学步园

两者都是求最小权匹配。

通过这次练习发现一个问题，就是求最小权匹配时，最好把W的赋值为-INF。在做第二题时，出现两者之间没有连边的匹配到了一块，所以最好赋值为-INF。输出时，只加上已经匹配边的长度。即：for(int i = 1; i <= m; i++) if(Left[i] && W[Left[i]][i] != -INF) ans += W[Left[i]][i];

#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 = 510;
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 <= m; 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 <= m; 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;
    }
    for(int j = 1; j <= m; j++)
    {
        if(T[j]) Ly[j] += a;
    }
}

void KM()
{
    memset(Left, 0, sizeof(Left));
    memset(Lx, 0, sizeof(Lx));
    memset(Ly, 0, sizeof(Ly));
    
    for(int i = 1; i <= n; i++)
    {
        for(int j = 1; j <= m; j++)
            Lx[i] = max(Lx[i], W[i][j]);
    }
    for(int i = 1; i <= n; i++)
    {
        for(;;)
        {
            for(int j = 1; j <= m; 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');
}

int num[maxn];
int N;
int X[maxn], Y[maxn];

void read_case()
{
	for(int i = 1; i <= N; i++) readint(num[i]);
}

void build()
{
	n = m = 1;
	
	for(int i = 1; i <= N; i++)
	{
		if(!num[i]) Y[m++] = i;
		else
		{
			while(num[i] > 1) X[n++] = i, num[i] -= 1;
		}
	}
	
	n--, m--;
	
	for(int i = 1; i <= n; i++)
	for(int j = 1; j <= m; j++) W[i][j] = -INF;
	
	for(int i = 1; i <= n; i++)
	for(int j = 1; j <= m; j++)
	{
		W[i][j] = -min(abs(X[i]-Y[j]), N-(abs(X[i]-Y[j])));
	}
}

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

int main()
{
	while(~scanf("%d", &N))
	{
		solve();
	}
	return 0;
}