Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Single Source Shortest Path II

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

All vertices are reachable from vertex $0$

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C++14 (judge verdict: Accepted)

/**
 * 
 */

// #include {{{
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <forward_list>
#include <functional>
#include <iomanip>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#ifdef DEBUG
#include <fmt/format.h>
#include <fmt/ostream.h>
#endif

using namespace std;
// }}}

// type {{{
using  s8 =   int8_t;
using  u8 =  uint8_t;
using s16 =  int16_t;
using u16 = uint16_t;
using s32 =  int32_t;
using u32 = uint32_t;
using s64 =  int64_t;
using u64 = uint64_t;

template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
// }}}

// hide {{{
#ifdef __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-const-variable"
#endif
// }}}

// ???????????´
//#define int s64

constexpr bool AUTOFLUSH = false;

constexpr bool STDIO_ENABLE = false;

constexpr int IOS_PREC = 10;

constexpr int INF_S32 =             1'010'000'000;
constexpr s64 INF_S64 = 1'010'000'000'000'000'000LL;

constexpr auto   INF = INF_S64;
constexpr double EPS = 1e-9;

constexpr s64 MOD = 1'000'000'007;

// hide {{{
#ifdef __clang__
#pragma clang diagnostic pop
#endif
// }}}

// util {{{
template<typename T>
constexpr bool is_odd(T x)
{
    return x % 2 == 1;
}

template<typename T>
constexpr bool is_even(T x)
{
    return x % 2 == 0;
}

template<typename T>
constexpr int cmp(T x, T y)
{
    return (x > y) - (x < y);
}

template<typename T>
constexpr int sgn(T x)
{
    return cmp(x, T(0));
}

template<typename T>
constexpr typename enable_if<is_signed<T>::value,T>::type modulo(T a, T b)
{
    assert(b > 0);
    T r = a % b;
    return r >= 0 ? r : r+b;
}

template<typename T>
constexpr T clamp(T x, T lo, T hi)
{
    assert(lo <= hi);
    if(x < lo)
        return lo;
    else if(x > hi)
        return hi;
    else
        return x;
}

int sqrti(int x)
{
    assert(x >= 0);
    return static_cast<int>(sqrt(x));
}

s64 sqrtl(s64 x)
{
    assert(x >= 0);
    return static_cast<s64>(sqrt(x));
}

template<typename T>
bool chmax(T& xmax, const T& x)
{
    if(x > xmax) {
        xmax = x;
        return true;
    }
    else {
        return false;
    }
}

template<typename T>
bool chmin(T& xmin, const T& x)
{
    if(x < xmin) {
        xmin = x;
        return true;
    }
    else {
        return false;
    }
}

template<typename T>
constexpr int SIZE(const T& c)
{
    return static_cast<int>(c.size());
}

template<typename T, size_t N>
constexpr int SIZE(const T (&)[N])
{
    return static_cast<int>(N);
}

template<typename InputIt, typename T>
int argfind(InputIt first, InputIt last, const T& x)
{
    auto it = find(first, last, x);
    return distance(first, it);
}

template<typename InputIt>
int argmax(InputIt first, InputIt last)
{
    auto it = max_element(first, last);
    return distance(first, it);
}

template<typename InputIt>
int argmin(InputIt first, InputIt last)
{
    auto it = min_element(first, last);
    return distance(first, it);
}

template<typename InputIt>
bool alltrue(InputIt first, InputIt last)
{
    return all_of(first, last, [](bool b) { return b; });
}

template<typename InputIt>
bool anytrue(InputIt first, InputIt last)
{
    return any_of(first, last, [](bool b) { return b; });
}

template<typename InputIt>
bool allfalse(InputIt first, InputIt last)
{
    return !anytrue(first, last);
}

template<typename InputIt>
bool anyfalse(InputIt first, InputIt last)
{
    return !alltrue(first, last);
}

template<typename T>
array<pair<T,T>,4> neighbor4(const T& x, const T& y)
{
    return array<pair<T,T>,4> {{
                    { x, y-1 },
        { x-1, y },             { x+1, y },
                    { x, y+1 },
    }};
}

