URAL - 1057 Amount of Degrees--数位dp

原题链接：​​http://vjudge.net/problem/URAL-1057​​

题意：[ x , y ]里一共有多少个数可以由k个b整数幂组成。

#define _CRT_SECURE_NO_DEPRECATE

#include<iostream>
#include<vector>
#include<cstring>
#include<queue>
#include<stack>
#include<algorithm>
#include<cmath>
#include<string>
#include<stdio.h>
#define INF 99999999
#define eps 0.0001
using namespace std;

int dp[35][35];//dp[i][j]表示深度为i有j个1的种类,根深度为0
int x, y, k, b;
int cnt[35];

void init()
{
  for (int i = 0; i <= 31; i++)
  {
    dp[i][0] = 1;
    for (int j = 1; j <= i; j++)
      dp[i][j] = dp[i - 1][j] + dp[i - 1][j - 1];
    
  }
}

int solve(int n)
{
  int len = 0;
  int ans = 0;
  int ik = k;
  int ib = b;
  while (n)
  {
    cnt[len++] = n%ib;
    n /= ib;
  }
  
  for (int i = len - 1; i >= 0; i--)
  {
    if (cnt[i] == 1)
    {
      ans += dp[i][ik];//以0开头，找到k个1；然后k--，固定开头为1，继续做
      ik--;
    }
    else if (cnt[i] > 1)
    {
      ans += dp[i + 1][ik];
      break;
    }
    if (ik < 0)//注意是小于0
      return ans;
  }

  if (ik == 0)//n本身满足
    ans++;
  return ans;
}

int main() 
{
  init();
  while (~scanf("%d%d%d%d", &x, &y, &k, &b))
  {
    printf("%d\n", solve(y) - solve(x - 1));
  }
  return 0;
}