Codeforces Gym 100431G Persistent Queue 可持久化队列

本文详细介绍了如何实现可持久化队列,并通过DFS离线算法优化队列操作,解决在线版本无限TLE的问题。重点在于理解队列的持久化特性及其在实际应用中的高效处理方式。

Problem G. Persistent Queue
Time Limit: 20 Sec

Memory Limit: 256 MB

题目连接

http://acm.hust.edu.cn/vjudge/contest/view.action?cid=88258#problem/G

Description

Persistent data structures are designed to allow access and modication of any version of data structure. In this problem you are asked to implement persistent queue. Queue is the data structure that maintains a list of integer numbers and supports two operations: push and pop. Operation push(x) adds x to the end of the list. Operation pop returns the rst element of the list and removes it. In persistent version of queue each operation takes one additional argument v. Initially the queue is said to have version 0. Consider the i-th operation on queue. If it is push(v, x), the number x is added to the end of the v-th version of queue and the resulting queue is assigned version i (the v-th version is not modied). If it is pop(v), the front number is removed from the v-th version of queue and the resulting queue is assigned version i (similarly, version v remains unchanged). Given a sequence of operations on persistent queue, print the result of all pop operations.

Input

The rst line of the input le contains n the number of operations (1 ≤ n ≤ 200 000). The following n lines describe operations. The i-th of these lines describes the i-th operation. Operation push(v, x) is described as 1 v x, operation pop(v) is described as -1 v. It is guaranteed that pop is never applied to an empty queue. Elements pushed to the queue t standard signed 32-bit integer type.

Output

For each pop operation print the element that was extracted.

Sample Input

10
1 0 1
1 1 2
1 2 3
1 2 4
-1 3
-1 5
-1 6
-1 4
-1 8
-1 9

Sample Output

1
2
3
1
2
4

HINT

 

题意

让你维护可持久化队列

1 v x 给状态v下的队列的尾部插入x

-1 v pop状态v的队列首部

题解

dfs离线搞一搞就好了

按照状态建成一个图

然后blabla就吼了……

 

一开始拿rope写的在线版本,无限TLE= =

代码:

//qscqesze
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define maxn 200051
#define mod 10007
#define eps 1e-9
int Num;
//const int inf=0x7fffffff;   //нчоч╢С
const int inf=0x3f3f3f3f;
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//**************************************************************************************

vector<pair<int,int> > ans;
vector<int> E[maxn];
vector<int> Q;
struct node
{
    int x,y,z;
};
node op[maxn];
void dfs(int x,int l)
{
    if(x==0)
    {
        for(int i=0;i<E[x].size();i++)
            dfs(E[x][i],l);
    }
    else if(op[x].x==1)
    {
        Q.push_back(op[x].z);
        for(int i=0;i<E[x].size();i++)
            dfs(E[x][i],l);
        Q.erase(Q.end()-1);
    }
    else
    {
        ans.push_back(make_pair(x,Q[l]));
        for(int i=0;i<E[x].size();i++)
            dfs(E[x][i],l+1);
    }
}
int main()
{
    freopen("queue.in","r",stdin);
    freopen("queue.out","w",stdout);
    int n=read();
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&op[i].x);
        if(op[i].x==1)
        {
            scanf("%d%d",&op[i].y,&op[i].z);
            E[op[i].y].push_back(i);
        }
        else
        {
            scanf("%d",&op[i].y);
            E[op[i].y].push_back(i);
        }
    }
    dfs(0,0);
    sort(ans.begin(),ans.end());
    for(int i=0;i<ans.size();i++)
        printf("%d\n",ans[i].second);
}

 

Codeforces Gym 101630 是一场编程竞赛,通常包含多个算法挑战问题。这些问题往往涉及数据结构算法设计、数学建模等多个方面,旨在测试参赛者的编程能力和解决问题的能力。 以下是一些可能出现在 Codeforces Gym 101630 中的题目类型及解决方案概述: ### 题目类型 1. **动态规划(DP)** 动态规划是编程竞赛中常见的题型之一。问题通常要求找到某种最优解,例如最小路径和、最长递增子序列等。解决这类问题的关键在于状态定义和转移方程的设计[^1]。 2. **图论** 图论问题包括最短路径、最小生成树、网络流等。例如,Dijkstra 算法用于求解单源最短路径问题,而 Kruskal 或 Prim 算法则常用于最小生成树问题[^1]。 3. **字符串处理** 字符串问题可能涉及模式匹配、后缀数组、自动机等高级技巧。KMP 算法和 Trie 树是解决此类问题的常用工具[^1]。 4. **数论组合数学** 这类问题通常需要对质数、模运算、排列组合等有深入的理解。例如,快速幂算法可以用来高效计算大数的模幂运算[^1]。 5. **几何** 几何问题可能涉及点、线、多边形的计算,如判断点是否在多边形内部、计算两个圆的交点等。向量运算和坐标变换是解决几何问题的基础[^1]。 ### 解决方案示例 #### 示例问题:动态规划 - 最长递增子序列 ```python def longest_increasing_subsequence(nums): if not nums: return 0 dp = [1] * len(nums) for i in range(len(nums)): for j in range(i): if nums[i] > nums[j]: dp[i] = max(dp[i], dp[j] + 1) return max(dp) # 示例输入 nums = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(nums)) # 输出: 4 ``` #### 示例问题:图论 - Dijkstra 算法 ```python import heapq def dijkstra(graph, start): distances = {node: float('infinity') for node in graph} distances[start] = 0 priority_queue = [(0, start)] while priority_queue: current_distance, current_node = heapq.heappop(priority_queue) if current_distance > distances[current_node]: continue for neighbor, weight in graph[current_node].items(): distance = current_distance + weight if distance < distances[neighbor]: distances[neighbor] = distance heapq.heappush(priority_queue, (distance, neighbor)) return distances # 示例输入 graph = { 'A': {'B': 1, 'C': 4}, 'B': {'A': 1, 'C': 2, 'D': 5}, 'C': {'A': 4, 'B': 2, 'D': 1}, 'D': {'B': 5, 'C': 1} } start = 'A' print(dijkstra(graph, start)) # 输出: {'A': 0, 'B': 1, 'C': 3, 'D': 4} ``` #### 示例问题:字符串处理 - KMP 算法 ```python def kmp_failure_function(pattern): m = len(pattern) lps = [0] * m length = 0 # length of the previous longest prefix suffix i = 1 while i < m: if pattern[i] == pattern[length]: length += 1 lps[i] = length i += 1 else: if length != 0: length = lps[length - 1] else: lps[i] = 0 i += 1 return lps def kmp_search(text, pattern): n = len(text) m = len(pattern) lps = kmp_failure_function(pattern) i = 0 # index for text j = 0 # index for pattern while i < n: if pattern[j] == text[i]: i += 1 j += 1 if j == m: print("Pattern found at index", i - j) j = lps[j - 1] elif i < n and pattern[j] != text[i]: if j != 0: j = lps[j - 1] else: i += 1 # 示例输入 text = "ABABDABACDABABCABAB" pattern = "ABABCABAB" kmp_search(text, pattern) # 输出: Pattern found at index 10 ``` ###
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