主题:第54次编程比赛
yxs0001 [专家分:9560] 发布于 2007-05-27 17:06:00
题目1(60分):对于一个自然数n,可以把它转换成对应的二进制数a[k] a[k-1] ..... a[1] a[0],其
中:n= ∑a[i] * 2^i 而且 a[i]=0 或1 (0=< i < k) , a[k]=1。如:10 转换为1010;5 转换为 101。
我们统计一下a[0]......a[k]这k+1 个数中的0 的个数和1 的个数。如果在这k+1 个数中,0 的个数比1
个数多,就称n为A类数。给定m,求1~m (包含1,m)中A类数的个数。
函数接口:int solve(int m)
例如:m=3 return 0
题目2(40分):已知n∈Q,则2n+1∈Q,4n+5∈Q;且 1∈Q,求Q中第k小元素。
函数接口:int Q(int k)
判分要求:
1、结果正确得分,错误该题0分。
2、结果正确者,计分方法:该题用时最少者满分,其他按与满分者用时比计算。(例如,第一题最佳时
间1s,某人用时2s,则 1/2*60 = 30)
3、二题得分之和最大者胜出。
格式要求:所有代码包含在参赛者名字的名字空间中。例如:
//名字空间
namespace yxs0001
{
//以下为参赛代码
int solve(int m)
{
return 0;
}
int Q(int k)
{
return 0;
}
}
或
namespace yxs0001
{
int solve(int m)
{
return 0;
}
}
namespace yxs0001
{
int Q(int k)
{
return 0;
}
}
回复列表 (共34个回复)
沙发
雨中飞燕 [专家分:18980] 发布于 2007-05-27 17:19:00
NOI啊??明显NOI的评分规则
干嘛弄两题啊
板凳
poemsea [专家分:90] 发布于 2007-05-27 19:17:00
namespace poemsea
{
int solve(int m)
{
int a=0,b=0,c=0,i,tmp;
for(i=1;i<=m;i++)
{
tmp=i;
a=0;b=0;
while(tmp>0)
{
if(tmp&1==1)
a++;
else
b++;
/*printf("%d",tmp&1);*/
tmp=tmp>>1;
}
/*printf("\n");*/
if(a<b)c++;
}
/*printf("a=%d b=%d\n",a,b);*/
return c;
}
}
3 楼
goal00001111 [专家分:4030] 发布于 2007-05-27 23:17:00
第一题:
/*
算法思路:
空间换时间的思想:把32位数分为4段,每段一个字节,所以有一个256大小供查询的表。预建立两个个表,分别存放0-255每个数中1和0的个数,然后分段查询。
*/
int FindOne(int lib[], int n)//求二进制数n中1的个数
{
int s = 0;
while (n > 0)
{
s += lib[n&255];
n >>= 8;
}
return s;
}
int FindZero(int lib[], int n)//求二进制数n中0的个数
{
int s = 0;
while (n > 0)
{
s += lib[n&255];
n >>= 8;
}
return s;
}
int solve(int m)
{
int lib_1[256] = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8};
int lib_0[256] = {1, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0};
int s = 0;
for (int i=1; i<=m; ++i)
{
if (FindOne(lib_1, i) < FindZero(lib_0, i))
++s;
}
return s;
}
4 楼
goal00001111 [专家分:4030] 发布于 2007-05-27 23:18:00
第2题:
int Insert(int a[], int len, int x)//用二分法将x插入有序数组a,若重复则不插入
{
int low = 0;
int high = len - 1;
int mid;
while (low <= high)
{
mid = (low + high) / 2;
if (a[mid] == x)//数组中已有与x相等的元素,不插入,直接返回
return len;
else if (a[mid] < x)
low = mid + 1;
else
high = mid - 1;
}
for (int i=len; i>low; --i)//插入x
{
a[i] = a[i-1];
}
a[low] = x;
return len + 1;//返回新数组的长度,即原长加1
}
int Q(int k)
{
int *a = new int[k+2];
a[0] = 1;
int len = 1;
int p = 0;
while (len < k)//先存储k个元素
{
len = Insert(a, len, 2*a[p]+1);
len = Insert(a, len, 4*a[p]+5);
++p;
}
while (len > k)//去掉多余的元素
--len;
while (2*a[p]+1 < a[k-1])//因为前面存储的元素并非前k个元素,需要继续计算,直至得到前k个元素
{
Insert(a, len, 2*a[p]+1);
Insert(a, len, 4*a[p]+5);
++p;
}
// for (int i=0; i<len; ++i)
// cout << a[i] << " ";
// cout << endl;
int num = a[k-1];
delete []a;
return num;
}
5 楼
goal00001111 [专家分:4030] 发布于 2007-05-28 00:13:00
想作弊就这样写吧,呵呵!
