【LOJ 10163】Amount of Degrees

1057. Amount of Degrees

Time limit: 1.0 second
Memory limit: 64 MB

Create a code to determine the amount of integers, lying in the set [X;Y] and being a sum of exactly K different integer degrees of B.

Example. Let X=15, Y=20, K=2, B=2. By this example 3 numbers are the sum of exactly two integer degrees of number 2:

17 = 24+20,
18 = 24+21,
20 = 24+22.

Input

The first line of input contains integers X and Y, separated with a space (1 ≤ X ≤ Y ≤ 231−1). The next two lines contain integers K and B (1 ≤ K ≤ 20; 2 ≤ B ≤ 10).

Output

Output should contain a single integer — the amount of integers, lying between X and Y, being a sum of exactly K different integer degrees of B.

Sample

input	output
15 20 2 2	3

Problem Source: Rybinsk State Avia Academy

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题解：食用：https://loj.ac/problem/10163 效果更佳。copy不来数字和字母。

数位DP，详细内容见jl课件。

#include<iostream>
#include<algorithm>
#include<queue>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<cstdio>
using namespace std;
int x,y,k,b;
int h[31],f[66][66];
void Yao_Chen_Lai_le(){
    f[0][0]=1; f[0][1]=1;
    for(int i=1;i<=31;i++){
        f[i][0]=1;
        for(int j=1;j<=i+1;j++)
            f[i][j]=f[i-1][j-1]+f[i-1][j];
    }
} 

int Cookies(int x){
    int top=-1;
    while(x){
        int p=x%b;
        x/=b; h[++top]=p;
    }
    int biu=0,ans=0;
    for(int i=top;i>=0;i--){
        if(h[i]==1){
            biu++;
            if(biu>k+1) break;
            if(i>0) ans+=f[i-1][k-biu+1]; 
        } 
        else {
            if(h[i]>1){
                ans+=f[i][k-biu];
                return ans;
            }
        } 
    }
    if(biu==k) ++ans;
    return ans;
}
int main(){
    freopen("10163.in","r",stdin);
    freopen("10163.out","w",stdout);
    scanf("%d %d %d %d",&x,&y,&k,&b);
    Yao_Chen_Lai_le(); 
    printf("%d
",Cookies(y)-Cookies(x-1));
    return 0;
}