950,23512,826099,695492,529517,381302,975708,672546,96407,485363,88828,896218,652958,674291,971086,292538,141973,276654,921735,547791,70127,21649,47591,994370,391600,399022,764518,402663,14739,267806,841054,97689,807670,183505,309533,337187,564807,801594,9733,661214,803309,614914,73784,456268,805557,44870,265158,947530,837877,703245,11673,908004,241246,59265,418726,632847,974639,183245,35510,505730,967403,392916,603419,775073,576421,429304,112260,141228,747250,638345,318794,550560,769611,392578,523180,575168,953801,304690,39050,308030,7935,50724,216034,249182,626341,151112,882029,600980,334357,433891,106710,818112,826807,226481,593185,919580,172137,221797,60808,919388,376495,895954,986300,146106,804884,509480,237627,275037,814170,276677,583067,338457,327401,315453,587639,953742,466566,986020,71074,317275,936263,694136,135388,763070,920617,728573,682650,92755,466723,259810,528495,843218,672116,514795,505676,477001,24275,259655,752038,354797,536333,335106,693254,380086,166911,797246,850181,633477,783266,921255,950753,719530,615392,86141,998952,52361,331066,197955,661468,797789,974117,189963,157359,646234,704758,179388,639587,245385,439043,907977,116534,491728,759435,809789,871815,926347,123387,721996,559824,423005,159603,510577,142535,774995,113070,657840,343709,444137,372147,5177,758278,346264,195141,915638,508850,416251,611378,664789,661637,50421,572767,294523,58502,332202,620664,930317,258549,744051,652313,818374,167057,811916,845303,825944,103264,474726,483784,446973,918863,855931,968502,677141,718548,163643,109131,743750,96247,720509,408540,274236,287283,981307,568759,862137,313509,189424,792454,88411,933475,961119,423137,616884,773035,268440,442829,392651,743166,442965,839624,178381,815249,324479,371875,533797,488122,481006,793899,100721,717868,202439,374957,521503,183746,943717,383640,13608,133141,692446,618371,582968,653565,41508,716205,942952,826300,159034,335604,85819,118351,691580,780552,933600,16059,152427,983749,20534,149786,777649,121255,384006,980088,496213,421861,680187,956282,321853,210147,605775,14299,828518,188743,667864,386378,904948,610816,212678,580334,462772,814849,698686,154353,595402,148638,170412,747829,132388,190946,897615,910037,828554,797973,406477,324767,219834,603016,281049,541687,813163,886824,555986,158033,591919,740202,60763,13220,867371,789794,109906,330143,604643,324944,484496,200045,473583,171261,464227,605971,878559,878194,32360,707113,676168,438837,31880,896002,41854,829281,954042,371369,232457,510028,45755,340729,766583,106518,353949,633954,896312,463855,964097,17308,788800,448594,733705,262383,619855,714284,384706,498414,592479,417066,721880,784999,855903,753760,197353,414109,99394,151395,301831,848203,177776,347586,188932,944359,970456,542881,578313,383121,523089,58762,400429,828241,507356,134134,606976,643563,848419,991682,658330,957250,408748,380210,258601,781003,650322,455954,195113,266068,123702,13296,114272,301478,360882,303204,762189,331338,846086,856854,714459,885527,915616,631240,713768,939325,281727,837096,99240,646498,828778,757570,603748,753878,654132,862349,534881,304455,834655,246346,86875,958357,259642,201147,776187,136876,504352,538376,984567,866790,911582,699026,268669,343551,846619,982437,282876,128346,819533,382116,774844,164663,656039,894944,918541,826523,273645,969774,647330,108300,732473,734206,66658,508467,935353,359197,161696,956057,413926,146263,339199,325508,361641,607868,669059,208260,106657,468287,336606,442542,366756,627802,607205,539147,522746,42098,365670,796391,528225,13001,421044,777050,747207,4054,285517,198912,363251,447213,154970,777177,593476,494169,619038,471470,102038,804449,679730,208695,272737,532689,651238,160491,774795,694992,199590,333246,60662,512333,861471,590015,933377,638521,337222,937431,440390,536135,300683,887604,691105,594212,997432,701626,213250,468902,320016,17700,664985,528712,806789,197674,696302,962634,874517,987449,173978,74107,320695,234640,102793,182166,824656,36170,337039,678230,489954,777430,214365,790637,181386,421822,901201,178818,639801,114452,164073,959817,648504,829058,4881,971645,543084,217535,934279,417601,204985,108257,8061,525680,859249,110854,224199,200257,663376,561238,878488,153330,855020,609205,460319,36406,547380,361521,731577,187181,992325,895650,146998,157181,241060,668232,128826,784144,885767,579457,718097,90752,687714,726158,132785,63315,353364,873336,263573,533093,950926,142061,686423,805947,267618,663095,842353,814998,540968,573930,518531,49645,985932,665530,206826,226992,850114,852004,527488,735881,431461,245586,342986,488096,475771,698842,357813,349107,962415,890906,300033,620828,93681,622332,404799,273128,464686,219797,814096,554968,738329,863741,540901,920211,586919,284245,770325,438923,811734,22558,870384,573672,365544,505911,578120,841315,721106,935933,706774,683521,343191,523160,820702,436873,145492,225501,710001,126530,961650,40450,681499,216331,904191,738752,136542,7463,22997,423219,446386,834731,445778,833123,924755,811322,339034,502876,168990,576492,438809,392116,260014,782001,431628,597068,735226,93473,338921,445227,220003,300571,2029,417854,516903,906221,156606,169797,430036,179604,593017,876422,530687,38795,709545,455443,366469,564932,958319,535459,141424,913480,443928,917790,211833,875556,31210,947059,969029,886483,908639,705385,187055,910668,123239,220310,333241,796198,906459,763277,492154,15828,156052,22841,570975,381949,994636,937445,463233,469307,989256,121010,899140,433184,555152,110973,308741,586363,58033,794122,472846};
System.out.println(InversePairs(array3));
}
*/
//超时程序
/*public static int InversePairs(int[] array) {
int count = 0;
int length = array.length;
for (int i = 0; i < length - 1; i++) {
for (int j = i + 1; j < length; j++) {
count = array[i] > array[j] ? count + 1 : count;
}
}
return count % 1000000007;
}*/