int Insert(int a[], int len, int x)//用二分法将x插入有序数组a,若重复则不插入
{
int low = 0;
int high = len - 1;
int mid;
while (low <= high)
{
mid = (low + high) / 2;
if (a[mid] == x)//数组中已有与x相等的元素,不插入,直接返回
return len;
else if (a[mid] < x)
low = mid + 1;
else
high = mid - 1;
}
for (int i=len; i>low; --i)//插入x
{
a[i] = a[i-1];
}
a[low] = x;
return len + 1;//返回新数组的长度,即原长加1
}
int Q(int k)
{//建立一个表,存储了k=[1-MAX]之间的答案。表还可以建大些
const int MAX = 10000;
6 楼
goal00001111 [专家分:4030] 发布于 2007-05-28 00:27:00
接上:
int lib[MAX]={1,3,7,9,15,17,19,31,33,35,39,41,63,65,67,71,73,79,81,83,127,129,131,135,137,143,145,147,159,161,163,167,169,255,257,259,263,265,271,273,275,287,289,291,295,297,319,321,323,327,329,335,337,339,511,513,515,519,521,527,529,531,543,545,547,551,553,575,577,579,583,585,591,593,595,639,641,643,647,649,655,657,659,671,673,675,679,681,1023,1025,1027,1031,1033,1039,1041,1043,1055,1057,1059,1063,1065,1087,1089,1091,1095,1097,1103,1105,1107,1151,1153,1155,1159,1161,1167,1169,1171,1183,1185,1187,1191,1193,1279,1281,1283,1287,1289,1295,1297,1299,1311,1313,1315,1319,1321,1343,1345,1347,1351,1353,1359,1361,1363,2047,2049,2051,2055,2057,2063,2065,2067,2079,2081,2083,2087,2089,2111,2113,2115,2119,2121,2127,2129,2131,2175,2177,2179,2183,2185,2191,2193,2195,2207,2209,2211,2215,2217,2303,2305,2307,2311,2313,2319,2321,2323,2335,2337,2339,2343,2345,2367,2369,2371,2375,2377,2383,2385,2387,2559,2561,2563,2567,2569,2575,2577,2579,2591,2593,2595,2599,2601,2623,2625,2627,2631,2633,2639,2641,2643,2687,2689,2691,2695,2697,2703,2705,2707,2719,2721,2723,2727,2729,4095,4097,4099,4103,4105,4111,4113,4115,4127,4129,4131,4135,4137,4159,4161,4163,4167,4169,4175,4177,4179,4223,4225,4227,4231,4233,4239,4241,4243,4255,4257,4259,4263,4265,4351,4353,4355,4359,4361,4367,4369,4371,4383,4385,4387,4391,4393,4415,4417,4419,4423,4425,4431,4433,4435,4607,4609,4611,4615,4617,4623,4625,4627,4639,4641,4643,4647,4649,4671,4673,4675,4679,4681,4687,4689,4691,4735,4737,4739,4743,4745,4751,4753,4755,4767,4769,4771,4775,4777,5119,5121,5123,5127,5129,5135,5137,5139,5151,5153,5155,5159,5161,5183,5185,5187,5191,5193,5199,5201,5203,5247,5249,5251,5255,5257,5263,5265,5267,5279,5281,5283,5287,5289,5375,5377,5379,5383,5385,5391,5393,5395,5407,5409,5411,5415,5417,5439,5441,5443,5447,5449,5455,5457,5459,8191,8193,8195,8199,8201,8207,8209,8211,8223,8225,8227,8231,8233,8255,8257,8259,8263,8265,8271,8273,8275,8319,8321,8323,8327,8329,8335,8337,8339,8351,8353,8355,8359,8361,8447,8449,8451,8455,8457,8463,8465,8467,8479,8481,8483,8487,8489,8511,8513,8515,8519,8521,8527,8529,8531,8703,8705,8707,8711,8713,8719,8721,8723,8735,8737,8739,8743,8745,8767,8769,8771,8775,8777,8783,8785,8787,8831,8833,8835,8839,8841,8847,8849,8851,8863,8865,8867,8871,8873,9215,9217,9219,9223,9225,9231,9233,9235,9247,9249,9251,9255,9257,9279,9281,9283,9287,9289,9295,9297,9299,9343,9345,9347,9351,9353,9359,9361,9363,9375,9377,9379,9383,9385,9471,9473,9475,9479,9481,9487,9489,9491,9503,9505,9507,9511,9513,9535,9537,9539,9543,9545,9551,9553,9555,10239,10241,10243,10247,10249,10255,10257,10259,10271,10273,10275,10279,10281,10303,10305,10307,10311,10313,10319,10321,10323,10367,10369,10371,10375,10377,10383,10385,10387,10399,10401,10403,10407,10