USACO 3.2 Stringsobits

Stringsobits
Kim Schrijvers

Consider an ordered set S of strings of N (1 <= N <= 31) bits. Bits, of course, are either 0 or 1.

This set of strings is interesting because it is ordered and contains all possible strings of length N that have L (1 <= L <= N) or fewer bits that are `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 for N bits with no more than L bits that are `1'.

PROGRAM NAME: kimbits

INPUT 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 that represents the Ith element from the order set, as described.

SAMPLE OUTPUT (file kimbits.out)

10011

———————————————————————————————————————————————

把组合数求出来处理成前缀和

我们发现当I大于一段k长所有情况总和时，那么k+1位一定是1

那么这道题就做完了

其实最坑的一点，sizeof（S）=2147483648

…………………………

 /*
 ID: ivorysi
 PROG: kimbits
 LANG: C++
 */
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <queue>
 #include <set>
 #include <vector>
 #define siji(i,x,y) for(int i=(x);i<=(y);++i)
 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j)
 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i)
 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j)
 #define inf 0x7fffffff
 #define MAXN 400005
 #define ivorysi
 #define mo 97797977
 #define ha 974711
 #define ba 47
 #define fi first
 #define se second
 //#define pis pair<int,string>
 using namespace std;
 typedef long long ll;
 int c[][];
 int n,l;
 ll k;
 int num[];
 void solve() {
     scanf("%d%d%lld",&n,&l,&k);
     siji(i,,n) c[i][]=;
     siji(i,,n)    {
         int z=min(l,i);
         siji(j,,z) {
             c[i][j]=c[i-][j-]+c[i-][j];
         }
     }
     siji(i,,n) siji(j,,l) {
         c[i][j]+=c[i][j-];
     }
     int cnt=l;
     gongzi(i,n-,) {
         if(c[i][cnt]<k) {k=k-c[i][cnt];num[i+]=;--cnt;}
     }
     gongzi(i,n,) {
         printf("%c",num[i]+'');
     }
     puts("");
 }
 int main(int argc, char const *argv[])
 {
 #ifdef ivorysi
     freopen("kimbits.in","r",stdin);
     freopen("kimbits.out","w",stdout);
 #else
     freopen("f1.in","r",stdin);
 #endif
     solve();
 }