Usaco 3.2 Stringsobits Digital DP

Stringsobits
Kim schrijvers

Consider an ordered set S of Strings of n (1 <= n <=) bits. Bits, of course, are either 0 or 1.

This set of strings are interesting because it is ordered and contains all possible strings of length N that has L (1 < = L <= N) or fewer bits that is ' 1 '.

Your task is to read a number I (1 <= I <= sizeof (S)) from the input and print the Ith element of the ordered set fo R N Bits with no further than L bits that is ' 1 '.

Program Name:kimbitsinput FORMAT

A single line with three space separated integers:n, L, and I.

SAMPLE INPUT (file kimbits.in)

5 3 19

OUTPUT FORMAT

A single line containing the integer this represents the Ith element from the order set, as described.

SAMPLE OUTPUT (file kimbits.out)

10011

The number of 1 for which the binary length is n (which can include the leading 0) does not exceed the number of L.

In counter-consideration, set the number of M, digital DP can easily find the [0,m] of the number of matching conditions (the binary length of n (can include the number of 1 of the leading 0) Count K, obviously M is the number of K.

So the direct two-point judgment is possible.

/*id:xidian5601prog:kimbitslang:c++*/#include<bits/stdc++.h>#defineREP (I,A,B) for (int i=a;i<=b;i++)#defineMS0 (a) memset (A,0,sizeof (a))using namespaceStd;typedefLong Longll;Const intmaxn=1000100;Const intinf=1e9+Ten; ll N,l,i;ll f[ +][ +];intnum[ +],len;ll DFS (intIintCntinte) {    if(i==-1)returncnt<=m; if(!e&&~f[i][cnt])returnf[i][cnt]; ll Res=0; intU=e?num[i]:1; REP (d,0, U) {        if(cnt+d<=l) Res+=dfs (i-1, cnt+d,e&&d==T); }    returne?res:f[i][cnt]=Res;} ll F (ll N) {len=0;  while(n) {Num[len++]=n%2; N/=2; }    returnDFS (len-1,0,1);}intCNT (ll N) {intres=0;  while(n) {res+=n%2; N/=2; }    returnRes;} ll bin (ll L,ll r,ll kth) { while(l<=R) {ll m= (l+r) >>1; ll T=f (m), c=CNT (m); if(c<=l&&t==kth)returnm; if(t==kth&&c>l) r=m-1; Else if(t>kth) r=m-1; Elsel=m+1; }}voidPrint (ll N) {len=0;  while(n) {num[++len]=n%2; N/=2; } REP (I,len+1, N) printf ("0");  for(inti=len;i>=1; i--) printf ("%d", Num[i]);p UTS ("");}intMain () {//freopen ("In.txt", "R", stdin);Freopen ("kimbits.in","R", stdin); Freopen ("Kimbits.out","W", stdout);  while(cin>>n>>l>>I) {memset (F,-1,sizeof(f)); Print (Bin (0, (1ll<<n)-1, I)); }    return 0;}

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Usaco 3.2 Stringsobits Digital DP