标签：
Description
A sequence of positive and non-zero integers called palindromic if it can be read the same forward and backward, for example:
15 2 6 4 6 2 15
20 3 1 1 3 20
We have a special kind of palindromic sequences, let‘s call it a special palindrome.
A palindromic sequence is a special palindrome if its values don‘t decrease up to the middle value, and of course they don‘t increase
from the middle to the end.
The sequences above is NOT special, while the following sequences are:
1 2 3 3 7 8 7 3 3 2 1
2 10 2
1 4 13 13 4 1
Let‘s define the function F(N), which represents the number of special sequences that the sum of their values is N.
For example F(7) = 5 which are : (7), (1 5 1), (2 3 2), (1 1 3 1 1), (1 1 1 1 1 1 1)
Your job is to write a program that compute the Value F(N) for given N‘s.
Input
The Input consists of a sequence of lines, each line contains a positive none zero integer N less than or equal to 250. The last line contains 0 which indicates the end of the input.
Output
Print one line for each given number N, which it the value F(N).
Sample Input
1 3 7 10 0
1 2 5 17
Source
UESTC 2016 Summer Training #21
My Solution
非递减的回文串、打表
比赛结束后看了下public 的代码就我们队是打表过的， 别人都是正规的过的， ⊙﹏⊙‖∣尴尬
分奇偶用 dfs 搞出非递减的左半边串， 然后求出这个的和 ans[sum + i]++;
对于偶数个的直接dfs， 对于奇数的则枚举mid， 然后依次dfs
void dfseven(int k, int sum)
{
if(2*sum > 50) return;
//cout<<"here1"<<endl;
for(int i = k; i <= 50; i++){
if(2*(sum + i) <= 50) {ans[2*(sum + i)]++; dfseven(i, sum + i);}
else return;
}
}
void dfsodd(int mid, int k, int sum)
{
if(2*sum + mid > 50) return;
//cout<<"here2"<<endl;
for(int i = k; i <= 50; i++){
if(2*(sum + i) + mid <= 50 && i <= mid) {ans[2*(sum + i) + mid]++; dfsodd(mid, i, sum + i);}
else return;
}
}所以把那前250个ans贴到 txt里， 然后写一个中间程序 把这些数据 转换成 printf("ans[%d] = %d;", i, val);的样子打到另一个txt文件里， 然后复杂粘贴到上去， 整理下就好了
打表代码
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long LL;
const int maxn = 250 + 8;
int ans[maxn];
//偶数个的
void dfseven(int k, int sum)
{
if(2*sum > 50) return;
//cout<<"here1"<<endl;
for(int i = k; i <= 50; i++){
if(2*(sum + i) <= 50) {ans[2*(sum + i)]++; dfseven(i, sum + i);}
else return;
}
}
void dfsodd(int mid, int k, int sum)
{
if(2*sum + mid > 50) return;
//cout<<"here2"<<endl;
for(int i = k; i <= 50; i++){
if(2*(sum + i) + mid <= 50 && i <= mid) {ans[2*(sum + i) + mid]++; dfsodd(mid, i, sum + i);}
else return;
}
}
int main()
{
#ifdef LOCAL
freopen("a.txt", "r", stdin);
freopen("b.txt", "w", stdout);
#endif // LOCAL
memset(ans, 0, sizeof ans);
//ans[2]++;
dfseven(1, 0);
//ans[1]++;
for(int i = 1; i <= 50; i++){
dfsodd(i, 1, 0);
}
for(int i = 1; i <= 50; i++){
printf("ans[%d] = %d;", i, ans[i] + 1);
}
/*
int n;
while(scanf("%d", &n)){
printf("%d", ans[n]);
}
*/
return 0;
}
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long LL;
const int maxn = 250 + 8;
LL ans[maxn];
int main()
{
ans[1] = 1;
ans[2] = 2;
ans[3] = 2;
ans[4] = 4;
ans[5] = 3;
ans[6] = 7;
ans[7] = 5;
ans[8] = 11;
ans[9] = 8;
ans[10] = 17;
ans[11] = 12;
ans[12] = 26;
ans[13] = 18;
ans[14] = 37;
ans[15] = 27;
ans[16] = 54;
ans[17] = 38;
ans[18] = 76;
ans[19] = 54;
ans[20] = 106;
ans[21] = 76;
ans[22] = 145;
ans[23] = 104;
ans[24] = 199;
ans[25] = 142;
ans[26] = 266;
ans[27] = 192;
ans[28] = 357;
ans[29] = 256;
ans[30] = 472;
ans[31] = 340;
ans[32] = 621;
ans[33] = 448;
ans[34] = 809;
ans[35] = 585;
ans[36] = 1053;
ans[37] = 760;
ans[38] = 1354;
ans[39] = 982;
ans[40] = 1740;
ans[41] = 1260;
ans[42] = 2218;
ans[43] = 1610;
ans[44] = 2818;
ans[45] = 2048;
ans[46] = 3559;
ans[47] = 2590;
ans[48] = 4485;
ans[49] = 3264;
ans[50] = 5616;
ans[51] = 4097;
ans[52] = 7018;
ans[53] = 5120;
ans[54] = 8728;
ans[55] = 6378;
ans[56] = 10826;
ans[57] = 7917;
ans[58] = 13373;
ans[59] = 9792;
ans[60] = 16484;
ans[61] = 12076;
ans[62] = 20236;
ans[63] = 14848;
ans[64] = 24793;
ans[65] = 18200;
ans[66] = 30275;
ans[67] = 22250;
ans[68] = 36886;
ans[69] = 27130;
ans[70] = 44810;
ans[71] = 32992;
ans[72] = 54329;
ans[73] = 40026;
