HDU 1533 Going Home-优快云博客

本文深入探讨了使用KM算法解决网络流匹配问题的实例，详细阐述了算法实现过程，包括输入输出规范、核心逻辑和优化策略。通过实例分析，展示了KM算法在实际应用中的高效性和实用性。

7月冒泡第三题。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <map>
using namespace std;

const int maxn = 310;
const int INF = 0x3f3f3f3f;

int n, m;

int W[maxn][maxn];
int Lx[maxn], Ly[maxn];

int Left[maxn];
bool S[maxn], T[maxn];

bool match(int i)
{
	S[i] = 1;
	for(int j = 1; j <= n; j++) if(Lx[i]+Ly[j] == W[i][j] && !T[j])
	{
		T[j] = 1;
		if(!Left[j] || match(Left[j]))
		{
			Left[j] = i;
			return 1;
		}
	}
	return 0;
}

void update()
{
	int a = INF;
	for(int i = 1; i <= n; i++) if(S[i])
	for(int j = 1; j <= n; j++) if(!T[j])
		a = min(a, Lx[i]+Ly[j]-W[i][j]);
		
	for(int i = 1; i <= n; i++)
	{
		if(S[i]) Lx[i] -= a;
		if(T[i]) Ly[i] += a;
	}
}

void KM()
{
	for(int i = 1; i <= n; i++)
	{
		Left[i] = Lx[i] = Ly[i] = 0;
		for(int j = 1; j <= n; j++)
			Lx[i] = max(Lx[i], W[i][j]);
	}
	for(int i = 1; i <= n; i++)
	{
		for(;;)
		{
			for(int j = 1; j <= n; j++) S[j] = T[j] = 0;
			if(match(i)) break; else update();
		}
	}
}

inline void readint(int &x)
{
	char c;
	c = getchar();
	while(!isdigit(c)) c = getchar();
	
	x = 0;
	while(isdigit(c)) x = x*10+c-'0', c = getchar();
}

inline void writeint(int x)
{
	if(x > 9) writeint(x/10);
	putchar(x%10+'0');
}

struct node
{
	int x, y;
	
	node(int x=0, int y=0): x(x), y(y) {}
}H[maxn], M[maxn];

int hh, mm;

char s[110][110];

void read_case()
{
	for(int i = 0; i < n; i++) scanf("%s", s[i]);
}

int Dist(node a, node b) { return abs(a.x-b.x) + abs(a.y-b.y); }

void build()
{
	hh = mm = 1;
	
	for(int i = 0; i < n; i++)
	for(int j = 0; j < m; j++)
	{
		if(s[i][j] == 'm')
		{
			M[mm++] = node(i, j);
		}
		
		if(s[i][j] == 'H')
		{
			H[hh++] = node(i, j); 
		}
	}
	
	mm--, hh--;
	
	n = hh, m = mm;
	
	for(int i = 1; i <= n; i++)
	{
		for(int j = 1; j <= n; j++)
		{
			W[i][j] = -(Dist(H[i], M[j]));
		}
	}
}

void solve()
{
	read_case();
	
	build();
	
	KM();
	
	int ans = 0;
	
	for(int i = 1; i <= n; i++) ans += W[Left[i]][i];
	
	writeint(-ans), puts("");
}

int main()
{
	readint(n), readint(m);
	for(; (n || m); readint(n), readint(m))
	{
		solve();
	}
	return 0;
}