template<typename T>
array<pair<T,T>,8> neighbor8(const T& x, const T& y)
{
    return array<pair<T,T>,8> {{
        { x-1, y-1 }, { x, y-1 }, { x+1, y-1 },
        { x-1, y   },             { x+1, y   },
        { x-1, y+1 }, { x, y+1 }, { x+1, y+1 },
    }};
}

template<typename T>
bool in_bounds(const T& x, const T& minx, const T& maxx)
{
    return !(x < minx) && !(maxx < x);
}

template<typename T>
bool in_bounds_2(
    const T& x,    const T& y,
    const T& minx, const T& miny,
    const T& maxx, const T& maxy)
{
    return in_bounds(x, minx, maxx) && in_bounds(y, miny, maxy);
}

template<typename T>
bool in_bounds_wh(const T& x, const T& y, const T& w, const T& h)
{
    return in_bounds_2(x, y, 0, 0, w-1, h-1);
}

struct pairhash {
    template<typename T1, typename T2>
    size_t operator()(const pair<T1,T2>& p) const
    {
        size_t ans = 17;
        ans = 31*ans + hash<T1>()(p.first);
        ans = 31*ans + hash<T2>()(p.second);
        return ans;
    }
};

template<typename K, typename V>
pair<typename map<K,V>::iterator, bool> insert_or_assign(map<K,V>& m, const K& k, const V& v)
{
    auto it = m.lower_bound(k);
    if(it != end(m) && !m.key_comp()(k,it->first)) {
        it->second = v;
        return make_pair(it, false);
    }
    else {
        auto it_ins = m.insert(it, make_pair(k,v));
        return make_pair(it_ins, true);
    }
}

template<typename K, typename V>
pair<typename unordered_map<K,V>::iterator, bool>
insert_or_assign(unordered_map<K,V>& m, const K& k, const V& v)
{
    auto it = m.find(k);
    if(it != end(m)) {
        it->second = v;
        return make_pair(it, false);
    }
    else {
        auto it_ins = m.insert(it, make_pair(k,v));
        return make_pair(it_ins, true);
    }
}

template<typename T>
string TO_STRING(const T& x)
{
    ostringstream out;
    out << x;
    return out.str();
}

template<typename InputIt>
string JOIN(InputIt first, InputIt last, const string& sep)
{
    ostringstream out;
    while(first != last) {
        out << *first++;
        if(first != last)
            out << sep;
    }
    return out.str();
}

template<typename InputIt>
auto SUM(InputIt first, InputIt last)
{
    using T = typename iterator_traits<InputIt>::value_type;
    return accumulate(first, last, T());
}

template<typename T>
void UNIQ(T& c)
{
    c.erase(unique(begin(c), end(c)), end(c));
}

template<typename T, typename C>
T POP(stack<T,C>& stk)
{
    T x = stk.top(); stk.pop();
    return x;
}

template<typename T, typename C>
T POP(queue<T,C>& que)
{
    T x = que.front(); que.pop();
    return x;
}

template<typename T, typename Cont, typename Cmp>
T POP(priority_queue<T,Cont,Cmp>& que)
{
    T x = que.top(); que.pop();
    return x;
}

template<typename T>
void RD(T& x)
{
    cin >> x;
#ifdef DEBUG
    if(!cin) assert(false);
#endif
}

// ?????? {{{
// FPRINTSEQ {{{
template<typename InputIt>
ostream& FPRINTSEQ(ostream& out, InputIt first, InputIt last)
{
    for(InputIt it = first; it != last; ++it) {
        if(it != first) out << ' ';
        out << *it;
    }
    return out;
}
template<typename InputIt>
ostream& PRINTSEQ(InputIt first, InputIt last)
{
    return FPRINTSEQ(cout, first, last);
}
template<typename InputIt>
ostream& DPRINTSEQ(InputIt first, InputIt last)
{
    return FPRINTSEQ(cerr, first, last);
}
// }}}

