题解 洛谷P1806 【跑步】

有趣的水题

只有这么几篇题解，那就发一篇吧

这道题我讲两种方法：动规和打表！

先讲讲有趣的打表吧！

一、打表

打表有什么好说的吗？

有，记得开long long！

还是直接上代码吧！

#include<bits/stdc++.h>
using namespace std;
int n;
long long ans[501]={0,0,0,0,0,2,3,4,5,7,9,11,14,17,21,26,31,37,45,53,63,75,88,103,121,141,164,191,221,255,295,339,389,447,511,584,667,759,863,981,1112,1259,1425,1609,1815,2047,2303,2589,2909,3263,3657,4096,4581,5119,5717,6377,7107,7916,8807,9791,10879,12075,13393,14847,16443,18199,20131,22249,24575,27129,29926,32991,36351,40025,44045,48445,53249,58498,64233,70487,77311,84755,92863,101697,111321,121791,133183,145577,159045,173681,189585,206847,225584,245919,267967,291873,317787,345855,376255,409173,444792,483329,525015,570077,618783,671417,728259,789639,855905,927405,1004543,1087743,1177437,1274117,1378303,1490527,1611387,1741520,1881577,2032289,2194431,2368799,2556283,2757825,2974399,3207085,3457026,3725409,4013543,4322815,4654669,5010687,5392549,5802007,6240973,6711479,7215643,7755775,8334325,8953855,9617149,10327155,11086967,11899933,12769601,13699698,14694243,15757501,16893951,18108417,19406015,20792119,22272511,23853317,25540981,27342420,29264959,31316313,33504745,35839007,38328319,40982539,43812109,46828031,50042055,53466623,57114843,61000703,65139007,69545357,74236383,79229675,84543781,90198445,96214549,102614113,109420548,116658615,124354421,132535701,141231779,150473567,160293887,170727423,181810743,193582641,206084095,219358314,233451097,248410815,264288461,281138047,299016607,317984255,338104629,359444903,382075867,406072421,431513601,458482687,487067745,517361669,549462335,583473183,619503295,657667583,698087423,740890785,786212445,834194699,884987528,938748851,995645335,1055852589,1119555487,1186949055,1258238719,1333640709,1413383025,1497705767,1586861605,1681116851,1780751882,1886061683,1997357055,2114965119,2239229959,2370513985,2509198527,2655684607,2810394453,2973772211,3146284869,3328423935,3520706303,3723675325,3937902687,4163989457,4402567323,4654300705,4919887991,5200062975,5495597247,5807301631,6136027873,6482671321,6848172603,7233519618,7639750521,8067955711,8519280127,8994926601,9496158207,10024300889,10580747263,11166959337,11784471547,12434895063,13119920927,13841323581,14600965704,15400801855,16242882559,17129359743,18062490973,19044644145,20078303619,21166075135,22310691191,23515017983,24782061069,26114971539,27517053881,28991772485,30542758737,32173819903,33888946599,35692320959,37588326641,39581557439,41676826623,43879178239,46193897031,48626519093,51182844671,53868949521,56691197083,59656252986,62771098023,66043042087,69479740553,73089209119,76879839743,80860419135,85040145749,89428647939,94036004867,98872765937,103949971455,109279176297,114872472063,120742510606,126902530815,133366383847,140148559929,147264218617,154729217535,162560142889,170774343641,179389964241,188425979303,197902232211,207839472389,218259394655,229184682869,240639052285,252647294207,265235325351,278430235903,292260340223,306755232573,321945841663,337864488191,354544947721,372022512607,390334057171,409518108689,429614917631,450666531449,472716874731,495811828758,519999315039,545329385791,571854313989,599628687917,628709513215,659156314787,691031243769,724399192575,759327910199,795888123109,834153664939,874201606889,916112394269,959969992703,1005862035460,1053879977631,1104119260917,1156679479969,1211664556453,1269182924647,1329347719189,1392276971519,1458093818815,1526926715867,1598909656577,1674182409147,1752890755071,1835186738751,1921228932215,2011182704477,2105220502771,2203522150409,2306275150209,2413675001277,2525925533945,2643239251487,2765837686783,2893951778821,3027822257407,3167700044479,3313846677247,3466534741117,3626048321047,3792683476991,3966748730793,4148565573658,4338469000205,4536808055807,4743946406975,4960262940967,5186152380863,5422025926435,5668311927091,5925456572863,6193924614093,6474200116479,6766787237063,7072211032063,7391018303853,7723778471935,8071084479443,8433553742946,8811829129613,9206579974149,9618503143423,10048324132443,10496798204735,10964711585279,11452882689343,11962163400705,12493440407999,13047636581997,13625712407807,14228667481437,14857542052793,15513418629883,16197423654281,16910729229127,17654554915429,18430169607103,19238893465515,20082099930207,20961217816575,21877733480959,22833193070487,23829204869147,24867441720077,25949643542055,27077619952639,28253252977151,29478499862527,30755396009351,32086058000383,33472686745953,34917570760096,36423089545253,37991717107135,39626025614145,41328689178999,43102487785005,44950311372459,46875164062333,48880168540671,50968570620479,53143743957459,55409194944511,57768567802879,60225649845545,62784376939519,65448839185791,68223286792199,71112136167456,74119976256079,77251575089317,80511886581727,83906057594563,87439435240797,91117574462853,94946245905983,98931444061527,103079395713069,107396568710143,111889681043071,116565710254335,121431903212543,126495786222431,131765175508647,137248188100781,142953253093375,148889123320639,155064887475475,161489982646591,168174207315549,175127734845951,182361127438193,189885350594523,197711788129023,205852257695743,214319026883033,223124829910883,232282884904959,241806911798585,251711150901901,262010382112695,272719944823231,283855758565429,295434344369602,307472846894367,319989057373737,333001437357055,346529143303467,360592052080639,375210787343945,390406746862529,406202130845495,422619971245763,439684162112801,457419491051263,475851671764997,495007377762303,514914277284171,535601069436937,557097521610169,579434508247039,602644050950308,626759360010787,651814877431175,677846321430325,704890732521791,732986521245023};
int main()
{
    cin>>n;
    cout<<ans[n]<<endl;
    return 0;
}

二、动规

想到背包了么？

背包的简化版？？！！

一维状态：dp[i]表示跑i圈的方案总数！

#include<bits/stdc++.h>
using namespace std;
int n;
long long dp[501];
int main()
{
    int i,j;
    cin>>n;
    dp[0]=1;
    for(i=1;i<=n;i++)
        for(j=n;j>=i;j--)
            dp[j]+=dp[j-i];
    cout<<dp[n]-1<<endl;
    return 0;
}

这题实在是没什么好说的，抱歉！