题意:
给出条形码系统
BC(n,k,m) is the set of all symbols with k bars that together extend over exactly n units, each bar being at most m units wide.
1、给出n,k,m,条形码第一条是黑色。问有多少种不同的划分方式。
2、给出条形码,求它的rank(字典序)
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第一问应该很好解决,BC(n,k,m)=sum(BC(n-i,k-1,m)),i=1,2..m
第二问也是用经典的逐位确定的方法,唯一要注意的是,白条要从大到小累加(因为0代表白色,显然,当前条0的位数越多,字典序越小),而黑条要从小到大累加
代码:
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# include <cstdio>
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# include <cstring>
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# include <algorithm>
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using namespace std;
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int c[35][35],n,k,m;
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int main()
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{
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scanf("%d%d%d",&n,&k,&m);
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memset(c,0,sizeof(c));
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for(int num=1;num<=min(n,m);num++)
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c[num][1]=1;
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for(int num=2;num<=n;num++)
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for(int i=2;i<=k;i++)
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for(int j=max(1,num-m);j<num;j++)
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c[num][i]+=c[j][i-1];
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printf("%d\n",c[n][k]);
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int num;
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scanf("%d",&num);
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while(num--)
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{
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char str[50];
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char color='1';
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int last=0,rank=0,co=1;
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scanf("%s",str);
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for(int i=0;i<strlen(str);i++)
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{
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if(str[i]!=color)
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{
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int len=i-last;
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switch(color)
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{
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case '1':
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for(int j=last+1;j<i;j++)
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rank+=c[n-j][k-co];
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color='0';
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break;
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case '0':
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for(int j=min(n-1,last+m);j>i;j--)
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rank+=c[n-j][k-co];
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color='1';
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break;
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};
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co++;
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last=i;
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}
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}
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printf("%d\n",rank);
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}
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return 0;
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}
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