409,10495,10497,10499,10503,10505,10511,10513,10515,10527,10529,10531,10535,10537,10559,10561,10563,10567,10569,10575,10577,10579,10751,10753,10755,10759,10761,10767,10769,10771,10783,10785,10787,10791,10793,10815,10817,10819,10823,10825,10831,10833,10835,10879,10881,10883,10887,10889,10895,10897,10899,10911,10913,10915,10919,10921,16383,16385,16387,16391,16393,16399,16401,16403,16415,16417,16419,16423,16425,16447,16449,16451,16455,16457,16463,16465,16467,16511,16513,16515,16519,16521,16527,16529,16531,16543,16545,16547,16551,16553,16639,16641,16643,16647,16649,16655,16657,16659,16671,16673,16675,16679,16681,16703,16705,16707,16711,16713,16719,16721,16723,16895,16897,16899,16903,16905,16911,16913,16915,16927,16929,16931,16935,16937,16959,16961,16963,16967,16969,16975,16977,16979,17023,17025,17027,17031,17033,17039,17041,17043,17055,17057,17059,17063,17065,17407,17409,17411,17415,17417,17423,17425,17427,17439,17441,17443,17447,17449,17471,17473,17475,17479,17481,17487,17489,17491,17535,17537,17539,17543,17545,17551,17553,17555,17567,17569,17571,17575,17577,17663,17665,17667,17671,17673,17679,17681,17683,17695,17697,17699,17703,17705,17727,17729,17731,17735,17737,17743,17745,17747,18431,18433,18435,18439,18441,18447,18449,18451,18463,18465,18467,18471,18473,18495,18497,18499,18503,18505,18511,18513,18515,18559,18561,18563,18567,18569,18575,18577,18579,18591,18593,18595,18599,18601,18687,18689,18691,18695,18697,18703,18705,18707,18719,18721,18723,18727,18729,18751,18753,18755,18759,18761,18767,18769,18771,18943,18945,18947,18951,18953,18959,18961,18963,18975,18977,18979,18983,18985,19007,19009,19011,19015,19017,19023,19025,19027,19071,19073,19075,19079,19081,19087,19089,19091,19103,19105,19107,19111,19113,20479,20481,20483,20487,20489,20495,20497,20499,20511,20513,20515,20519,20521,20543,20545,20547,20551,20553,20559,20561,20563,20607,20609,20611,20615,20617,20623,20625,20627,20639,20641,20643,20647,20649,20735,20737,20739,20743,20745,20751,20753,20755,20767,20769,20771,20775,20777,20799,20801,20803,20807,20809,20815,20817,20819,20991,20993,20995,20999,21001,21007,21009,21011,21023,21025,21027,21031,21033,21055,21057,21059,21063,21065,21071,21073,21075,21119,21121,21123,21127,21129,21135,21137,21139,21151,21153,21155,21159,21161,21503,21505,21507,21511,21513,21519,21521,21523,21535,21537,21539,21543,21545,21567,21569,21571,21575,21577,21583,21585,21587,21631,21633,21635,21639,21641,21647,21649,21651,21663,21665,21667,21671,21673,21759,21761,21763,21767,21769,21775,21777,21779,21791,21793,21795,21799,21801,21823,21825,21827,21831,21833,21839,21841,21843,32767,32769,32771,32775,32777,32783,32785,32787,32799,32801,32803,32807,32809,32831,32833,32835,32839,32841,32847,32849,32851,32895,32897,32899,32903,32905,32911,32913,32915,32927,32929,32931,32935,32937,33023,33025,33027,33031,33033,33039,33041,33043,33055,33057,33059,33063,33065,33087,33089,33091,33095,33097,33103,33105,33107,33279,33281,33283,33287,33289,33295,33297,33299,33311,33313,33315,33319,33321,33343,33345,33347,33351,33353,33359,33361,33363,33407,33409,33411,33415,33417,33423,33425,33427,33439,33441,33443,33447,33449,33791,33793,33795,33799,33801,33807,33809,33811,33823,33825