题目链接：点击打开链接
MYQ10 - Mirror Number
A number is called a Mirror number if on lateral inversion, it gives the same number i.e it looks the same in a mirror. For example 101 is a mirror number while 100 is not.
Given two numbers a and b, find the number of mirror numbers in between them (inclusive of a and b).
Input
First line contains T, number of testcases <= 10^5.
Each testcase is described in a single line containing two numbers a and b.
0 <= a<=b <= 10^44
Output
For each test case print the number of mirror numbers between a and b in a single line.
Example
Input: 30 1010 201 4 Output: 311
题意：
给定一个区间[l,r] 问区间内有多少个数是中心对称的。
首先能对称的数一定只由0 1 8组成。
dp[cur][start][flag] 表示长度为start的数字，已经寻找了start-cur+1位, 是或不是镜像对称数字的个数
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Queue;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
public class Main {
boolean three(char c){return c=='0'||c=='1'||c=='8';}
boolean three_num(int c){return c==0||c==1||c==8;}
int[] num = new int[N], tmp = new int[N];
long[][][] dp = new long[N][N][2];
//cur：当前位数，start：镜像回文判断的开始地方，flag：是否是镜像回文，limit：边界判断
long dfs(int cur, int start, int flag, boolean limit){
if(cur==-1)return flag;
if(!limit && dp[cur][start][flag] != -1)return dp[cur][start][flag];
long ans = 0;
int end = limit?num[cur]:9;
for(int i = 0; i <= end; i++)
if(three_num(i))
{
boolean st = (cur == start && i == 0);
int newFlag = flag;
if(flag > 0){
if(!st && cur<(start+1)/2)
newFlag = (tmp[start-cur] == i)?1:0;
}
tmp[cur] = i;
ans += dfs(cur-1, st?start-1:start, newFlag, limit&&(i==end));
}
if(!limit)dp[cur][start][flag] = ans;
return ans;
}
long solve(String x){
for(int i = 0; i < x.length(); i++)
num[i] = x.charAt(x.length()-1-i) - '0';
num[x.length()] = 0;
return dfs(x.length()-1, x.length()-1, 1, true);
}
void work() throws Exception{
for(int i = 0; i < N; i++)for(int j = 0; j < N; j++)Arrays.fill(dp[i][j], -1);
int T = Int();
while(T-->0){
String l = Next(), r = Next();
long ans = 1;
for(int i = 0; i < l.length(); i++)
if(!three(l.charAt(i)) || l.charAt(i)!=l.charAt(l.length()-1-i))ans = 0L;
out.println((solve(r)-solve(l)+ans));
}
}
public static void main(String[] args) throws Exception{
Main wo = new Main();
in = new BufferedReader(new InputStreamReader(System.in));
out = new PrintWriter(System.out);
// in = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
// out = new PrintWriter(new File("output.txt"));
wo.work();
out.close();
}
static int N = 50;
static int M = N*N * 10;
DecimalFormat df=new DecimalFormat("0.0000");
static long inf = 1000000000000L;
static long inf64 = (long) 1e18*2;
static double eps = 1e-8;
static double Pi = Math.PI;
static int mod = 2520 ;
private String Next() throws Exception{
while (str == null || !str.hasMoreElements())
str = new StringTokenizer(in.readLine());
return str.nextToken();
}
private int Int() throws Exception{
return Integer.parseInt(Next());
}
private long Long() throws Exception{
return Long.parseLong(Next());
}
StringTokenizer str;
static BufferedReader in;
static PrintWriter out;
/*
class Edge{
int from, to, nex;
Edge(){}
Edge(int from, int to, int nex){
this.from = from;
this.to = to;
this.nex = nex;
}
}
Edge[] edge = new Edge[M<<1];
int[] head = new int[N];
int edgenum;
void init_edge(){for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}
void add(int u, int v){
edge[edgenum] = new Edge(u, v, head[u]);
head[u] = edgenum++;
}/**/
int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
int pos = r;
r--;
while (l <= r) {
int mid = (l + r) >> 1;
if (A[mid] <= val) {
l = mid + 1;
} else {
pos = mid;
r = mid - 1;
}
}
return pos;
}
int Pow(int x, int y) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
double Pow(double x, int y) {
double ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
int Pow_Mod(int x, int y, int mod) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
long Pow(long x, long y) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
long Pow_Mod(long x, long y, long mod) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
int Gcd(int x, int y){
if(x>y){int tmp = x; x = y; y = tmp;}
while(x>0){
y %= x;
int tmp = x; x = y; y = tmp;
}
return y;
}
long Gcd(long x, long y){
if(x>y){long tmp = x; x = y; y = tmp;}
while(x>0){
y %= x;
long tmp = x; x = y; y = tmp;
}
return y;
}
int Lcm(int x, int y){
return x/Gcd(x, y)*y;
}
long Lcm(long x, long y){
return x/Gcd(x, y)*y;
}
int max(int x, int y) {
return x > y ? x : y;
}
int min(int x, int y) {
return x < y ? x : y;
}
double max(double x, double y) {
return x > y ? x : y;
}
double min(double x, double y) {
return x < y ? x : y;
}
long max(long x, long y) {
return x > y ? x : y;
}
long min(long x, long y) {
return x < y ? x : y;
}
int abs(int x) {
return x > 0 ? x : -x;
}
double abs(double x) {
return x > 0 ? x : -x;
}
long abs(long x) {
return x > 0 ? x : -x;
}
boolean zero(double x) {
return abs(x) < eps;
}
double sin(double x){return Math.sin(x);}
double cos(double x){return Math.cos(x);}
double tan(double x){return Math.tan(x);}
double sqrt(double x){return Math.sqrt(x);}
}
SPOJ MYQ10 Mirror Number 数位dp'
时间： 2024-10-12 14:20:03