ans[74] = 65683;
ans[75] = 48446;
ans[76] = 79265;
ans[77] = 58499;
ans[78] = 95419;
ans[79] = 70488;
ans[80] = 114650;
ans[81] = 84756;
ans[82] = 137447;
ans[83] = 101698;
ans[84] = 164496;
ans[85] = 121792;
ans[86] = 196445;
ans[87] = 145578;
ans[88] = 234221;
ans[89] = 173682;
ans[90] = 278720;
ans[91] = 206848;
ans[92] = 331143;
ans[93] = 245920;
ans[94] = 392722;
ans[95] = 291874;
ans[96] = 465061;
ans[97] = 345856;
ans[98] = 549781;
ans[99] = 409174;
ans[100] = 649019;
ans[101] = 483330;
ans[102] = 764959;
ans[103] = 570078;
ans[104] = 900373;
ans[105] = 671418;
ans[106] = 1058191;
ans[107] = 789640;
ans[108] = 1242061;
ans[109] = 927406;
ans[110] = 1455820;
ans[111] = 1087744;
ans[112] = 1704261;
ans[113] = 1274118;
ans[114] = 1992458;
ans[115] = 1490528;
ans[116] = 2326608;
ans[117] = 1741521;
ans[118] = 2713398;
ans[119] = 2032290;
ans[120] = 3160899;
ans[121] = 2368800;
ans[122] = 3677789;
ans[123] = 2757826;
ans[124] = 4274556;
ans[125] = 3207086;
ans[126] = 4962526;
ans[127] = 3725410;
ans[128] = 5755174;
ans[129] = 4322816;
ans[130] = 6667228;
ans[131] = 5010688;
ans[132] = 7716070;
ans[133] = 5802008;
ans[134] = 8920663;
ans[135] = 6711480;
ans[136] = 10303379;
ans[137] = 7755776;
ans[138] = 11888671;
ans[139] = 8953856;
ans[140] = 13705118;
ans[141] = 10327156;
ans[142] = 15784173;
ans[143] = 11899934;
ans[144] = 18162385;
ans[145] = 13699699;
ans[146] = 20879933;
ans[147] = 15757502;
ans[148] = 23983452;
ans[149] = 18108418;
ans[150] = 27524280;
ans[151] = 20792120;
ans[152] = 31561603;
ans[153] = 23853318;
ans[154] = 36160845;
ans[155] = 27342421;
ans[156] = 41397124;
ans[157] = 31316314;
ans[158] = 47353396;
ans[159] = 35839008;
ans[160] = 54124796;
ans[161] = 40982540;
ans[162] = 61816437;
ans[163] = 46828032;
ans[164] = 70548311;
ans[165] = 53466624;
ans[166] = 80453313;
ans[167] = 61000704;
ans[168] = 91682668;
ans[169] = 69545358;
ans[170] = 104403741;
ans[171] = 79229676;
ans[172] = 118806744;
ans[173] = 90198446;
ans[174] = 135102223;
ans[175] = 102614114;
ans[176] = 153528658;
ans[177] = 116658616;
ans[178] = 174350347;
ans[179] = 132535702;
ans[180] = 197865953;
ans[181] = 150473568;
ans[182] = 224406247;
ans[183] = 170727424;
ans[184] = 254344551;
ans[185] = 193582642;
ans[186] = 288094273;
ans[187] = 219358315;
ans[188] = 326120818;
ans[189] = 248410816;
ans[190] = 368939881;
ans[191] = 281138048;
ans[192] = 417130912;
ans[193] = 317984256;
ans[194] = 471335560;
ans[195] = 359444904;
ans[196] = 532274004;
ans[197] = 406072422;
ans[198] = 600743477;
ans[199] = 458482688;
ans[200] = 677637038;
ans[201] = 517361670;
ans[202] = 763943462;
ans[203] = 583473184;
ans[204] = 860768675;
ans[205] = 657667584;
ans[206] = 969336374;
ans[207] = 740890786;
ans[208] = 1091013811;
ans[209] = 834194700;
ans[210] = 1227313238;
ans[211] = 938748852;
ans[212] = 1379921672;
ans[213] = 1055852590;
ans[214] = 1550704877;
ans[215] = 1186949056;
ans[216] = 1741741564;
ans[217] = 1333640710;
ans[218] = 1955329266;
ans[219] = 1497705768;
ans[220] = 2194025352;
ans[221] = 1681116852;
ans[222] = 2460655086;
ans[223] = 1886061684;
ans[224] = 2758359212;
ans[225] = 2114965120;
ans[226] = 3090606588;
ans[227] = 2370513986;
ans[228] = 3461249193;
ans[229] = 2655684608;
ans[230] = 3874538905;
ans[231] = 2973772212;
ans[232] = 4335193118;
ans[233] = 3328423936;
ans[234] = 4848416380;
ans[235] = 3723675326;
ans[236] = 5419976831;
ans[237] = 4163989458;
ans[238] = 6056235989;
ans[239] = 4654300706;
ans[240] = 6764237552;
ans[241] = 5200062976;
ans[242] = 7551745299;
ans[243] = 5807301632;
ans[244] = 8427348786;
ans[245] = 6482671322;
ans[246] = 9400510845;
ans[247] = 7233519619;
ans[248] = 10481691022;
ans[249] = 8067955712;
ans[250] = 11682407480;
int n;
while(scanf("%d", &n)){
if(n == 0) break;
printf("%I64d\n", ans[n]);
}
return 0;
}Thank you!
------from ProLights
Gym 100952H Special Palindrome 非递减的回文串、dfs打表、查数列网站OEIS
标签：
原文地址：http://blog.csdn.net/prolightsfxjh/article/details/52167591
