《算法艺术与信息学竞赛》之 堆 积水

本文介绍了一个平面积水计算问题,给出了一种使用小根堆和floodfill法的解决方案。通过扫描边界并逐步拓展,判断每个格子是否可能积水并计算总积水量。

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前几天机房断网没时间更新。这地道歉顺便祝大家新年快乐。
非常遗憾,这道题在网上没有找到,题目较为简单所以我直接说思路了。
题目大意是给定一个平面,每一个点都有一个高度,一场雨后,问那些格子有积水,并求出总的积水量。(边界上的格子是不会积水的)
这道题非常的基础,有些地方想清楚就非常简单了,根据生活常识,我们知道一个地方有积水当且仅当其四周都比它高时才有可能。我们首先将所有边界上的格子都加入一个小根堆中,每次取出高度最低的一个格子进行拓展,将其四周的格子都扫一遍,如果扫到比它高的显然不可能积水,则入堆,找到矮的则很简单的看其周围的高度是否比他高。这既是我所谓的floodfill法(这看起来其实和bfs没有什么实质性的区别)
具体实现时我想应该需要一个h数组首先存放正无穷,然后每次更新其值会比较方便。

算法艺术信息学竞赛题目完全解析 1.1 程序=算法+数据结构..............................................................................................4 1.2 基本算法...................................................................................................................4 1.2.1 枚举...................................................................................................................4 Pku1116-----Library..................................................................................................4 1.2.2 贪心...................................................................................................................8 Pku1042--Gone Fishing............................................................................................8 Pku1700--Crossing River........................................................................................11 1.2.3 递归分治算法.............................................................................................13 1.2.4 递推.................................................................................................................13 Pku1090-Chain........................................................................................................13 Pku2351--Time Zones.............................................................................................16 1.3数据结构(1)------入门.................................................................................................20 1.3.1 栈和队列.........................................................................................................20 Pku1363--Rails........................................................................................................20 Pku1879-Tempus et mobilius Time and motion.....................................................23 1.3.2 串.....................................................................................................................26 Pku1961-Period.......................................................................................................26 Pku2406--Power Strings.........................................................................................28 Pku2752--Seek the Name, Seek the Fame..............................................................30 1.3.3 树和二叉树.....................................................................................................32 Pku2255--Tree Recovery........................................................................................32 Pku1470--Closest Common Ancestors...................................................................34 Pku1330--Nearest Common Ancestors...................................................................37 Pku3264--Balanced Lineup.....................................................................................40 1.3.4 图及其基本算法.............................................................................................44 1.3.5 排序检索算法.............................................................................................44 Pku1064--Cable master...........................................................................................44 Pku1723--SOLDIERS.............................................................................................47 Pku1433--Exchanges...............................................................................................49 1.4 数据结构(2)-----拓宽应用举例..........................................................................50 1.4.1 并查集.............................................................................................................50 Pku1703--Find them, Catch them...........................................................................50 Pku1182--食物链....................................................................................................53 Pku1988--Cube Stacking........................................................................................55 Pku1733--Parity game.............................................................................................58 Pku2492--A Bug's Life...........................................................................................60 Pku2236--Wireless Network...................................................................................63 1.4.2 及其变种...................................................................................................67 Pku2274--The Race.................................................................................................67 Pku1197--Depot Description...................................................................................68 1.4.2 字典树的两种实现方式: 哈希表,二叉搜索树.........................................72 Pku2503--Babelfish.................................................................................................72 Pku2352--Stars........................................................................................................75
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