分段打表，但比另一個打表題解快了近20倍！

因為ta不知道你谷可以交50kb的程式碼

Solution

如果暴力一一驗證，複雜度是 \(\mathcal O(n\log n)\) 的，但 \(r\le2\times10^9\)，幾分鐘還是可以跑完的。

因為是查詢一個區間，我們可以想到打表字首和，不過若全打出來空間不夠且程式碼太長，於是想到分段打表。

分段，即每 \(blo(塊的長度)\) 個數變成一段記錄字首和，類似於分塊的思想，就可以直接查詢整塊，邊角暴力，複雜度 \(\mathcal O(blo)\)。

顯然 \(blo\) 越小越好，但程式碼長度限制我們只能打大約 \(5000\) 個數，即 \(blo=\dfrac{2\times10^9}{5000}=4\times10^5\)

Code

打表程式碼：

#include<bits/stdc++.h>
using namespace std;
const int n=2e9,blo=400000,tot=n/blo+(n%blo!=0);
int sum[tot+5];
int main(){
    freopen("P6218table.txt","w",stdout);
    for(register int i=1;i<=n;i++){
        int c[2]={},j=i;
        for(;j;j>>=1)c[j&1]++;
        sum[(i-1)/blo+1]+=(c[0]>=c[1]);
    }
    for(register int i=1;i<=tot;i++)
        printf("%d,",sum[i]+=sum[i-1]);
    return 0;
}
 

