中南大学算法实验报告

算法设计与分析基础——实验报告姓名：周建权学号：0909122820班级：信安1202实验一分治—最近点对一．问题ProblemHave you ever played quoit in a playground? Quoit is a game in which flat rings are pitched at some toys, with all the toys encircled awarded.In the field of Cyberground, the position of each toy is fixed, and the ring is carefully designed so it can only encircle one toy at a time. On the other hand, to make the game look more attractive, the ring is designed to have the largest radius. Given a configuration of the field, you are supposed to find the radius of such a ring.Assume that all the toys are points on a plane. A point is encircled by the ring if the distance between the point and the center of the ring is strictly less than the radius of the ring. If two toys are placed at the same point, the radius of the ring is considered to be 0.InputThe input consists of several test cases. For each case, the first line contains an integer N (2 <= N <= 100,000), the total number of toys in the field. Then N lines follow, each contains a pair of (x, y) which are the coordinates of a toy. The input is terminated by N = 0.OutputFor each test case, print in one line the radius of the ring required by the Cyberground manager, accurate up to 2 decimal places.二．分析思路题目是给n个点的坐标，求距离最近的一对点之间距离的一半。

第一行是一个数n表示有n个点，接下来n行是n个点的x坐标和y坐标。

首先，假设点是n个，编号为1到n。

找一个中间的编号mid，先求出1到mid点的最近距离设为d1，还有mid+1到n的最近距离设为d2。

如果说最近点对中的两点都在1-mid 集合中，或者mid+1到n集合中，则d就是最小距离了。

但是还有可能的是最近点对中的两点分属这两个集合，若存在，则把这个最近点对的距离记录下来，去更新d。

这样就得到最小的距离d了。

三．源代码#include<stdio.h>#include<math.h>#include<algorithm>using namespace std;#define N 1000010struct point{double x;double y;}p1[N],p2[N];double dis ( point a , point b ){return sqrt( pow (a.x-b.x,2) + pow ( a.y-b.y,2 ) );}double min ( double a , double b ){return a<b?a:b;}bool cpx ( point a , point b ){return a.x < b.x ;}bool cpy ( point a , point b ){return a.y < b.y ;}double mindis ( int l , int r ){if( l + 1 == r )return dis ( p1[l] ,p1[r] );if( l + 2 == r )return min ( dis ( p1[l] , p1[l+1] ) , min ( dis ( p1[l+1] , p1[r] ) , dis ( p1[l] , p1[r] ) ) ); else{int mid , count=0 ;double mini;mid = ( l + r) /2 ;mini = min ( mindis ( l , mid ) , mindis ( mid+1 , r ) );for( int i = l ; i <= r ; i++ ){if ( fabs ( p1[i].x - p1[mid].x ) <= mini )p2[count++]=p1[i];}sort ( p2 , p2+count , cpy );for ( int i=0 ; i < count ; i++ ){for ( int j = i+1; j < count ;j++){if ( p2[j].y-p2[i].y>=mini)break;elseif(dis (p2[j],p2[i])<mini)mini=dis(p2[j],p2[i]);}}return mini;}}int main(){int n ;double dia ;while(scanf("%d",&n)==1&&n) {for(int i=0;i<n;i++)scanf("%lf%lf",&p1[i].x,&p1[i].y); sort ( p1 , p1 + n-1 , cpx );dia = mindis ( 0 , n-1 );printf("%.2f\n", dia / 2 );}return 0;}四．运行结果实验二回溯—堡垒问题一．问题Problem DescriptionSuppose that we have a square city with straight streets. A map of a city is asquare board with n rows and n columns, each representing a street or apiece 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.InputThe 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.OutputFor each test case, output one line containing the maximum number of blockhouses that can be placed in the city in a legal configuration.二．分析思路对于每个点，若能放置大炮则能选择放或者不放两种情况，若不能放置大炮则就只有一种情况。

直接搜索，回溯的时候把点的状态恢复.三．源代码#include<stdio.h>#include<stdlib.h>#include<string.h>#define MAX_SIZE 10char map[MAX_SIZE][MAX_SIZE];int d[4][2]={0,1,0,-1,1,0,-1,0};int N,cnt;int ok(int x, int y){if(map[x][y]!='.')return 0;int i,xx,yy;for(i=0;i<4;i++){xx=x+d[i][0];yy=y+d[i][1];while(xx>=0 && xx<N && yy>=0 && yy<N && map[xx][yy]!='X'){if(map[xx][yy]=='o')return 0;xx+=d[i][0];yy+=d[i][1];}}return 1;}int search(int x, int y, int c){int i,j;for(j=y;j<N;j++)if(ok(x,j)){map[x][j]='o';search(x,j+1,c+1);map[x][j]='.';}for(i=x+1;i<N;i++)for(j=0;j<N;j++)if(ok(i,j)){map[i][j]='o';search(i,j+1,c+1);map[i][j]='.';}if(c>cnt)cnt=c;return 0;}int main()int i;while(scanf("%d",&N)&&N){for(i=0;i<N;i++)scanf("%s",map[i]);cnt=0;search(0,0,0);printf("%d\n",cnt);}return 0;}四．运行结果实验三动态规划—免费馅饼一．问题Problem Description都说天上不会掉馅饼，但有一天gameboy正走在回家的小径上，忽然天上掉下大把大把的馅饼。