UVa11157 - Dynamic Frog(最大流)

文章探讨了在受农药污染的河流中,一只青蛙从左岸到右岸并返回家最短跳跃距离的问题。通过输入描述河流两岸石头的位置和类型,求解青蛙在不接触污染水的情况下最小化单次跳跃的最大距离。

Withthe increased use of pesticides, the local streams and rivers have become socontaminated that it has become almost impossible for the aquatic animals tosurvive.

Frog Fred is on the left bank of such a river. Nrocks are arranged in a straight line from the left bank to the right bank. Thedistance between the left and the right bank is D meters. There arerocks of two sizes. The bigger ones can withstand any weight but the smallerones start to drown as soon as any mass is placed on it. Fred has to go to theright bank where he has to collect a gift and return to the left bank where hishome is situated.

He can land on every small rock at most one time,but can use the bigger ones as many times as he likes. He can never touch thepolluted water as it is extremely contaminated.

Can you plan the itinerary so that the maximumdistance of a single leap is minimized?

 

Input

The first line of input is an integer T(T<100) that indicatesthe number of test cases. Each case starts with a line containing two integers N(0≤N≤100)and D(1≤D≤1000000000). The next line gives the descriptionof the N stones. Eachstone is defined by S-M. Sindicates the type Big(B) or Small(S)and M(0<M<D)determines the distance of that stone from the left bank. The stones will begiven in increasing order of M.

Output

For every case, output the case number followed by the minimized maximumleap.

Sample Input

Output for Sample Input

3
1 10
B-5
1 10
S-5
2 10
B-3 S-6
Case 1: 5
Case 2: 10
Case 3: 7
#include <cstdio>
#include <vector>
#include <cstring>
#include <queue>
#include <algorithm>

using namespace std;

const int N = 220;
const int INF = 0x7f7f7f7f;

struct Edge
{
	int from, to, cap, flow;
};

struct Rock
{
	char kind;
	int size;
};

Rock rock[N];
vector<Edge> edges;
vector<int> adjList[N];
int n, D;
int source, sink;
bool vis[N];
int d[N];
int cur[N];

void input();
int solve();
void addEdge(int u, int v, int c);
void clearAll(int n);
int maxflow();
bool bfs();
int dfs(int u, int a);

int main()
{
	#ifndef ONLINE_JUDGE
		freopen("d:\\OJ\\uva_in.txt", "r", stdin);
	#endif
	
	int t;
	scanf("%d", &t);
	for (int i = 1; i <= t; i++) {
		input();
		int ans = solve();
		printf("Case %d: %d\n", i, ans);
	}
	return 0;
}


void input()
{
	scanf("%d%d", &n, &D);
	rock[0].kind = 'B', rock[0].size = 0;
	rock[n + 1].kind = 'B', rock[n + 1].size = D;
	
	for (int i = 1; i <= n; i++) {
		scanf(" %c-%d", &rock[i].kind, &rock[i].size);
	}
}

void addEdge(int u, int v, int c)
{
	edges.push_back((Edge){u, v, c, 0});
	edges.push_back((Edge){v, u, 0, 0});
	
	int size = edges.size();
	adjList[u].push_back(size - 2);
	adjList[v].push_back(size - 1);
}

void clearAll(int n)
{
	for (int i = 0; i < n; i++) adjList[i].clear();
	edges.clear();
}

bool bfs()
{
	memset(vis, false, sizeof(vis));
	queue<int> q;
	d[source] = 0;
	q.push(source);
	vis[source] = true;
	
	while (!q.empty()) {
		int u = q.front(); q.pop();
		for (size_t i = 0; i < adjList[u].size(); i++) {
			Edge edge = edges[adjList[u][i]];
			int v = edge.to;
			if (!vis[v] && edge.cap - edge.flow > 0) {
				q.push(v);
				d[v] = d[u] + 1;
				vis[v] = true;
			}
		}
	}
	
	return vis[sink];
}

int dfs(int u, int a)
{
	if (u == sink || a == 0) return a;
	int flow = 0;
	int f;
	
	for (int& i = cur[u]; i < adjList[u].size(); i++) {
		Edge &edge = edges[adjList[u][i]];
		int v = edge.to;
		if (d[v] == d[u] + 1 && (f = dfs(v, min(a, edge.cap - edge.flow))) > 0) {
			edge.flow += f;
			edges[adjList[u][i] ^ 1].flow -= f;
			a -= f;
			flow += f;
			if (a == 0) break;
		}
	}
	
	return flow;
}

int maxflow()
{
	int ans = 0;
	
	while (bfs()) {
		memset(cur, 0x00, sizeof(cur));
		ans += dfs(source, INF);
	}
	
	return ans;
}

int solve()
{
	int l = 0, r = D;
	
	int ans = D;
	while (l <= r) {
		int mid = (l + r) >> 1;
		clearAll(2 * n + 4);
		source = 0, sink = 2 * n + 3;
		for (int i = 0; i <= n + 1; i++) {
			if (rock[i].kind == 'B') {
				addEdge(i, i + n + 2, INF);
			} else {
				addEdge(i, i + n + 2, 1);
			}
			
			for (int j = i + 1; j <= n + 1; j++) {
				if (rock[j].size - rock[i].size <= mid) {
					addEdge(i + n + 2, j, INF);
				}
			}
		}
		
		if (maxflow() >= 2) {
			ans = mid;
			r = mid - 1;
		} else {
			l = mid + 1;
		}
	}
	
	return ans;
}




内容概要:本文系统介绍了算术优化算法(AOA)的基本原理、核心思想及Python实现方法,并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法,其核心思想来源于四则运算,利用乘除运算进行全局勘探,加减运算进行局部开发,通过数学优化器加速函数(MOA)和数学优化概率(MOP)动态控制搜索过程,在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略,并提供了完整的Python代码实现,结合Rastrigin函数进行测试验证。进一步地,以Flask框架搭建前后端分离系统,将AOA应用于图像分割任务,展示了其在实际工程中的可行性与高效性。最后,通过收敛速度、寻优精度等指标评估算法性能,并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群:具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员,尤其适合从事人工智能、图像处理、智能优化等领域的从业者;; 使用场景及目标:①理解元启发式算法的设计思想与实现机制;②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法;③学习如何将优化算法集成到Web系统中实现工程化应用;④为算法性能评估与改进提供实践参考; 阅读建议:建议读者结合代码逐行调试,深入理解算法流程中MOA与MOP的作用机制,尝试在不同测试函数上运行算法以观察性能差异,并可进一步扩展图像分割模块,引入更复杂的预处理或后处理技术以提升分割效果。
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