清华集训2014 day2 task3 矩阵变换

题目

算法 稳定婚姻系统（其实就是贪心）

一个方案不合法，当且仅当下面这种情况：

设第\(i\)行选了数字\(x\)，如果第\(j\)行有一个\(x\)在第\(i\)行的\(x\)后面，并且第\(j\)行所选的数字在第\(j\)行的\(x\)后面。

分析到这里就是典型的稳定婚姻系统了。

代码

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <assert.h>
using namespace std;

#ifdef debug
#define ep(...) fprintf(stderr, __VA_ARGS__)
#else
#define ep(...) assert(true)
#endif 

	template <class T>
void relax(T &a, const T &b)
{
	if (b > a) a = b;
}

	template <class T>
void tension(T &a, const T &b)
{
	if (b < a) a = b;
}

int geti()
{
	int ret = 0;
	char ch = getchar();
	while (ch < '0' || ch > '9') ch = getchar();
	do
	{
		ret = ret * 10 + (int) ch - 48;
		ch = getchar();
	}while (ch >= '0' && ch <= '9');
	return ret;
}

const int MaxN = 203;
const int MaxM = 403;

int n, m;
int A[MaxN][MaxM];

void output(const int *x)
{
	ep("answer ");
	for (int i = 0; i < n; i ++)
	{
		printf("%d ", x[i]);
		ep("%d ", x[i]);
	}
	printf("\n");
	ep("\n");
}

void output_nosolution()
{
	ep("no solution\n");
	printf("\\\n");
}

int posi[MaxN][MaxN];

int choice[MaxN];

void next_choice(const int &i)
{
	int &tmp = choice[i];
	tmp ++;
	while (tmp < m && A[i][tmp] == 0)
		tmp ++;
	if (tmp >= m) tmp = -1;
}

void Main()
{
	n = geti();
	m = geti();
	for (int i = 0; i < n; i ++)
		for (int j = 0; j < m; j ++)
		{
			A[i][j] = geti();
			if (A[i][j])
				posi[i][ A[i][j] ] = j;
		}
	{
		for (int i = 0; i < n; i ++)
		{
			choice[i] = -1;
			next_choice(i);
		}

		static int row_love[MaxN], num_love[MaxN];
		for (int i = 0; i < n; i ++)
			row_love[i] = num_love[i + 1] = -1;
		int cnt = 0;
		while (cnt < n)
		{
			for (int i = 0; i < n; i ++)
			{
				if (row_love[i] == -1)
				{
					int num = A[i][choice[i]];
					assert(num != -1);
					next_choice(i);

					if (num_love[num] == -1)
					{
						cnt ++;
						row_love[i] = num;
						num_love[num] = i;
					}
					else if (posi[i][num] > posi[ num_love[num] ][num])
					{
						row_love[num_love[num]] = -1;
						row_love[i] = num;
						num_love[num] = i;
					}
				}
			}
		}
		output(row_love);
	}
}

int main()
{
#if defined(debug) || defined(local)
	freopen("c.in", "r", stdin);
	freopen("c.out", "w", stdout);
#endif

	int cases = geti();
	for (int i = 0; i < cases; i ++)
		Main();

	return 0;
}