1036C Classy Numbers(數位dp)
描述
Let’s call some positive integer classy if its decimal representation contains no more than 33 non-zero digits. For example, numbers 44, 200000200000, 1020310203 are classy and numbers 42314231, 102306102306, 72774200007277420000 are not.
You are given a segment [L;R][L;R]. Count the number of classy integers xx such that L≤x≤RL≤x≤R.
Each testcase contains several segments, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer TT (1≤T≤1041≤T≤104) — the number of segments in a testcase.
Each of the next TT lines contains two integers LiLi and RiRi (1≤Li≤Ri≤10181≤Li≤Ri≤1018).
Output
Print TT lines — the ii-th line should contain the number of classy integers on a segment [Li;Ri][Li;Ri].
input
4
1 1000
1024 1024
65536 65536
999999 1000001
output
1000
1
0
2
思路
先說題意,給你t
組資料,詢問區間[L,R]
內非0
數字出現次數<=3
次的數的個數.
定義狀態:dp[i][j]
表示前i
位數字,非0
數字出現j
次的方案數。
模板修改:
num代表當前這一位,為0數字出現的次數.
所以當pos列舉完之後,直接判斷num
<=3
即可.
程式碼
#include <bits/stdc++.h>
using namespace std;
#define mem(a, b) memset(a, b, sizeof(a))
typedef long long ll;
const ll N = 3e5 + 10;
ll dp[20][20], a[20];
ll dfs(ll pos, ll num, ll limit)
{
if (pos == -1)
return num <= 3;
if (!limit && ~dp[pos][num])
return dp[pos][num];
ll up = limit ? a[pos] : 9, ans = 0;
for (ll i = 0; i <= up; i++)
ans += dfs(pos - 1, num + (i != 0), limit && (i == up));
return limit ? ans : dp[pos][num] = ans;
}
ll solve(ll x)
{
ll pos = 0;
while (x)
{
a[pos++] = x % 10;
x /= 10;
}
return dfs(pos - 1, 0, 1);
}
int main()
{
ll n, m, t;
mem(dp, -1);
scanf("%lld", &t);
while (t--)
{
scanf("%lld%lld", &n, &m);
printf("%lld\n", solve(m) - solve(n - 1));
}
return 0;
}