洛谷 P1514 引水入城

题意简述

有一个n*m的矩阵，每个格子都有一个高度，第一行可以放蓄水站，可以向四周比这格高度小的格子送水。问可不可以让第n行都有水，若可以输出最少建几个蓄水站，否则输出第n行最少有几个格子没有水。

题解思路

搜索+动态规划

代码

#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;
const int fx[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int n, m, ans;
int d[501], map[501][501];
bool b[501][501], dp[501][501];
struct zb{
	int x, y;
};
queue <zb> qq;
void bfs(int x)
{
	memset(b, 0, sizeof(b));
	b[1][x] = 1;
	zb xx;
	xx.x = 1;
	xx.y = x;
	qq.push(xx);
	while (!qq.empty())
	{
		zb xx, yy;
		xx = qq.front();
		qq.pop();
		for (int i = 0; i < 4; ++i)
		{
			yy = xx;
			yy.x += fx[i][0];
			yy.y += fx[i][1];
			if (yy.x >= 1 && yy.x <= n && yy.y >= 1 && yy.y <= m && !b[yy.x][yy.y] && map[xx.x][xx.y] > map[yy.x][yy.y])
			{
				qq.push(yy);
				b[yy.x][yy.y] = 1;
			}
		}
	}
	for (int i = 1; i <= m; ++i)
		for (int j = i; j <= m; ++j)
			if (b[n][i] && b[n][j])
				dp[i][j] = 1;
}
int main()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= m; ++j)
			scanf("%d", &map[i][j]);
	for (int i = 1; i <= m; ++i)
	{
		b[1][i] = 1;
		zb xx;
		xx.x = 1;
		xx.y = i;
		qq.push(xx);
	}
	while (!qq.empty())
	{
		zb xx, yy;
		xx = qq.front();
		qq.pop();
		for (int i = 0; i < 4; ++i)
		{
			yy = xx;
			yy.x += fx[i][0];
			yy.y += fx[i][1];
			if (yy.x >= 1 && yy.x <= n && yy.y >= 1 && yy.y <= m && !b[yy.x][yy.y] && map[xx.x][xx.y] > map[yy.x][yy.y])
			{
				qq.push(yy);
				b[yy.x][yy.y] = 1;
			}
		}
	}
	for (int i = 1; i <= m; ++i)
		if (!b[n][i])
			ans++;
	if (ans != 0)
	{
		printf("0
%d
", ans);
		return 0;
	}
	for (int i = 1; i <= m; ++i)
		bfs(i);
	for (int i = 1; i <= m; ++i)
		if (dp[1][i]) d[i] = 1;
		else d[i] = 0x7fffffff;
	for (int i = 1; i <= m; ++i)
		for (int j = 1; j <= i; ++j)
			if (dp[j + 1][i] && d[i] > d[j] + 1)
				d[i] = d[j] + 1;
	printf("1
%d
", d[m]);
}