poj 3169 Layout

Layout

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 8803		Accepted: 4236

Description

Like everyone else, cows like to stand close to their friends when queuing for feed. FJ has N (2 <= N <= 1,000) cows numbered 1..N standing along a straight line waiting for feed. The cows are standing in the same order as they are numbered, and since they
can be rather pushy, it is possible that two or more cows can line up at exactly the same location (that is, if we think of each cow as being located at some coordinate on a number line, then it is possible for two or more cows to share the same coordinate). 

Some cows like each other and want to be within a certain distance of each other in line. Some really dislike each other and want to be separated by at least a certain distance. A list of ML (1 <= ML <= 10,000) constraints describes which cows like each other
and the maximum distance by which they may be separated; a subsequent list of MD constraints (1 <= MD <= 10,000) tells which cows dislike each other and the minimum distance by which they must be separated. 

Your job is to compute, if possible, the maximum possible distance between cow 1 and cow N that satisfies the distance constraints.
Input

Line 1: Three space-separated integers: N, ML, and MD. 

Lines 2..ML+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at most D (1 <= D <= 1,000,000) apart. 

Lines ML+2..ML+MD+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at least D (1 <= D <= 1,000,000) apart.
Output

Line 1: A single integer. If no line-up is possible, output -1. If cows 1 and N can be arbitrarily far apart, output -2. Otherwise output the greatest possible distance between cows 1 and N.
Sample Input

4 2 1
1 3 10
2 4 20
2 3 3

Sample Output

27

Hint

Explanation of the sample: 

There are 4 cows. Cows #1 and #3 must be no more than 10 units apart, cows #2 and #4 must be no more than 20 units apart, and cows #2 and #3 dislike each other and must be no fewer than 3 units apart. 

The best layout, in terms of coordinates on a number line, is to put cow #1 at 0, cow #2 at 7, cow #3 at 10, and cow #4 at 27.

#include <iostream>
#include <cstdio>
using namespace std;
const int MAX_N = 10001;
const int INF = 1000001;
int N, ML, MD; //牛数，亲密关系数，疏远关系数
int AL[MAX_N], BL[MAX_N], DL[MAX_N]; //亲密关系，牛AL[i]和牛BL[i]最远距离不大于DL[i]
int AD[MAX_N], BD[MAX_N], DD[MAX_N]; //疏远关系，牛AD[i]和牛BD[i]最远距离不小于DD[i]

int d[MAX_N]; //最短距离

//思路：
//可以将该问题提取出三个不等式
//d[i] ≤ d[i+1]
//AL[i] + DL[i] ≥ BL[i]
//AD[i] + DD[i] ≤ BD[i]
//可以转化为DP方程：
//d[i] = min(d[i] , d[i + 1])
//d[BL[i] - 1] = min(d[BL[i] - 1], d[AL[i] - 1] + DL[i])
//d[AD[i] - 1] = min(d[AD[i] - 1], d[BD[i] - 1] - DD[i])
void solve(){
fill(d, d + N, INF);
d[0] = 0;

//Bellman-Ford算法
for(int k = 0; k < N; ++k){
//从i+1到i的权值为0
for(int i = 0; i + 1 < N; ++i){
if(d[i + 1] < INF){
d[i] = min(d[i] , d[i + 1]);
}
}

//从AL到BL的权值为DL
for(int i = 0; i < ML; ++i){
if(d[AL[i] - 1] < INF){
d[BL[i] - 1] = min(d[BL[i] - 1], d[AL[i] - 1] + DL[i]);
}
}

//从BD到AD的权值为-DD
for(int i = 0; i < MD; ++i){
if(d[BD[i] - 1] < INF){
d[AD[i] - 1] = min(d[AD[i] - 1], d[BD[i] - 1] - DD[i]);
}
}
}
int res = d[N - 1];
if(d[0] < 0){ //存在负圈
res = -1;
} else if(res == INF) {
res = -2;
}
printf("%d\n", res);
}

int main(){
while(scanf("%d%d%d", &N, &ML, &MD) != EOF){
for(int i = 0; i < ML; ++i){
scanf("%d%d%d", &AL[i], &BL[i], &DL[i]);
}
for(int i = 0; i < MD; ++i){
scanf("%d%d%d", &AD[i], &BD[i], &DD[i]);
}
solve();
}

return 0;
}