AC程式碼：

#include<bits/stdc++.h>
using namespace std;
const int blo=4e5,sum[5005]={0,193089,395896,597220,773925,912008,1157070,1399860,1584651,1786716,1936710,2139581,2389622,2582137,2798866,2953836,3101012,3281245,3430004,3558911,3666046,3727488,4073045,4367750,4637470,4888435,5098407,5359879,5599489,5784841,5985204,6135499,6342130,6591835,6778503,6997710,7150060,7301173,7476620,7626492,7759888,7863932,7933069,8276772,8570899,8841202,9091048,9295711,9560929,9799167,9988999,10183117,10332725,10542928,10792963,10975302,11195805,11345708,11498962,11677401,11825190,11960070,12061347,12136954,12422337,12647109,12847270,13021938,13147691,13354661,13513784,13638078,13753008,13838605,13999872,14173972,14280973,14429050,14516891,14618715,14726176,14804289,14881917,14930897,14992366,15366960,15712894,16038247,16353263,16625115,16950748,17253027,17514784,17775583,17998696,18268984,18581272,18830773,19125386,19350893,19575038,19825556,20039049,20247235,20412596,20548986,20883830,21177881,21448036,21697973,21888932,22167168,22398109,22593551,22772734,22921271,23142848,23394145,23573126,23793516,23944182,24105991,24282794,24415314,24555406,24649517,24753466,25086967,25380430,25650375,25899457,26085565,26369206,26596092,26793047,26967731,27118870,27347989,27596842,27777047,27991458,28143089,28307608,28483298,28610955,28751667,28846232,28953950,29222925,29446521,29645428,29820747,29930041,30150088,30299376,30430558,30539230,30620542,30799998,30970150,31084403,31219320,31304953,31413007,31518310,31584664,31667252,31710777,31814402,32181769,32527953,32854088,33167294,33418917,33760410,34055961,34326731,34577871,34794957,35084383,35395499,35650524,35930512,36153842,36384854,36635786,36830436,37047039,37202519,37368535,37692107,37984324,38251930,38499465,38677198,38971194,39196933,39398039,39573456,39710853,39958625,40199951,40385330,40585113,40736367,40907482,41083298,41198876,41344966,41432979,41573188,41892002,42183400,42451791,42702594,42882438,43173463,43398235,43599020,43775676,43906876,44160530,44398222,44587157,44784315,44934441,45107146,45281022,45394333,45541625,45627800,45766154,46014697,46240338,46443306,46616525,46732786,46946636,47097659,47228023,47334412,47401068,47601056,47762713,47885075,48002942,48088092,48203079,48308614,48363358,48448125,48488761,48628665,48943727,49235880,49508491,49753191,49940124,50223598,50447803,50647285,50821778,50946740,51213234,51447873,51639722,51826299,51975858,52151721,52326241,52431729,52582071,52669622,52820528,53071797,53287273,53494317,53661982,53786646,53990643,54139486,54271505,54378112,54439359,54649601,54804200,54931498,55041310,55126405,55242648,55348037,55405732,55488162,55529764,55672423,55922617,56134466,56342666,56507355,56636150,56836115,56986942,57117284,57223338,57281767,57496304,57649461,57777333,57883974,57968801,58089661,58195105,58254186,58331732,58372625,58498196,58674313,58804546,58944775,59038794,59121009,59242335,59328137,59400927,59454657,59477906,59624440,59710599,59783077,59838502,59878002,59949943,60000381,60027745,60060711,60076643,60259504,60643583,61015544,61384956,61739336,62061321,62430520,62775321,63102208,63415911,63670504,64040214,64385220,64712722,65027775,65319293,65625939,65937282,66191985,66473788,66698497,66957412,67316089,67649417,67984879,68288036,68556571,68881770,69174862,69442860,69691123,69865255,70211512,70506740,70777285,71028168,71242172,71500093,71743044,71927618,72130110,72279782,72514357,72873602,73203960,73540776,73841081,74113401,74433974,74726814,74993797,75243073,75422375,75767950,76062801,76332676,76583375,76793753,77054868,77294730,77480193,77680480,77830866,78060056,78374089,78636769,78924323,79152330,79365952,79616994,79839891,80042327,80216876,80332947,80621812,80846697,81047747,81223038,81352675,81554249,81716473,81838842,81958693,82044088,82276494,82635306,82958307,83298939,83593908,83872636,84187511,84481307,84753126,85000355,85185284,85527185,85821279,86090867,86340306,86540180,86811000,87046983,87238531,87427305,87576880,87818990,88131937,88385668,88675526,88900647,89123322,89374314,89592928,89798109,89967525,90094434,90375641,90599524,90797774,90975179,91097101,91307573,91464160,91588917,91701463,91786620,92021539,92334149,92583169,92877836,93103714,93327544,93578090,93791835,93999860,94165312,94298565,94574304,94799020,94999986,95175515,95292685,95505844,95660996,95788119,95896432,95981371,96189939,96441247,96620172,96840765,96991627,97153009,97330085,97462900,97602872,97697091,97787988,97987128,98136940,98267639,98373054,98430817,98577081,98663526,98735891,98789229,98830728,99093802,99452764,99768256,100111289,100405921,100692484,101006822,101285026,101562657,101801714,102005944,102336625,102630018,102898017,103147925,103329339,103616490,103840435,104039580,104217610,104364096,104632412,104944805,105198292,105483137,105707251,105936318,106185295,106385365,106599986,106758842,106910321,107173793,107398235,107597220,107771551,107877826,108098898,108252091,108384485,108491946,108569162,108836782,109148004,109403058,109683298,109906642,110137304,110388236,110583251,110799860,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int l,r,lb,rb,ans,c[2];
int main(){
	scanf("%d%d",&l,&r);
	lb=(l-1)/blo+1;rb=(r-1)/blo+1;
	ans=sum[rb]-sum[lb-1];//整塊查詢
	for(register int i=(lb-1)*blo+1;i<l;i++){
		int j=i;c[0]=c[1]=0;
		for(;j;j>>=1)c[j&1]++;
		ans-=(c[0]>=c[1]);
	}//左邊角
	for(register int i=r+1;i<=rb*blo;i++){
		int j=i;c[0]=c[1]=0;
		for(;j;j>>=1)c[j&1]++;
		ans-=(c[0]>=c[1]);
	}//右邊角
	printf("%d\n",ans);
	return 0;
}