fire net
2016-03-30 07:09
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Problem Description
Suppose that we have a square city with straight streets. A map of a city is a square board with n rows and n columns, each representing a street or a piece of wall.
A blockhouse is a small castle that has four openings through which to shoot. The four openings are facing North, East, South, and West, respectively. There will be one machine gun shooting through each opening.
Here we assume that a bullet is so powerful that it can run across any distance and destroy a blockhouse on its way. On the other hand, a wall is so strongly built that can stop the bullets.
The goal is to place as many blockhouses in a city as possible so that no two can destroy each other. A configuration of blockhouses is legal provided that no two blockhouses are on the same horizontal row or vertical column in a map unless there is at least
one wall separating them. In this problem we will consider small square cities (at most 4x4) that contain walls through which bullets cannot run through.
The following image shows five pictures of the same board. The first picture is the empty board, the second and third pictures show legal configurations, and the fourth and fifth pictures show illegal configurations. For this board, the maximum number of blockhouses
in a legal configuration is 5; the second picture shows one way to do it, but there are several other ways.
Your task is to write a program that, given a description of a map, calculates the maximum number of blockhouses that can be placed in the city in a legal configuration.
Input
The input file contains one or more map descriptions, followed by a line containing the number 0 that signals the end of the file. Each map description begins with a line containing a positive integer n that is the size of the city; n will be at most 4. The
next n lines each describe one row of the map, with a '.' indicating an open space and an uppercase 'X' indicating a wall. There are no spaces in the input file.
Output
For each test case, output one line containing the maximum number of blockhouses that can be placed in the city in a legal configuration.
Sample Input
Sample Output
用一个数字K,表示位置,简化问题。
这个方法类似于深搜,算是把所有情况讨论一遍,然后把最优解得出。
如果这个位置可以放,则放,递归,然后抹除放置的标记,不在此处放以分类讨论。
Problem Description
Suppose that we have a square city with straight streets. A map of a city is a square board with n rows and n columns, each representing a street or a piece of wall.
A blockhouse is a small castle that has four openings through which to shoot. The four openings are facing North, East, South, and West, respectively. There will be one machine gun shooting through each opening.
Here we assume that a bullet is so powerful that it can run across any distance and destroy a blockhouse on its way. On the other hand, a wall is so strongly built that can stop the bullets.
The goal is to place as many blockhouses in a city as possible so that no two can destroy each other. A configuration of blockhouses is legal provided that no two blockhouses are on the same horizontal row or vertical column in a map unless there is at least
one wall separating them. In this problem we will consider small square cities (at most 4x4) that contain walls through which bullets cannot run through.
The following image shows five pictures of the same board. The first picture is the empty board, the second and third pictures show legal configurations, and the fourth and fifth pictures show illegal configurations. For this board, the maximum number of blockhouses
in a legal configuration is 5; the second picture shows one way to do it, but there are several other ways.
Your task is to write a program that, given a description of a map, calculates the maximum number of blockhouses that can be placed in the city in a legal configuration.
Input
The input file contains one or more map descriptions, followed by a line containing the number 0 that signals the end of the file. Each map description begins with a line containing a positive integer n that is the size of the city; n will be at most 4. The
next n lines each describe one row of the map, with a '.' indicating an open space and an uppercase 'X' indicating a wall. There are no spaces in the input file.
Output
For each test case, output one line containing the maximum number of blockhouses that can be placed in the city in a legal configuration.
Sample Input
4 .X.. .... XX.. .... 2 XX .X 3 .X. X.X .X. 3 ... .XX .XX 4 .... .... .... .... 0
Sample Output
5 1 5 2 4
#include<stdio.h> //城市的尺寸 int n; //城市的地图,最多是4*4 char map[4][4]; //最多放的炮塔数 int bestn; //看炮塔是否能够放置 int canput(int row,int col) { int i; for(i=row-1;i>=0;i--) { if(map[i][col]=='X') { break; } if(map[i][col]=='o') { return 0; } } for(i=col-1;i>=0;i--) { if(map[row][i]=='X') { break; } if(map[row][i]=='o') { return 0; } } return 1; } //K表示放置炮塔的位置 void backtrack(int k,int current) { int x,y; if(k>=n*n) { if(current>bestn) { bestn=current; } return; } else { x=k/n; y=k%n; if(map[x][y]=='.'&&canput(x,y)) { map[x][y]='o'; backtrack(k+1,current+1); map[x][y]='.'; } backtrack(k+1,current); } } void initial() { int i,j; for(i=0;i<4;i++) { for(j=0;j<4;j++) { map[i][j]='.'; } } } int main() { scanf("%d",&n); while(n) { int i,j; bestn=0; initial(); for(i=0;i<n;i++) { for(j=0;j<n;j++) { char ch; ch=getchar(); if(ch=='\n') { j--; continue; } else { map[i][j]=ch; } } } backtrack(0,0); printf("%d\n",bestn); scanf("%d",&n); } return 0; }
用一个数字K,表示位置,简化问题。
这个方法类似于深搜,算是把所有情况讨论一遍,然后把最优解得出。
如果这个位置可以放,则放,递归,然后抹除放置的标记,不在此处放以分类讨论。
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