[USACO 08JAN]Haybale Guessing
Description
The cows, who always have an inferiority complex about their intelligence, have a new guessing game to sharpen their brains.
A designated 'Hay Cow' hides behind the barn and creates N (1 ≤ N ≤ 1,000,000) uniquely-sized stacks (conveniently numbered 1..N) of hay bales, each with 1..1,000,000,000 bales of hay.
The other cows then ask the Hay Cow a series of Q (1 ≤ Q ≤ 25,000) questions about the the stacks, all having the same form:
What is the smallest number of bales of any stack in the range of stack numbers Ql..Qh (1 ≤ Ql ≤ N; Ql ≤ Qh ≤ N)?The Hay Cow answers each of these queries with a single integer A whose truthfulness is not guaranteed.
Help the other cows determine if the answers given by the Hay Cow are self-consistent or if certain answers contradict others.
给一段长度为n,每个位置上的数都不同的序列a[1..n]和q和问答,每个问答是(x, y, r)代表RMQ(a, x, y) = r, 要你给出最早的有矛盾的那个问答的编号。
Input
Line 1: Two space-separated integers: N and Q
- Lines 2..Q+1: Each line contains three space-separated integers that represent a single query and its reply: Ql, Qh, and A
Output
- Line 1: Print the single integer 0 if there are no inconsistencies among the replies (i.e., if there exists a valid realization of the hay stacks that agrees with all Q queries). Otherwise, print the index from 1..Q of the earliest query whose answer is inconsistent with the answers to the queries before it.
Sample Input
20 4
1 10 7
5 19 7
3 12 8
11 15 12
Sample Output
3
题解
二分求解。
二分答案,将答案范围内的最小值$Ai$进行降序排序 然后我们可以观察一下得到的这些区间
对于不同$Ai$想一想如果它被之前出现的区间(比它大的$Ai$)都覆盖了,那么肯定就是有矛盾的
给点提示:对于同样的$Ai$询问要用交集,覆盖要用并集
这样就可以很明显地用线段树来搞了
1 //It is made by Awson on 2017.10.27 2 #include <set> 3 #include <map> 4 #include <cmath> 5 #include <ctime> 6 #include <queue> 7 #include <stack> 8 #include <vector> 9 #include <cstdio> 10 #include <string> 11 #include <cstdlib> 12 #include <cstring> 13 #include <iostream> 14 #include <algorithm> 15 #define LL long long 16 #define Max(a, b) ((a) > (b) ? (a) : (b)) 17 #define Min(a, b) ((a) < (b) ? (a) : (b)) 18 #define Lr(o) (o<<1) 19 #define Rr(o) (o<<1|1) 20 using namespace std; 21 const int N = 1000000; 22 const int INF = ~0u>>1; 23 24 int n, q; 25 struct tt { 26 int l, r, a; 27 } a[N+5], b[N+5]; 28 bool comp(const tt &a, const tt &b) { 29 if (a.a != b.a) return a.a > b.a; 30 return a.l == b.l ? a.r < b.r : a.l < b.l; 31 } 32 struct segment { 33 int sgm[(N<<2)+5], lazy[(N<<2)+5]; 34 void build(int o, int l, int r) { 35 lazy[o] = 0; 36 if (l == r) { 37 sgm[o] = INF; return; 38 } 39 int mid = (l+r)>>1; 40 build(Lr(o), l, mid); 41 build(Rr(o), mid+1, r); 42 sgm[o] = Max(sgm[Lr(o)], sgm[Rr(o)]); 43 } 44 void pushdown(int o) { 45 if (lazy[o]) { 46 sgm[Lr(o)] = sgm[Rr(o)] = lazy[Lr(o)] = lazy[Rr(o)] = lazy[o]; 47 lazy[o] = 0; 48 } 49 } 50 void update(int o, int l, int r, int a, int b, int key) { 51 if (a <= l && r <= b) { 52 sgm[o] = lazy[o] = key; return; 53 } 54 pushdown(o); 55 int mid = (l+r)>>1; 56 if (a <= mid) update(Lr(o), l, mid, a, b, key); 57 if (mid < b) update(Rr(o), mid+1, r, a, b, key); 58 sgm[o] = Max(sgm[Lr(o)], sgm[Rr(o)]); 59 } 60 int query(int o, int l, int r, int a, int