LightOJ 1140 How Many Zeroes? (数位DP)

题意：统计在给定区间内0的数量。

析：数位DP，dp[i][j] 表示前 i 位 有 j 个0，注意前导0.

代码如下:

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 1e5 + 5;
const int mod = 1e9 + 7;
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, 1, 0, -1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline int Min(int a, int b){ return a < b ? a : b; }
inline int Max(int a, int b){ return a > b ? a : b; }
inline LL Min(LL a, LL b){ return a < b ? a : b; }
inline LL Max(LL a, LL b){ return a > b ? a : b; }
inline bool is_in(int r, int c){
    return r >= 0 && r < n && c >= 0 && c < m;
}
LL dp[15][15];
int a[15];

LL dfs(int pos, int num, bool is, bool ok){
    if(!pos)  return is ? 1 : num;
    LL &ans = dp[pos][num];
    if(!ok && ans >= 0 && !is)  return ans;

    LL res = 0;
    int n = ok ? a[pos] : 9;
    for(int i = 0; i <= n; ++i){
        if(is)  res += dfs(pos-1, num, !i, ok && i == n);
        else if(!i)  res += dfs(pos-1, num+1, false, ok && i == n);
        else res += dfs(pos-1, num, false, ok && i == n);
    }
    if(!ok && !is)  ans = res;
    return res;
}

LL solve(LL n){
    if(n == -1)  return 0;
    int len = 0;
    while(n > 0){
        a[++len] = n % 10;
        n /= 10;
    }
    return dfs(len, 0, true, true);
}

int main(){
    memset(dp, -1, sizeof dp);
    LL x, y;
    int T;  cin >> T;
    for(int kase = 1; kase <= T; ++kase){
        scanf("%lld %lld", &x, &y);
        printf("Case %d: %lld
", kase, solve(y)-solve(x-1));
    }
    return 0;
}