,33827,33831,33833,33855,33857,33859,33863,33865,33871,33873,33875,33919,33921,33923,33927,33929,33935,33937,33939,33951,33953,33955,33959,33961,34047,34049,34051,34055,34057,34063,34065,34067,34079,34081,34083,34087,34089,34111,34113,34115,34119,34121,34127,34129,34131,34815,34817,34819,34823,34825,34831,34833,34835,34847,34849,34851,34855,34857,34879,34881,34883,34887,34889,34895,34897,34899,34943,34945,34947,34951,34953,34959,34961,34963,34975,34977,34979,34983,34985,35071,35073,35075,35079,35081,35087,35089,35091,35103,35105,35107,35111,35113,35135,35137,35139,35143,35145,35151,35153,35155,35327,35329,35331,35335,35337,35343,35345,35347,35359,35361,35363,35367,35369,35391,35393,35395,35399,35401,35407,35409,35411,35455,35457,35459,35463,35465,35471,35473,35475,35487,35489,35491,35495,35497,36863,36865,36867,36871,36873,36879,36881,36883,36895,36897,36899,36903,36905,36927,36929,36931,36935,36937,36943,36945,36947,36991,36993,36995,36999,37001,37007,37009,37011,37023,37025,37027,37031,37033,37119,37121,37123,37127,37129,37135,37137,37139,37151,37153,37155,37159,37161,37183,37185,37187,37191,37193,37199,37201,37203,37375,37377,37379,37383,37385,37391,37393,37395,37407,37409,37411,37415,37417,37439,37441,37443,37447,37449,37455,37457,37459,37503,37505,37507,37511,37513,37519,37521,37523,37535,37537,37539,37543,37545,37887,37889,37891,37895,37897,37903,37905,37907,37919,37921,37923,37927,37929,37951,37953,37955,37959,37961,37967,37969,37971,38015,38017,38019,38023,38025,38031,38033,38035,38047,38049,38051,38055,38057,38143,38145,38147,38151,38153,38159,38161,38163,38175,38177,38179,38183,38185,38207,38209,38211,38215,38217,38223,38225,38227,40959,40961,40963,40967,40969,40975,40977,40979,40991,40993,40995,40999,41001,41023,41025,41027,41031,41033,41039,41041,41043,41087,41089,41091,41095,41097,41103,41105,41107,41119,41121,41123,41127,41129,41215,41217,41219,41223,41225,41231,41233,41235,41247,41249,41251,41255,41257,41279,41281,41283,41287,41289,41295,41297,41299,41471,41473,41475,41479,41481,41487,41489,41491,41503,41505,41507,41511,41513,41535,41537,41539,41543,41545,41551,41553,41555,41599,41601,41603,41607,41609,41615,41617,41619,41631,41633,41635,41639,41641,41983,41985,41987,41991,41993,41999,42001,42003,42015,42017,42019,42023,42025,42047,42049,42051,42055,42057,42063,42065,42067,42111,42113,42115,42119,42121,42127,42129,42131,42143,42145,42147,42151,42153,42239,42241,42243,42247,42249,42255,42257,42259,42271,42273,42275,42279,42281,42303,42305,42307,42311,42313,42319,42321,42323,43007,43009,43011,43015,43017,43023,43025,43027,43039,43041,43043,43047,43049,43071,43073,43075,43079,43081,43087,43089,43091,43135,43137,43139,43143,43145,43151,43153,43155,43167,43169,43171,43175,43177,43263,43265,43267,43271,43273,43279,43281,43283,43295,43297,43299,43303,43305,43327,43329,43331,43335,43337,43343,43345,43347,43519,43521,43523,43527,43529,43535,43537,43539,43551,43553,43555,43559,43561,43583,43585,43587,43591,43593,43599,43601,43603,43647,43649,43651,43655,43657,43663,43665,43667,43679,43681,43683,43687,43689,65535,65537,65539,65543,65545,65551,65553,65555,65567,65569,65571,65575,65577,65599,65601,65603,65607,65609,65615,65617