HDU 4734 F(x)
F(x)
Problem Description
For a decimal number x with n digits (AnAn-1An-2 ... A2A1), we define its weight as F(x) = An * 2n-1 + An-1 * 2n-2 + ... + A2 * 2 + A1 *
1. Now you are given two numbers A and B, please calculate how many numbers are there between 0 and B, inclusive, whose weight is no more than F(A).
Input
The first line has a number T (T <= 10000) , indicating the number of test cases.
For each test case, there are two numbers A and B (0 <= A,B < 109)
For each test case, there are two numbers A and B (0 <= A,B < 109)
Output
For every case,you should output "Case #t: " at first, without quotes. The t is the case number starting from 1. Then output the answer.
Sample Input
3 0 100 1 10 5 100
Sample Output
Case #1: 1 Case #2: 2 Case #3: 13
Source
解题思路
给定A,B, 在[0,B]之间的数字假设为i,问你有多少数字 f[i] 值小于f[A]
解题思路:
数位DP,只需按照位数转移为缩短1位的子问题即可
解题代码:
#include <iostream> #include <vector> #include <cstring> using namespace std; const int maxn=50000; int dp[10][maxn]; int DP(int len,int sum){ if(sum<0) return 0; if(len==0) return 1; if(dp[len][sum]!=-1) return dp[len][sum]; int ans=0; for(int i=0;i<=9;i++){ ans+=DP(len-1,sum-i*(1<<(len-1)) ); } return dp[len][sum]=ans; } int f(int x){ int s=0,sum=0; while(x>0){ sum+=(1<<s)*(x%10); x/=10; s++; } return sum; } int dfs(int a,int b){ vector <int> v; while(b>0){ v.push_back(b%10); b/=10; } int ans=0,sum=f(a); for(int i=v.size()-1;i>=0;i--){ for(int t=0;t<v[i];t++){ ans+=DP(i,sum); sum-=(1<<i); } if(i==0) ans+=DP(i,sum); } return ans; } int main(){ memset(dp,-1,sizeof(dp)); int t,a,b; cin>>t; for(int i=1;i<=t;i++){ cin>>a>>b; cout<<"Case #"<<i<<": "<<dfs(a,b)<<endl; } return 0; }