2015多校第6场 HDU 5361 并查集，最短路

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5361

题意：有n个点1-n, 每个点到相邻点的距离是1，然后每个点可以通过花费c[i]的钱从i点走到距离i点大于等于l[i]并且小于等于r[i]的点，问从节点1到每个节点的最短距离是多少？不能到达的话，输出-1。

题解参考：http://blog.csdn.net/jtjy568805874/article/details/47341905

解法：这题的难点主要在于边的条数过多，不能像普通的最短路那样子跑。不过此题的特点在于对于每个点来说，从这个点出去能到的任何点这个过程的花费是相同的，都是cost[i]。于是假设到达该点的距离为dis[i]则从该点能到的任何点j的值都是dis[j]=min(dis[j],dis[i]+cost[i]);于是只要按照dis[i]+cost[i]排序，当前最先的第一个点能到的点的距离一定都是最近的，这些点在这之后都不会再被更新了。这样只要维护一个并查集压缩路径，或者维护一个set存可能还会被更新的点就好了。

 

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn = 2e5+10;
struct FastIO
{
    static const int S = 1310720;
    int wpos;
    char wbuf[S];
    FastIO() : wpos(0) {}
    inline int xchar()
    {
        static char buf[S];
        static int len = 0, pos = 0;
        if(pos == len)
            pos = 0, len = fread(buf, 1, S, stdin);
        if(pos == len)
            exit(0);
        return buf[pos ++];
    }
    inline unsigned long long xuint()
    {
        int c = xchar();
        unsigned long long x = 0;
        while(c <= 32)
            c = xchar();
        for(; '0' <= c && c <= '9'; c = xchar())
            x = x * 10 + c - '0';
        return x;
    }
    inline long long xint()
    {
        long long s = 1;
        int c = xchar(), x = 0;
        while(c <= 32)
            c = xchar();
        if(c == '-')
            s = -1, c = xchar();
        for(; '0' <= c && c <= '9'; c = xchar())
            x = x * 10 + c - '0';
        return x * s;
    }
    inline void xstring(char *s)
    {
        int c = xchar();
        while(c <= 32)
            c = xchar();
        for(; c > 32; c = xchar())
            * s++ = c;
        *s = 0;
    }
    inline double xdouble()
    {
        bool sign = 0;
        char ch = xchar();
        double x = 0;
        while(ch <= 32)
            ch = xchar();
        if(ch == '-')
            sign = 1, ch = xchar();
        for(; '0' <= ch && ch <= '9'; ch = xchar())
            x = x * 10 + ch - '0';
        if(ch == '.')
        {
            double tmp = 1;
            ch = xchar();
            for(; ch >= '0' && ch <= '9'; ch = xchar())
                tmp /= 10.0, x += tmp * (ch - '0');
        }
        if(sign)
            x = -x;
        return x;
    }
    inline void wchar(int x)
    {
        if(wpos == S)
            fwrite(wbuf, 1, S, stdout), wpos = 0;
        wbuf[wpos ++] = x;
    }
    inline void wint(long long x)
    {
        if(x < 0)
            wchar('-'), x = -x;
        char s[24];
        int n = 0;
        while(x || !n)
            s[n ++] = '0' + x % 10, x /= 10;
        while(n--)
            wchar(s[n]);
    }
    inline void wstring(const char *s)
    {
        while(*s)
            wchar(*s++);
    }
    inline void wdouble(double x, int y = 6)
    {
        static long long mul[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000LL, 100000000000LL, 1000000000000LL, 10000000000000LL, 100000000000000LL, 1000000000000000LL, 10000000000000000LL, 100000000000000000LL};
        if(x < -1e-12)
            wchar('-'), x = -x;
        x *= mul[y];
        long long x1 = (long long) floorl(x);
        if(x - floor(x) >= 0.5)
            ++x1;
        long long x2 = x1 / mul[y], x3 = x1 - x2 * mul[y];
        wint(x2);
        if(y > 0)
        {
            wchar('.');
            for(size_t i = 1; i < y && x3 * mul[i] < mul[y]; wchar('0'), ++i);
            wint(x3);
        }
    }
    ~FastIO()
    {
        if(wpos)
            fwrite(wbuf, 1, wpos, stdout), wpos = 0;
    }
} io;
LL n, T, d[maxn], l[maxn], r[maxn], c[maxn], fa[maxn], ans, sum;
struct cmp{
    bool operator ()(const LL &x, const LL &y) const{
        return d[x]+c[x]>d[y]+c[y];
    }
};

namespace DSU{
    int fa[maxn];
    void init(){
        for(int i=1; i<=n+1; i++) fa[i]=i;
    }
    int find_set(int x){
        if(x == fa[x]) return x;
        else return fa[x] = find_set(fa[x]);
    }
    void union_set(int x, int y){
        int fx = find_set(x), fy = find_set(y);
        if(fx != fy){
            fa[fx] = fy;
        }
    }
}

using namespace DSU;

void Dijstra(int x)
{
    priority_queue<LL,vector<LL>,cmp>q;
    d[x] = 0;
    q.push(x);
    while(q.size())
    {
        LL L,R,u = q.top(); q.pop();
        L = u-r[u], R = u-l[u];
        if(R>0){
            for(LL j=max(L,1LL); ; j++){
                j = find_set(j);
                if(j>min(R,n)) break;
                if(d[j] > d[u]+c[u]){
                    d[j] = d[u]+c[u];
                    q.push(j);
                }
                union_set(j,j+1);
            }
        }
        L = u+l[u], R = u+r[u];
        if(L<=n){
            for(LL j=L;;j++){
                j = find_set(j);
                if(j>min(R,n)) break;
                if(d[j]>d[u]+c[u]){
                    d[j] = d[u]+c[u];
                    q.push(j);
                }
                union_set(j,j+1);
            }
        }
    }
    return;
}

int main()
{
    int T;
    T = io.xint();
    while(T--)
    {
        n = io.xint();
        sum = 0;
        for(int i=1; i<=n; i++) l[i] = io.xint();
        for(int i=1; i<=n; i++) r[i] = io.xint();
        for(int i=1; i<=n; i++) c[i] = io.xint(), sum+=c[i];
        init();
        for(int i=1; i<=n; i++) d[i] = sum+1;
        Dijstra(1);
        for(int i=1; i<=n; i++){
            if(d[i] == sum+1) d[i] = -1;
            if(i<n) printf("%lld ", d[i]);
            else printf("%lld\n", d[i]);
        }
    }
    return 0;
}