poj 3683 Priest John's Busiest Day

John is the only priest in his town. September 1st is the John's busiest day in a year because there is an old legend in the town that the couple who get married on that day will be forever blessed by the God of Love. This year N couples plan to get married on the blessed day. The i-th couple plan to hold their wedding from time S_ito time T_i. According to the traditions in the town, there must be a special ceremony on which the couple stand before the priest and accept blessings. The i-th couple need D_i minutes to finish this ceremony. Moreover, this ceremony must be either at the beginning or the ending of the wedding (i.e. it must be either from S_ito S_i + D_i, or from T_i - D_i to T_i). Could you tell John how to arrange his schedule so that he can present at every special ceremonies of the weddings.

Note that John can not be present at two weddings simultaneously.

Input

The first line contains a integer N ( 1 ≤ N ≤ 1000). 
The next N lines contain the S_i, T_i and D_i. S_i and T_i are in the format of hh:mm.

Output

The first line of output contains "YES" or "NO" indicating whether John can be present at every special ceremony. If it is "YES", output another N lines describing the staring time and finishing time of all the ceremonies.

Sample Input

2
08:00 09:00 30
08:15 09:00 20

Sample Output

YES
08:00 08:30
08:40 09:00

---

　　2-sat输出任意解。缩点缩完后，建反图，拓扑排序。

　　注意端点的问题，任意两人的婚礼时间不能重叠。

Code

/**
 * poj
 * Problem#3683
 * Accepted
 * Time:172ms
 * Memory:17132k
 */
#include <iostream>
#include <cstdio>
#include <ctime>
#include <cmath>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <fstream>
#include <sstream>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <vector>
#include <stack>
#ifndef WIN32
#define Auto "%lld"
#else
#define Auto "%I64d"
#endif
using namespace std;
typedef bool boolean;
const signed int inf = (signed)((1u << 31) - 1);
const double eps = 1e-6;
const int binary_limit = 128;
#define smin(a, b) a = min(a, b)
#define smax(a, b) a = max(a, b)
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))
template<typename T>
inline boolean readInteger(T& u){
    char x;
    int aFlag = 1;
    while(!isdigit((x = getchar())) && x != '-' && x != -1);
    if(x == -1) {
        ungetc(x, stdin);    
        return false;
    }
    if(x == '-'){
        x = getchar();
        aFlag = -1;
    }
    for(u = x - '0'; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - '0');
    ungetc(x, stdin);
    u *= aFlag;
    return true;
}

///map template starts
typedef class Edge{
    public:
        int end;
        int next;
        Edge(const int end = 0, const int next = 0):end(end), next(next){}
}Edge;

typedef class MapManager{
    public:
        int ce;
        int *h;
        vector<Edge> edge;
        MapManager(){}
        MapManager(int points):ce(0){
            h = new int[(const int)(points + 1)];
            memset(h, 0, sizeof(int) * (points + 1));
            edge.push_back(Edge());
        }
        inline void addEdge(int from, int end){
//            printf("%d->%d
", from, end);
            edge.push_back(Edge(end, h[from]));
            h[from] = ++ce;
        }
        inline void addDoubleEdge(int from, int end){
            addEdge(from, end);
            addEdge(end, from);
        }
        Edge& operator [] (int pos) {
            return edge[pos];
        }
}MapManager;
#define m_begin(g, i) (g).h[(i)]
///map template ends

int n;
MapManager g;
int *ls, *rs, *lasts;

inline int readTime() {
    static int a, b;
    readInteger(a);
    readInteger(b);
    return a * 60 + b;
}

boolean isOn(int l1, int r1, int l2, int r2) {
//    printf("checking:[%d, %d][%d, %d]
", l1, r1, l2, r2);
    return !(r1 <= l2 || l1 >= r2);        // Notice that use '<=' and '>=' instead of '<' and '>'
}

inline void init() {
    readInteger(n);
    ls = new int[n + 1];
    rs = new int[n + 1];
    lasts = new int[n + 1];
    for(int i = 1; i <= n; i++) {
        ls[i] = readTime();
        rs[i] = readTime();
        readInteger(lasts[i]);
    }
}