// 1?¬????????????? {{{
template<typename T, size_t N>
ostream& FPRINTARRAY1(ostream& out, const T (&c)[N])
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}
template<typename T, size_t N>
ostream& PRINTARRAY1(const T (&c)[N])
{
    return FPRINTARRAY1(cout, c);
}
template<typename T, size_t N>
ostream& DPRINTARRAY1(const T (&c)[N])
{
    return FPRINTARRAY1(cerr, c);
}
// }}}

// 2?¬????????????? {{{
template<typename T, size_t N1, size_t N2>
ostream& FPRINTARRAY2(ostream& out, const T (&c)[N1][N2])
{
    out << '\n';
    for(const auto& e : c) {
        FPRINTARRAY1(out, e) << '\n';
    }
    return out;
}
template<typename T, size_t N1, size_t N2>
ostream& PRINTARRAY2(const T (&c)[N1][N2])
{
    return FPRINTARRAY2(cout, c);
}
template<typename T, size_t N1, size_t N2>
ostream& DPRINTARRAY2(const T (&c)[N1][N2])
{
    return FPRINTARRAY2(cerr, c);
}
// }}}

// ???map???????????? {{{
template<typename T>
ostream& operator<<(ostream& out, const vector<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

// ?????\??±???
template<typename T>
ostream& operator<<(ostream& out, const vector<vector<T>>& c)
{
    out << '\n';
    for(const auto& e : c) {
        out << e << '\n';
    }
    return out;
}

// ?????\??±???
ostream& operator<<(ostream& out, const vector<string>& c)
{
    out << '\n';
    for(const string& e : c) {
        out << e << '\n';
    }
    return out;
}

template<typename T>
ostream& operator<<(ostream& out, const deque<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const list<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const forward_list<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const set<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const unordered_set<T>& c)
{
    return out << set<T>(cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const multiset<T>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const unordered_multiset<T>& c)
{
    return out << multiset<T>(cbegin(c), cend(c));
}

template<typename T, size_t N>
ostream& operator<<(ostream& out, const array<T,N>& c)
{
    return FPRINTSEQ(out, cbegin(c), cend(c));
}
// }}}

// map???????????? {{{
template<typename InputIt>
ostream& FPRINTMAP(ostream& out, InputIt first, InputIt last)
{
    out << "{\n";
    for(auto it = first; it != last; ++it) {
        out << "  " << it->first << " : " << it->second << '\n';
    }
    out << "}\n";
    return out;
}
template<typename InputIt>
ostream& PRINTMAP(InputIt first, InputIt last)
{
    return FPRINTMAP(cout, first, last);
}
template<typename InputIt>
ostream& DPRINTMAP(InputIt first, InputIt last)
{
    return FPRINTMAP(cerr, first, last);
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const map<K,V>& c)
{
    return FPRINTMAP(out, cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const unordered_map<K,V>& c)
{
    return out << map<K,V>(cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const multimap<K,V>& c)
{
    return FPRINTMAP(out, cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const unordered_multimap<K,V>& c)
{
    return out << multimap<K,V>(cbegin(c), cend(c));
}
// }}}

// stack/queue/priority_queue {{{
template<typename T, typename C>
ostream& operator<<(ostream& out, stack<T,C> c)
{
    while(!c.empty()) {
        out << c.top();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}

template<typename T, typename C>
ostream& operator<<(ostream& out, queue<T,C> c)
{
    while(!c.empty()) {
        out << c.front();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}

template<typename T, typename Cont, typename Cmp>
ostream& operator<<(ostream& out, priority_queue<T,Cont,Cmp> c)
{
    while(!c.empty()) {
        out << c.top();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}
// }}}

// pair/tuple {{{
template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1,T2>& p)
{
    return out << '(' << p.first << ',' << p.second << ')';
}

template<typename Tuple, size_t Pos>
ostream& FPRINTTUPLE(ostream& out, const Tuple&)
{
    return out;
}

template<typename Tuple, size_t Pos, typename T, typename... TS>
ostream& FPRINTTUPLE(ostream& out, const Tuple& t)
{
    if(Pos != 0)
        out << ',';
    out << get<Pos>(t);
    return FPRINTTUPLE<Tuple,Pos+1,TS...>(out, t);
}

template<typename... TS>
ostream& operator<<(ostream& out, const tuple<TS...>& t)
{
    out << '(';
    FPRINTTUPLE<tuple<TS...>,0,TS...>(out, t);
    out << ')';
    return out;
}
// }}}

