2021杭电多校赛2021“MINIEYE杯”中国大学生算法设计超级联赛（10）签到题2题

Posted 2021-09-09 小哈里

Solved Pro.ID Title Ratio(Accepted / Submitted)
1001 Pty loves sequence 25.00%(52/208)
1002 Pty with card 13.33%(2/15)
1003 Pty loves lines 11.97%(443/3700)（打表，dp到某个数为止后面连续）
1004 Pty hates prime numbers 5.89%(44/747)（容斥原理，处理到某个数为止前面打表）
1005 Pty loves book 0.00%(0/4)
1006 Pty loves lcm 19.30%(11/57)
1007 Pty loves graph 4.28%(14/327)
1008 Pty loves string 13.87%(113/815)
1009 Pty loves SegmentTree 22.22%(6/27)
1010 Pty plays game 6.82%(36/528)

1003 Pty loves lines

题意：

• 平面上有n条直线，且无三线共点，问这些直线能有多少种不同交点数，输出方案，n<=700

思路：

• 原题是HDOJ1466，不过数据只有20。
• 首先考虑原本简单情况下的做法是dp：
  • 我们知道，n条直线互不平行且无三线共点的最多交点数max=1+2+……(n-1)=n(n-1)/2。
  • 假设一共有n=a+b条直线（即n条直线分成2组，分别为a条和b条）则总的交点数= a内的交点数＋b内的交点数＋a，b之间的交点数
  • 我们将n条直线分为两部分,平行的直线数目r，和不平行的数目n-r；分析可以知道r的取值是0<=r<=n;
  • n条直线相交的方案数=(n-r）条平行线的交点方案（为0）+r条直线本身的交点方案+（n-r）条平行线与r条直线交叉的交点数方案= r条直线本身的交点方案 +（n-r）条平行线与r条直线交叉的交点数方案。=（m-r）*r+r条之间本身的交点方案数（0<=r<=n）
• 再考虑本题的做法，我们打表后可以发现，答案有一段连续的可行后缀，于是我们可以dp预处理出所有的后缀，存到数组里面，每次dp到可行后缀的开始就停止枚举，然后直接输出即可。
• 大佬也可以用bitset来优化转移，就不需要打表了。

