11.1T1打表

3810 -- 【模拟试题】圣主的考验

Description

　　若对于二叉树 T 的每个节点 v，其左子树的高度L和右子树的高度R均满足|L–R|≤1，则这个树T有可能来自超自然之界。规定若某节点子树为空，则该子树的高度是0。你的任务是求有N个节点的可能来自超自然之界的树的数目。

Input

　　每个测试点包含若干个测试数据。 
　　每个测试数据占一行，包含一个整数N。 
　　输入文件以0结尾。

Output

　　对于每个测试数据，在单独的一行内输出结果。由于结果可能会很大，你只需要输出答案mod 1000000000

Sample Input

2 3 5 30 0

Sample Output

2 1 6 11307920

Hint

【数据规模和约定】 
　　对于30% 的测试点，N≤100。 
　　对于70% 的测试点，N≤1000。 
　　对于100% 的测试点，1≤N≤3000。

 

 

打表出奇迹：

code：

#include<iostream>
#include<cstdio>
using namespace std;
int a[3005]={0,1,2,1,4,6,4,17,32,44,60,70,184,476,872,1553,2720,4288,6312,9004,16088,36900,82984,174374,346048,653096,1199384,2160732,3812464,6617304,11307920,18978577,31327104,51931296,90400704,170054336,341729616,711634072,491256624,84996748,246978752,360863368,970232968,784743460,510498224,166545624,52102480,293458982,360103104,376725248,176834992,275731496,954496368,300625128,414063440,433951772,310322560,249708880,811887600,938737368,864074336,71770480,448334368,690385169,500412928,511348096,358818624,434524320,948108160,468289216,650489344,526806528,302230656,30608880,751558192,753974936,535251360,634709584,25955872,475657868,623272896,157046656,780889712,505696136,184012880,923143544,725654512,179238116,193093504,648778256,195169008,403948504,362621408,864754992,328296992,732797990,909857024,100434624,750503552,294983424,658676064,27643600,820941984,605847528,419698560,33053008,700157392,284353768,173377888,534200240,364198816,612120092,328301952,511927808,765916000,791204688,955687520,494289936,435348256,445938776,748964608,786203936,5329504,811664240,5235904,660865504,340971072,871030033,686708224,267286528,937673472,767666048,539442304,298792896,390380672,372720800,288230400,15133824,425853568,727404736,189572608,59891456,799414656,960291328,113612416,244620032,545004832,798627312,946809824,551285200,544833952,234031384,610934016,354837728,93055264,807835472,10965696,162396768,932303552,52823692,732816640,839707584,49841792,474600320,992794336,588125712,348645152,598947016,325494912,52194800,194699248,141172088,861231136,603581200,753023456,40378596,97468800,918820352,485205984,910903824,638643296,400297488,155822624,403697496,943586048,549090720,294336736,473898800,380465856,449011168,685336128,269563942,38168576,239393024,562957696,973458112,832738048,489663616,497243648,125980288,334921984,12147232,500452256,817917648,527342784,939825760,98792128,617267688,837879168,814150400,775773792,165143376,485814816,591824688,561589088,764832360,623511808,100080160,296566240,855122352,74772928,909202272,177895488,537422876,288112640,821416320,161867520,514818560,473732800,934477728,101335360,348175056,55250688,418945312,149612576,210908176,127587264,549849312,924159040,780987480,451649280,237824000,125234624,975001888,195767232,378458528,503547712,254463088,443395072,286591040,541436608,861880800,479836544,847018944,880962176,554525969,424632832,600944128,723718144,939867136,343530496,102447360,423660032,102498688,432941056,532155776,879801216,83339712,120469248,348120960,857805056,627426464,29088768,55353344,18714880,134613120,827029760,144271232,316520704,690852544,269748736,907547648,651153408,228088576,395804416,511092608,797881344,495818240,779948032,175160448,10316544,497932032,825706048,415726048,107442112,889617776,669746432,814177696,111243680,121352144,514538176,201625184,894976320,121367832,559719168,674217472,731617856,243881184,275351872,453462752,444249024,352973392,276406272,681023040,59616448,203589216,755607680,163871040,138264960,795041420,666269696,856695040,968040320,289797568,106498304,18414208,766482944,37576960,163313920,66802848,210581536,618699280,898110400,638234080,106440384,721866952,41274496,856897792,566408992,583363056,697223520,164104464,403304224,777345016,260482816,113265248,145095072,50358544,6186304,981862176,73460928,414450404,868483072,22464896,538498304,120805376,416365504,237988128,138046528,150512528,710048000,622539552,907216416,373368848,154506176,989574112,636967488,391317848,284671744,893899776,460700352,512962976,613114560,761463072,178527296,99263024,428680192,832214080,95321280,240288224,282881408,852686272,457263744,175459366,786828800,142502912,554002944,237278464,917246720,45813376,132910848,205309120,118127616,617532160,129750272,563649152,537049600,791844352,640221952,309879424,697511680,833636864,751416768,553640992,94978112,628245088,876532416,753616848,189451264,622135872,545828800,505964128,320717952,662888512,641919616,215155176,817519104,884425088,472105216,433767680,977497280,49989792,123953984,519965648,616946432,955813984,895668832,371680560,16202560,941883040,514595008,95687784,317220608,77707776,45864896,664881696,859485888,89673760,345931328,194959024,835483648,594401088,739508160,918295904,83771776,487197632,585232000,780267036,189414912,393669632,65787136,164059008,282492928,757031168,526655488,750216960,147328000,537648704,69579584,581926304,11365248,138688704,50578816,431849168,985873664,19136000,956960192,471058208,229958976,236602848,664013248,811573520,331145216,971900224,543612608,741343968,377436544,40366016,35149440,834309720,162202112,663868672,69648896,213387264,493090688,501939776,385350272,708991520,645157376,478234432,100312384,910484896,92683648,914066112,259057792,813944432,742197248,959000064,14813056,496663616,404128128,805794112,511393920,542852576,742640128,236958848,943847808,480152000,634774272,825492352,199630080,343462161,684392448,774540288,187437056,17732096,49687040,913434112,74095616,877187072,414193664,431921152,192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int main(){
    int n;
    while(cin>>n&&n){
        cout<<a[n]<<'\n';
    }
    return 0;
}

over