,65619,65663,65665,65667,65671,65673,65679,65681,65683,65695,65697,65699,65703,65705,65791,65793,65795,65799,65801,65807,65809,65811,65823,65825,65827,65831,65833,65855,65857,65859,65863,65865,65871,65873,65875,66047,66049,66051,66055,66057,66063,66065,66067,66079,66081,66083,66087,66089,66111,66113,66115,66119,66121,66127,66129,66131,66175,66177,66179,66183,66185,66191,66193,66195,66207,66209,66211,66215,66217,66559,66561,66563,66567,66569,66575,66577,66579,66591,66593,66595,66599,66601,66623,66625,66627,66631,66633,66639,66641,66643,66687,66689,66691,66695,66697,66703,66705,66707,66719,66721,66723,66727,66729,66815,66817,66819,66823,66825,66831,66833,66835,66847,66849,66851,66855,66857,66879,
7 楼
goal00001111 [专家分:4030] 发布于 2007-05-28 00:31:00
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8 楼
goal00001111 [专家分:4030] 发布于 2007-05-28 00:32:00
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9 楼
goal00001111 [专家分:4030] 发布于 2007-05-28 00:34:00
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63815,663817,663823,663825,663827,663839,663841,663843,663847,663849,663871,663873,663875,663879,663881,663887,663889,663891,664063,664065,664067,664071,664073,664079,664081,664083,664095,664097,664099,664103,664105,664127,664129,664131,664135,664137,664143,664145,664147,664191,664193,664195,664199,664201,664207,664209,664211,664223,664225,664227,664231,664233,664575,664577,664579,664583,664585,664591,664593,664595,664607,664609,664611,664615,664617,664639,664641,664643,664647,664649,664655,664657,664659,664703,664705,664707,664711,664713,664719,664721,664723,664735,664737,664739,664743,664745,664831,664833,664835,664839,664841,664847,664849,664851,664863,664865,664867,664871,664873,664895,664897,664899,664903,664905,664911,664913,664915,665599,665601,665603,665607,665609,665615,665617,665619,665631,665633,665635,665639,665641,665663,665665,665667,665671,665673,665679,665681,665683,665727,665729,665731,665735,665737,665743,665745,665747,665759,665761,665763,665767,665769,665855,665857,665859,665863,665865,665871,665873,665875,665887,665889,665891,665895,665897,665919,665921,665923,665927,665929,665935,665937,665939,666111,666113,666115,666119,666121,666127,666129,666131,666143,666145,666147,666151,666153,666175,666177,666179,666183,666185,666191,666193,666195,666239,666241,666243,666247,666249,666255,666257,666259,666271,666273,666275,666279,666281,671743,671745,671747,671751,671753,671759,671761,671763,671775,671777,671779,671783,671785,671807,671809,671811,671815,671817,671823,671825,671827,671871,671873,671875,671879,671881,671887,671889,671891,671903,671905,671907,671911,671913,671999,672001,672003,672007,672009,672015,672017,672019};
if (k <= MAX)
return lib[k-1];
int *a = new int[k+2];
for (int i=0; i<MAX; ++i)
a[i] = lib[i];
int len = MAX;
int p = MAX / 3;
while (len < k)//先存储k个元素
{
len = Insert(a, len, 2*a[p]+1);//cout << "len = " << len << " ";
len = Insert(a, len, 4*a[p]+5);//cout << "len = " << len << " ";
++p;
}
while (len > k)//去掉多余的元素
--len;
while (2*a[p]+1 < a[k-1])//因为前面存储的元素并非前k个元素,需要继续计算,直至得到前k个元素
{
Insert(a, len, 2*a[p]+1);
Insert(a, len, 4*a[p]+5);
++p;
}
10 楼
jinrunfa [专家分:0] 发布于 2007-05-28 09:45:00
还有奖牌啊
我来回复