codeforces 758 D. Ability To Convert
2017-01-20 04:34
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D. Ability To Convert
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he
will write the number 10. Thus, by converting the number 475from
decimal to hexadecimal system, he gets 11311 (475 = 1·162 + 13·161 + 11·160).
Alexander lived calmly until he tried to convert the number back to the decimal number system.
Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he
will get the number k.
Input
The first line contains the integer n (2 ≤ n ≤ 109).
The second line contains the integer k (0 ≤ k < 1060),
it is guaranteed that the number kcontains no more than 60 symbols.
All digits in the second line are strictly less than n.
Alexander guarantees that the answer exists and does not exceed 1018.
The number k doesn't contain leading zeros.
Output
Print the number x (0 ≤ x ≤ 1018) —
the answer to the problem.
Examples
input
output
input
output
input
output
input
output
Note
In the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12·130 or 15 = 1·131 + 2·130.
......ABC太简单了不想写题解.....D还凑合....
首先容易想到位数越少一定越优,那就尽可能把相邻两个数字放在一个n进制数的数位里
想一想画一画发现从低位向高位贪心划分比高位到低位更优
但是贪心划分一定最优吗?不会证....
那就写2^len暴力对拍,发现确实如此,AC......
代码:
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he
will write the number 10. Thus, by converting the number 475from
decimal to hexadecimal system, he gets 11311 (475 = 1·162 + 13·161 + 11·160).
Alexander lived calmly until he tried to convert the number back to the decimal number system.
Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he
will get the number k.
Input
The first line contains the integer n (2 ≤ n ≤ 109).
The second line contains the integer k (0 ≤ k < 1060),
it is guaranteed that the number kcontains no more than 60 symbols.
All digits in the second line are strictly less than n.
Alexander guarantees that the answer exists and does not exceed 1018.
The number k doesn't contain leading zeros.
Output
Print the number x (0 ≤ x ≤ 1018) —
the answer to the problem.
Examples
input
13 12
output
12
input
16 11311
output
475
input
20 999
output
3789
input
17 2016
output
594
Note
In the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12·130 or 15 = 1·131 + 2·130.
......ABC太简单了不想写题解.....D还凑合....
首先容易想到位数越少一定越优,那就尽可能把相邻两个数字放在一个n进制数的数位里
想一想画一画发现从低位向高位贪心划分比高位到低位更优
但是贪心划分一定最优吗?不会证....
那就写2^len暴力对拍,发现确实如此,AC......
代码:
#include<iostream> #include<algorithm> #include<cstdio> #include<cstring> #include<cstdlib> #include<cmath> #include<climits> #include<queue> #include<string> #include<stack> #include<map> #include<set> #define N 20020 #define inf 1LL<<60 using namespace std; typedef long long ll; ll n,m,num ,tot,pw ,ans,pw10 ; char ch[66]; void solve() { ll now=0,next,nexp,cnt=0; pw10[0]=1;bool f=0; for(int i=1;i<20;i++)pw10[i]=pw10[i-1]*10; for(int i=m;i>0;i=nexp) { ll j,nu; if(ch[i]!='0') { next=now+(ll)(ch[i]-'0')*pw10[cnt]; nexp=i-1; } else { j=i,nu=0; while(ch[j]=='0'&&j)j--,nu++; if(nu>10)next=inf; else if(!j)next=now,nexp=j; else { next=(ch[j]-'0')*pw10[nu+cnt]+now; nexp=j-1,cnt+=nu; } } if(next>=n) { if(now||i!=m)num[++tot]=now; now=ch[i]-'0',cnt=1; nexp=i-1;//if(ch[i]=='0')next=0,cnt-=nu; }else { now=next,cnt++;if(ch[i]!='0')nexp=i-1; } } num[++tot]=now; pw[1]=1; for(int i=2;i<=tot;i++)pw[i]=pw[i-1]*n; for(int i=1;i<=tot;i++) ans+=num[i]*pw[i]; printf("%I64d\n",ans); } int main() { // freopen("in.txt","r",stdin); // freopen("my.txt","w",stdout); scanf("%I64d",&n); scanf("%s",ch+1); m=strlen(ch+1); solve(); }
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