#include<bits/stdc++.h>
using namespace std;
int ed[] = {0, 0,0,2,3,6,11,14,15,23,27,30,41,46,59,65,71,84,91,98,105,108,119,126,143,140,159,185,194,203,227,237,247,257,267,273,287,293,327,365,377,389,371,382,425,437,443,461,473,514,563,540,591,605,619,633,647,695,710,725,740,755,770,785,759,815,827,887,903,875,935,951,1019,980,1053,1070,1087,1104,1121,1138,1155,1172,1243,1206,1279,1297,1315,1333,1351,1369,1387,1405,1415,1433,1523,1542,1561,1580,1599,1549,1567,1656,1675,1694,1713,1732,1751,1770,1865,1885,1905,1925,1945,1965,1985,2005,2025,2045,2065,2085,2105,2125,2145,2165,2185,2292,2313,2334,2355,2375,2397,2418,2439,2460,2481,2502,2627,2649,2671,2693,2715,2733,2759,2781,2803,2825,2847,2869,2891,2913,2935,2957,3093,3116,3139,3162,3185,3208,3231,3383,3407,3431,3455,3479,3503,3527,3551,3438,3599,3623,3647,3671,3695,3719,3743,3767,3791,3815,3839,3863,3887,3911,3935,3959,3983,4007,4031,4190,4215,4240,4127,4290,4315,4340,4527,4721,4748,4775,4802,4829,4856,4883,4910,4937,4964,4991,5018,5045,5072,5099,5126,5153,5177,5207,5402,5430,5458,5486,5514,5542,5570,5598,5623,5654,5682,5710,5738,5766,5794,5822,5850,5878,5906,5934,6148,6177,6206,6235,6264,6293,6527,6557,6587,6617,6647,6677,6707,6737,6767,6797,6827,6857,6887,6917,6947,6977,7007,7022,7067,7097,7127,7367,7398,7429,7460,7491,7522,7553,7367,7615,7646,7677,7708,7739,7770,7801,7832,7863,7894,7925,7956,7987,8018,8279,8311,8343,8375,8407,8439,8471,8503,8535,8567,8599,8631,8663,8695,8727,8759,8791,8823,8855,8887,8919,8951,8983,9266,9299,9332,9365,9398,9431,9464,9497,9530,9563,9596,9629,9662,9695,9728,9761,9794,9559,9860,9893,9926,9959,9992,10025,10331,10365,10399,10433,10467,10497,10535,10569,10603,10637,10671,10705,10739,10773,10807,10841,10875,10909,10943,10977,11011,11045,11079,11113,11147,11181,11215,11249,11283,11613,11648,11683,11718,11753,11788,11823,11858,11893,11928,11963,11998,12033,12068,12103,12138,12173,12208,12243,12278,12313,12348,12707,12743,12779,12815,12851,12887,12923,12959,12995,13031,13067,13103,13139,13175,13211,13247,13283,13319,13355,13391,13427,13463,13499,13535,13571,13607,13643,13679,13715,13751,13787,14168,14205,14242,14279,14691,15107,15146,15185,15224,15263,15302,15341,15380,15419,15458,15497,15536,15575,15614,15653,15692,15731,15770,15809,15848,15887,15926,15965,16004,16043,16082,15717,16160,16577,16617,16657,16697,16737,16777,16817,16857,16897,16937,16977,17017,16667,17097,17137,17177,17217,17257,17297,17337,17377,17417,17457,17497,17537,17577,17617,17657,17697,18142,18183,18224,18265,18306,18347,18388,18429,18470,18511,18552,18593,18634,18675,18716,18757,18798,18839,18880,18921,18962,19003,19044,19085,19126,19167,19208,19249,19290,19331,19372,19413,19454,19495,19536,19577,19618,19659,19700,19741,19782,19823,19864,19905,19946,19987,20028,20069,20110,20151,20192,20233,20274,20315,20356,20397,20438,20479,20520,20561,21035,21077,21119,21161,21203,21245,21287,21329,21371,21413,21455,21497,21539,21581,21623,21665,21707,21749,21791,21833,21875,21917,21959,22001,22043,22085,22127,22169,22211,22253,22295,22337,22871,23437,23481,23525,23569,23613,23657,23701,23745,23789,23833,23877,23921,23965,24009,24053,24097,24141,24185,24229,24273,24317,24361,24405,24449,24493,24537,24581,24625,24669,24713,24757,24801,24845,25412,25457,25502,25547,25592,25637,25682,25727,25772,25817,25862,25907,25952,25997,26042,26087,26132,26177,26222,26267,26312,26357,26402,26447,26492,26537,26582,26627,26672,26717,26762,26807,26852,26897,26942,26987,27032,27077,27122,27167,27767,27813,27859,27905,27951,27997,28043,28089,28135,28181,28227,28273,28319,28365,28411,28457,28503,28549,28595,28641,28687,28733,28779,28825,28871,28917,28963,29009,29055,29695,29742,29789,29836,29883,29930,29977,30024,30071,30118,30165,30212,30259,30306,30353,30400,30447,30494,30541,30588,30635,30682,30729,30776,30823,30870,30917,30964,31011,31058,31105,31152};
int big[] = {0,1,2,3,5,7,9,13,18,21,27,34,39,46,54,61,72,83,92,106,118,130,145,162,176,193,209,226,246,265,284,308,330,352,375,402,426,453,480,508,538,570,598,631,661,694,730,765,800,835,872,911,951,992,1030,1071,1115,1158,1203,1251,1295,1343,1392,1440,1491,1541,1590,1642,1695,1750,1806,1861,1917,1977,2033,2092,2154,2216,2276,2340,2404,2467,2535,2605,2672,2741,2812,2882,2951,3024,3096,3170,3245,以上是关于2021杭电多校赛2021“MINIEYE杯”中国大学生算法设计超级联赛（10）签到题2题的主要内容，如果未能解决你的问题，请参考以下文章
 
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