Bomb
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 19698 Accepted Submission(s): 7311
Problem Description
The counter-terrorists found a time bomb in the dust. But this time the terrorists improve on the time bomb. The number sequence of the time bomb counts from 1 to N. If the current number sequence includes the sub-sequence "49", the power of the blast would add one point.
Now the counter-terrorist knows the number N. They want to know the final points of the power. Can you help them?
Now the counter-terrorist knows the number N. They want to know the final points of the power. Can you help them?
Input
The first line of input consists of an integer T (1 <= T <= 10000), indicating the number of test cases. For each test case, there will be an integer N (1 <= N <= 2^63-1) as the description.
The input terminates by end of file marker.
The input terminates by end of file marker.
Output
For each test case, output an integer indicating the final points of the power.
Sample Input
3
1
50
500
1
50
500
Sample Output
0
1
15
1
15
Hint
From 1 to 500, the numbers that include the sub-sequence "49" are "49","149","249","349","449","490","491","492","493","494","495","496","497","498","499",
so the answer is 15.
代码(dfs解法):
#include<iostream>
#include<cstring>
#define LL long long
using namespace std; LL bit[25], dp[25][2]; LL dfs(int pos, int is4, int lim)//pos当前位, is4上一位是否为4, lim上一位是否取到最大值
{
if(pos<0) return 1;
if(!lim && dp[pos][is4]!=-1) return dp[pos][is4];
int las=lim?bit[pos]:9;//若上以一位没有取最大值位则可以0~9循环
LL res=0;
for(int i=0; i<=las; ++i)
if(!(is4 && i==9))//搜索不含49的,结果取反
res+=dfs(pos-1, i==4, lim&&i==las);
if(!lim) dp[pos][is4]=res;
return res;
} int main()
{
int T;
memset(dp, -1, sizeof(dp));
cin>>T;
while(T--)
{
LL n;
cin>>n;
LL len=0, m=n;
while(n)
{
bit[len++]=n%10;
n/=10;
}
LL ans=m-dfs(len-1, 0, 1)+1;//结果取反, 且搜索过程中会包含0, 故+1
cout<<ans<<endl;
}
return 0;
}
代码(传统dp):
#include<iostream>
#include<cstring>
#include<cstdio>
#define LL long long
using namespace std; LL num[25], dp[25][3]; int main()
{
int T;
memset(dp, 0, sizeof(dp));
dp[0][0]=1;
for(int i=1; i<21; ++i)
{
dp[i][0]=dp[i-1][0]*10-dp[i-1][1];//dp[i][0]表示i位数不包含49且最高位不是9的数目
dp[i][1]=dp[i-1][0];//dp[i][1]表示i位数不包含49且最高位是9的数目
dp[i][2]=dp[i-1][2]*10+dp[i-1][1];//dp[i][2]表示i位数包含49的数目
}
cin>>T;
while(T--)
{
LL n;
cin>>n;
int len=0;
memset(num, 0, sizeof(num));
while(n)
{
num[++len]=n%10;
n/=10;
}
int las=0;
bool flag=false;
LL ans=0;
for(int i=len; i>=1; --i)
{
ans+=(dp[i-1][2]*num[i]);//若n=789, 则i=3时此处计算700以内的结果
if(flag) ans+=dp[i-1][0]*num[i];//若之前已包含49
if(!flag && num[i]>4) ans+=dp[i-1][1];//若之前未包含49
if(las==4 && num[i]==9) flag=true;
las=num[i];
}
if(flag) ans++;
cout<<ans<<endl;
}
return 0;
}