// PRINT {{{
ostream& FPRINT(ostream& out) { return out; }

template<typename T, typename... TS>
ostream& FPRINT(ostream& out, const T& x, const TS& ...args)
{
    out << x;
    if(sizeof...(args))
        out << ' ';
    return FPRINT(out, args...);
}

template<typename... TS>
ostream& FPRINTLN(ostream& out, const TS& ...args)
{
    FPRINT(out, args...);
    return out << '\n';
}

template<typename... TS>
ostream& PRINT(const TS& ...args)
{
    return FPRINT(cout, args...);
}

template<typename... TS>
ostream& PRINTLN(const TS& ...args)
{
    return FPRINTLN(cout, args...);
}

template<typename... TS>
ostream& DPRINT(const TS& ...args)
{
    return FPRINT(cerr, args...);
}

template<typename... TS>
ostream& DPRINTLN(const TS& ...args)
{
    return FPRINTLN(cerr, args...);
}
// }}}
// }}}

void FLUSH()
{
    if(STDIO_ENABLE)
        fflush(stdout);
    else
        cout.flush();
}

[[noreturn]] void EXIT()
{
#ifdef DEBUG
    fflush(stdout);
    fflush(stderr);
    cout.flush();
    cerr.flush();
#else
    FLUSH();
#endif
    //quick_exit(0); // does not work on codeforces
    _Exit(0);
}

struct IoInit {
    IoInit()
    {
#ifndef DEBUG
        cin.tie(nullptr);
        if(!STDIO_ENABLE)
            ios::sync_with_stdio(false);
#endif
        cout << fixed << setprecision(IOS_PREC);

        if(AUTOFLUSH) {
            if(STDIO_ENABLE)
                setvbuf(stdout, nullptr, _IONBF, 0);
            cout << unitbuf;
        }
    }
} IOINIT;

#define FOR(i, start, end) for(s64 i = (start); i < (end); ++i)
#define REP(i, n) FOR(i, 0, n)

#define ALL(f,c,...) (([&](decltype((c)) cc) { return (f)(begin(cc), end(cc), ## __VA_ARGS__); })(c))

#define MEMSET(a,v) memset((a), (v), sizeof(a))

#define DBG(x) DPRINTLN('L', __LINE__, ':', #x, ':', (x))
// }}}

s64 N;
vector<vector<pair<int,int>>> G; // to,cost

vector<s64> dijkstra(s64 start)
{
    vector<s64> d(N, INF);
    deque<bool> done(N, false);
    min_heap<pair<s64,s64>> que; // dist,vertex

    d[start] = 0;
    que.emplace(0, start);

    s64 n_remain = N; // ????¢????????????°
    while(!que.empty()) {
        s64 dmin,vmin; tie(dmin,vmin) = POP(que);

        if(d[vmin] < dmin) continue;

        done[vmin] = true;
        if(--n_remain == 0) break;

        for(const auto& p : G[vmin]) {
            s64 to,cost; tie(to,cost) = p;
            if(done[to]) continue;

            s64 d_new = dmin + cost;
            if(d_new < d[to]) {
                d[to] = d_new;
                que.emplace(d_new, to);
            }
        }
    }

    return d;
}

void solve()
{
    vector<s64> d = dijkstra(0);

    REP(i, N) {
        PRINTLN(i, d[i]);
    }
}

signed main(signed /*argc*/, char** /*argv*/)
{
    RD(N);
    G.resize(N);

    REP(_, N) {
        s64 from; RD(from);
        s64 k;    RD(k);
        G[from].reserve(k);
        REP(_i, k) {
            s64 to;   RD(to);
            s64 cost; RD(cost);
            G[from].emplace_back(to, cost);
        }
    }

#ifdef DEBUG
    
#endif

    solve();

    EXIT();
}