ZOJ-3962-数位dp

Seven Segment Display Time Limit: 2 Seconds       Memory Limit: 65536 KB A seven segment display, or seven segment indicator, is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays. Seven segment displays are widely used in digital clocks, electronic meters, basic calculators, and other electronic devices that display numerical information. Edward, a student in Marjar University, is studying the course "Logic and Computer Design Fundamentals" this semester. He bought an eight-digit seven segment display component to make a hexadecimal counter for his course project. In order to display a hexadecimal number, the seven segment display component needs to consume some electrical energy. The total energy cost for display a hexadecimal number on the component is the sum of the energy cost for displaying each digit of the number. Edward found the following table on the Internet, which describes the energy cost for display each kind of digit. Digit Energy Cost (units/s) 0 6 1 2 2 5 3 5 4 4 5 5 6 6 7 3 Digit Energy Cost (units/s) 8 7 9 6 A 6 B 5 C 4 D 5 E 5 F 4 For example, in order to display the hexadecimal number "5A8BEF67" on the component for one second, 5 + 6 + 7 + 5 + 5 + 4 + 6 + 3 = 41 units of energy will be consumed. Edward's hexadecimal counter works as follows: The counter will only work for n seconds. After n seconds the counter will stop displaying. At the beginning of the 1st second, the counter will begin to display a previously configured eight-digit hexadecimal number m. At the end of the i-th second (1 ≤ i < n), the number displayed will be increased by 1. If the number displayed will be larger than the hexadecimal number "FFFFFFFF" after increasing, the counter will set the number to 0 and continue displaying. Given n and m, Edward is interested in the total units of energy consumed by the seven segment display component. Can you help him by working out this problem? Input There are multiple test cases. The first line of input contains an integer T (1 ≤ T ≤ 105), indicating the number of test cases. For each test case: The first and only line contains an integer n (1 ≤ n ≤ 109) and a capitalized eight-digit hexadecimal number m (00000000 ≤ m ≤ FFFFFFFF), their meanings are described above. We kindly remind you that this problem contains large I/O file, so it's recommended to use a faster I/O method. For example, you can use scanf/printf instead of cin/cout in C++. Output For each test case output one line, indicating the total units of energy consumed by the eight-digit seven segment display component. Sample Input 3 5 89ABCDEF 3 FFFFFFFF 7 00000000 Sample Output 208 124 327 Hint For the first test case, the counter will display 5 hexadecimal numbers (89ABCDEF, 89ABCDF0, 89ABCDF1, 89ABCDF2, 89ABCDF3) in 5 seconds. The total units of energy cost is (7 + 6 + 6 + 5 + 4 + 5 + 5 + 4) + (7 + 6 + 6 + 5 + 4 + 5 + 4 + 6) + (7 + 6 + 6 + 5 + 4 + 5 + 4 + 2) + (7 + 6 + 6 + 5 + 4 + 5 + 4 + 5) + (7 + 6 + 6 + 5 + 4 + 5 + 4 + 5) = 208. For the second test case, the counter will display 3 hexadecimal numbers (FFFFFFFF, 00000000, 00000001) in 3 seconds. The total units of energy cost is (4 + 4 + 4 + 4 + 4 + 4 + 4 + 4) + (6 + 6 + 6 + 6 + 6 + 6 + 6 + 6) + (6 + 6 + 6 + 6 + 6 + 6 + 6 + 2) = 124. Author:  ZHOU, Jiayu Source:  The 14th Zhejiang Provincial Collegiate Programming Contest Sponsored by TuSimple Submit     Status

 

　　　　 16进制下的数位dp，由于固定了位数，可以出现前导零，反而简化了问题，和十进制异曲同工，只需要注意边界，对于[l,r],如果r>max,则分成[l,max-1]+max+[0,r-max-1],这是因为对于cal(N,x)函数来说计算的是[0,N)之间x的 出现次数,并不包括N，如果只是简单的把max+1传进去的话就不是八位数了，这

样乱改函数的话更麻烦还不如直接把max抽出来计算方便。

　　　　

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define LL long long 
 4 LL c[20]={6,2,5,5,4,5,6,3,
 5           7,6,6,5,4,5,5,4};
 6 LL f[20]={0,1};
 7 LL p16[20]={1};
 8 LL bit[20];
 9 void init(){
10     for(LL i=1;i<=10;++i) p16[i]=p16[i-1]*16;
11     for(LL i=2;i<=10;++i) f[i]=f[i-1]*16+p16[i-1];
12 }
13 LL cal(LL N,LL x){
14     LL len=0,ans=0,tot=0;
15     while(N){
16         bit[len++]=N%16;
17         N/=16;
18     }
19     while(len<8) bit[len++]=0;
20     bit[len]=-1;
21     for(LL i=len-1;i>=0;--i){
22         ans+=f[i]*bit[i];
23         if(bit[i]>x) ans+=p16[i];
24         ans+=tot*bit[i]*p16[i];
25         if(bit[i]==x) tot++;
26     }
27     return ans;
28 }
29 LL to10(char *s){
30     LL ans=0,len=strlen(s);
31     for(int i=0;i<len;++i){
32         LL tmp=isdigit(s[i])?s[i]-'0':(s[i]-'A'+10);
33         ans=ans*16+tmp;
34     }
35     return ans;
36 }
37 int main(){init();
38     char s[15];
39     LL l,r,t,n,i,j,k;
40     LL MAX=to10("FFFFFFFF");
41     scanf("%lld",&t);
42     while(t--){
43         scanf("%lld",&k);
44         scanf("%s",s);
45         LL l=to10(s);
46         LL r=l+k-1;
47         LL ans=0;
48         
49         if(r<=MAX){
50             for(i=0;i<=15;++i) ans+=c[i]*(cal(r+1,i)-cal(l,i));
51         }
52         else{
53             for(i=0;i<=15;++i) if(MAX>=l)ans+=c[i]*(cal(MAX,i)-cal(l,i));
54             ans+=c[15]*8;
55             for(i=0;i<=15;++i) ans+=c[i]*cal(r-MAX,i);
56         }
57         printf("%lld\n",ans);
58     }
59     return 0;
60 }
61 /*
62 10
63 5 89ABCDEF
64 3 FFFFFFFF
65 7 00000000
66 */