2014-03-30 大臣的旅费(回溯思想，最长路径)

题目

大臣的旅费

大臣J从城市4到城市5要花费135的路费。

思想

根据题目的特性，只会有n-1条边，考虑到本图非常稀疏，采用结构体存顶点和值。本题最主要其实就是求两点的最长路径，本思想是求每一个叶子节点网上回溯，回溯到分支节点时减去回溯的支数，最后总能回溯到最后一个节点（度数最大的那个节点，若有多个度数相同的节点，本程序是任取一个来处理）。

程序实现

#include<stdlib.h>
#include<stdio.h>

struct Distance_notes{
	int child_nodes_number;
	int max_distance;
	int second_distance;
};

struct Map_notes{
	int source;
	int destination;
	int distance;
};

int total_number;
struct Distance_notes* dn;
struct Map_notes* map_nodes;

void execute_distance()
{
	int i,j;
	int temp;
	 for(i=0;i<total_number;i++){
		if(dn[i].child_nodes_number > 1){
			for(j=0;j<total_number-1;j++){
	 			if(map_nodes[j].source == i+1){
					if(dn[map_nodes[j].destination-1].child_nodes_number == 1){
						temp = map_nodes[j].distance + dn[map_nodes[j].destination-1].max_distance;
						if(dn[i].max_distance <= temp){
							dn[i].second_distance = dn[i].max_distance;
							dn[i].max_distance = temp;
							dn[i].child_nodes_number--;
							dn[map_nodes[j].destination-1].child_nodes_number--; //avoid double execute
							continue;
						}

						if(dn[i].second_distance < temp){
							dn[i].second_distance = temp;
							dn[i].child_nodes_number--;
							dn[map_nodes[j].destination-1].child_nodes_number--;
							continue;
						}	
						dn[i].child_nodes_number--;
						dn[map_nodes[j].destination-1].child_nodes_number--;
					}
				}

				if(map_nodes[j].destination== i+1){
					if(dn[map_nodes[j].source-1].child_nodes_number == 1){
						temp = map_nodes[j].distance + dn[map_nodes[j].source-1].max_distance;
						if(dn[i].max_distance<= temp){
							dn[i].second_distance = dn[i].max_distance;
							dn[i].max_distance = temp;
							dn[i].child_nodes_number--;
							dn[map_nodes[j].source-1].child_nodes_number--;
							continue;
						}

						if(dn[i].second_distance < temp){
							dn[i].second_distance = temp;
							dn[i].child_nodes_number--;
							dn[map_nodes[j].source-1].child_nodes_number--;
							continue;
						}	
						dn[i].child_nodes_number--;
						dn[map_nodes[j].source-1].child_nodes_number--;
					}
				}
	 		}
		}
	 }
}

int main(void)
{
	scanf("%d", &total_number);
	 dn = (struct Distance_notes *)malloc(sizeof(struct Distance_notes) * total_number);
	 map_nodes =(struct Map_notes *)malloc(sizeof(struct Map_notes) * (total_number-1));

	//initialization
	int i;
	 for(i=0;i<total_number;i++){
		dn[i].child_nodes_number= 0;
		dn[i].max_distance = 0;
		dn[i].second_distance = 0;
	 }
	 
	 for(i=0;i<total_number-1;i++){
		scanf("%d %d %d", &map_nodes[i].source,  &map_nodes[i].destination,   &map_nodes[i].distance);
		dn[map_nodes[i].source-1].child_nodes_number++;
		dn[map_nodes[i].destination-1].child_nodes_number++;
	 }

	 for(i=0;i<total_number;i++){
		if(dn[i].child_nodes_number > 1){
			execute_distance();
			i = -1;
		}
	 }
	 
	int sum=0;
	int temp;
	 for(i=0;i<total_number;i++){
		temp=dn[i].max_distance + dn[i].second_distance;
		//printf("distance %d %d\n", dn[i].max_distance ,dn[i].second_distance);
		if(temp>sum){
			sum=temp;
		}
	}
	 printf("\n\n%d %d\n", sum, sum*10+sum*(1+sum)/2);
	 free(dn);
	 free(map_nodes);
	return 0;
}

2014-03-30 大臣的旅费(回溯思想，最长路径),布布扣,bubuko.com

2014-03-30 大臣的旅费(回溯思想，最长路径)

原文：http://blog.csdn.net/sykpour/article/details/22596405