b) { 61 if (a <= l && r <= b) return sgm[o]; 62 pushdown(o); 63 int mid = (l+r)>>1; 64 int a1 = 0, a2 = 0; 65 if (a <= mid) a1 = query(Lr(o), l, mid, a, b); 66 if (mid < b) a2 = query(Rr(o), mid+1, r, a, b); 67 return Max(a1, a2); 68 } 69 }T; 70 71 bool get(int l, int r, int &x, int &y) { 72 int ll = b[l].l, rr = b[l].r; 73 for (int i = l+1; i <= r; i++) { 74 int lll = b[i].l, rrr = b[i].r; 75 if (rr < lll) return false; 76 ll = lll; 77 } 78 x = ll, y = rr; 79 return true; 80 } 81 bool judge(int mid) { 82 T.build(1, 1, n); 83 for (int i = 1; i <= mid; i++) b[i] = a[i]; 84 sort(b+1, b+1+mid, comp); 85 for (int i = 1; i <= mid; i++) { 86 int loc, l, r; 87 for (loc = i; loc <= mid; loc++) if (b[loc].a != b[i].a) break; 88 loc--; 89 if (!get(i, loc, l, r)) return false; 90 int t = T.query(1, 1, n, l, r); 91 if (t != INF && t != b[i].a) return false; 92 for (int k = i; k <= loc; k++) 93 T.update(1, 1, n, b[k].l, b[k].r, b[k].a); 94 i = loc; 95 } 96 return true; 97 } 98 void work() { 99 scanf("%d%d", &n, &q); 100 for (int i = 1; i <= q; i++) 101 scanf("%d%d%d", &a[i].l, &a[i].r, &a[i].a); 102 int L = 1, R = q, ans = 0; 103 while (L <= R) { 104 int mid = (L+R)>>1; 105 if (judge(mid)) L = mid+1; 106 else R = mid-1, ans = mid; 107 } 108 printf("%d\n", ans); 109 } 110 int main() { 111 work(); 112 return 0; 113 }
转载于:https://www.cnblogs.com/NaVi-Awson/p/7745103.html
[USACO 08JAN]Haybale Guessing相关推荐
- 线段树 + 二分答案:Haybale Guessing G
参考文献:题解 P2898 [[USACO08JAN]haybale猜测Haybale Guessing] - レムの小屋 - 洛谷博客 题目链接:[USACO08JAN]Haybale Guessi ...
- POJ Haybale Guessing
Description The cows, who always have an inferiority complex about their intelligence, have a new gu ...
- Haybale Guessing (POJ-3657)
Problem Description The cows, who always have an inferiority complex about their intelligence, have ...
- P2898 [USACO08JAN]haybale猜测Haybale Guessing
好题. 搬运一下luogu的题解, 讲的挺清楚的. 题意:给出一些区间的最小值 求问 最早哪个问题会产生矛盾 输出 我们可以二分判断 哪个地方最早出现矛盾 然后每次针对二分的一个值 我去判断一下是否成 ...
- 《题目与解读》红书 训练笔记目录《ACM国际大学生程序设计竞赛题目与解读》
虽然2012年出版的老书了,但是是由三次世界冠军的上海交大ACM队出版的书籍,选择的题目是ACM经典中的经典,书中有非常详细的题解,可以学到很多东西,值得一刷. 目录 第一部分 第一章 数学 1.1 ...
- 树形结构 —— 并查集
[概述] 并查集(Union-Find Set)是一种用于分离集合操作的抽象数据类型,其处理的是集合(set)之间的关系,一般处理的是图的连通分量,当给出两个的元素的一个无序对 (a,b) 时,需要快 ...
- jzoj 1594: 【USACO】The Chivalrous Cow(骑士牛)( 待加入)
1594: [USACO] 题目描述 Farmer John traded one of his cows for a cow that Farmer Don called 'The Knight' ...
- 如何准备好2023年的USACO?
目录 1. 注册 2. 刷题 3. 备考 4. 考试流程/介绍 5. 铜组例题 关于usaco usaco是美国中学生的官方竞赛网站.是美国著名在线题库,专门为信息学竞赛选手准备.推荐直接阅读英语原文 ...
- usaco Shaping Regions
这就是usaco 前面的windows area的变形. /* ID:jinbo wu TASK:rect1 LANG:C++ */ #include<iostream> #include ...
最新文章
- pytorch的一些函数
- Maven构建java项目
- RTX Server SDK跨服务器
- 另一种launch SAP CRM AET的方式
- 多线程—Thread类及线程三种创建方式及对比
- .Net Core 认证系统之基于Identity Server4 Token的JwtToken认证源码解析
- MongoDB的可视化工具之Navicat
- Spring Boot(3)---Spring Boot入门:系统要求
- WORD2010每次启动都要配置
- oracle数据库给用户解锁和修改密码和提升权限的命令
- php cms 新闻采集,自动新闻采集软件快速入门图文详细教程
- Java概述、Jdk的安装、关键字
- Scott Page 斯科特佩奇《模型思维》读书笔记
- 如何使用Keil5开发MSP430及Tiva系列开发板
- python基础教程:__call__用法
- 岁月如水-指间流逝-难觅难留
- JS实现简易图片时钟效果
- 网站进入前10名的需要的操作
- win11怎么升级更新显卡驱动
- 如何设计帮助中心才能真正地帮助客户解决问题?