inline void init_map() {
    g = MapManager(2 * n + 3);
    for(int i = 1; i < n; i++) {
        for(int j = i + 1; j <= n; j++) {
            if(isOn(ls[i], ls[i] + lasts[i], ls[j], ls[j] + lasts[j])) {
                g.addEdge(2 * i - 1, 2 * j);
                g.addEdge(2 * j - 1, 2 * i);
            }
            if(isOn(ls[i], ls[i] + lasts[i], rs[j] - lasts[j], rs[j])) {
                g.addEdge(2 * i - 1, 2 * j - 1);
                g.addEdge(2 * j, 2 * i);
            }
            if(isOn(rs[i] - lasts[i], rs[i], ls[j], ls[j] + lasts[j])) {
                g.addEdge(2 * i, 2 * j);
                g.addEdge(2 * j - 1, 2 * i - 1);
            }
            if(isOn(rs[i] - lasts[i], rs[i], rs[j] - lasts[j], rs[j])) {
                g.addEdge(2 * i, 2 * j - 1);
                g.addEdge(2 * j, 2 * i - 1);
            }
        }
    }
}

int cnt = 0, scc = 0;
int* visitID;
int* exitID;
boolean* visited;
boolean* instack;
stack<int> s;
int* belong;
inline void init_tarjan() {
    int an = 2 * n + 3;
    visitID = new int[(an)];
    exitID = new int[(an)];
    visited = new boolean[(an)];
    instack = new boolean[(an)];
    belong = new int[(an)];
    memset(visited, false, sizeof(boolean) * an);
    memset(instack, false, sizeof(boolean) * an);
}

void tarjan(int node) {
    visitID[node] = exitID[node] = cnt++;
    visited[node] = instack[node] = true;
    s.push(node);
    
    for(int i = m_begin(g, node); i; i = g[i].next) {
        int& e = g[i].end;
        if(!visited[e]) {
            tarjan(e);
            smin(exitID[node], exitID[e]);
        } else if(instack[e]) {
            smin(exitID[node], visitID[e]);
        }
    }
    
    if(visitID[node] == exitID[node]) {
        int now = -1;
        scc++;
        while(now != node) {
            now = s.top();
            s.pop();
            instack[now] = false;
            belong[now] = scc;
        }
    }
}

int* opp;
int* col;
int* dag;
MapManager rg;
inline void rebuild() {
    delete[] visitID;
    delete[] exitID;
    delete[] visited;
    delete[] instack;
    
    rg = MapManager(scc);
    col = new int[(scc + 1)];
    opp = new int[(scc + 1)];
    dag = new int[(scc + 1)];
    memset(col, 0, sizeof(int) * (scc + 1));
    memset(dag, 0, sizeof(int) * (scc + 1));
    for(int i = 1; i <= (2 * n); i++) {
        if(i & 1) opp[belong[i]] = belong[i + 1];
        else opp[belong[i]] = belong[i - 1];
        for(int j = m_begin(g, i); j; j = g[j].next) {
            if(belong[i] != belong[g[j].end])
                rg.addEdge(belong[g[j].end], belong[i]), dag[belong[i]]++;
        }
    }
}

void dfs(int node) {
    if(col[node])    return;
    col[node] = 2;
    for(int i = m_begin(rg, node); i; i = rg[i].next)
        dfs(rg[i].end);
}

queue<int> que;
inline void topu() {
    for(int i = 1; i <= scc; i++) {
        if(!dag[i])
            que.push(i);
    }
    while(!que.empty()) {
        int e = que.front();
        que.pop();
        if(col[e])    continue;
        col[e] = 1;
        dfs(opp[e]);
        for(int i = m_begin(rg, e); i; i = rg[i].next) {
            int& eu = rg[i].end;
            dag[eu]--;
            if(dag[eu] == 0)
                que.push(eu);
        }
    }
}

inline void check() {
    for(int i = 1; i < (n << 1); i += 2)
        if(belong[i] == belong[i + 1]) {
            puts("NO");
            exit(0);
        }
}

inline void printTime(int x) {
    printf("%.2d:%.2d", x / 60, x % 60);
}

inline void solve() {
    puts("YES");
    for(int i = 1; i <= n; i++) {
        if(col[belong[i * 2 - 1]] == 1)    printTime(ls[i]), putchar(' '), printTime(ls[i] + lasts[i]);
        else printTime(rs[i] - lasts[i]), putchar(' '), printTime(rs[i]);
        putchar('
');
    }
}

int main() {
    init();
    init_map();
    init_tarjan();
    for(int i = 1; i <= 2 * n; i++)
        if(!visited[i])
            tarjan(i);
    check();
    rebuild();
    topu();
    solve();
    return 0;
}