# competitive-programming-library

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# Shortest Path Faster Algorithm (graph/shortest_path_faster_algorithm.hpp)

## Code

#pragma once
#include <cassert>
#include <climits>
#include <cstdint>
#include <deque>
#include <tuple>
#include <utility>
#include <vector>
#include "utils/macros.hpp"

/**
* @brief Shortest Path Faster Algorithm
* @note the interface is same to one of Bellman Ford
*/
std::vector<int64_t> shortest_path_faster_algorithm(int root, std::vector<std::vector<std::pair<int, int64_t> > > const & g) {
assert (not g.empty());
int n = g.size();
std::vector<int64_t> dist(n, INT64_MAX);
std::deque<int> cur, nxt;
std::vector<bool> pushed(n);
dist[root] = 0;
nxt.push_back(root);
pushed[root] = true;

REP (iteration, 2 * n - 2) {
cur.swap(nxt);
while (not cur.empty()) {
int x = cur.front();
cur.pop_front();
pushed[x] = false;
for (const auto & edge : g[x]) {
int y; int64_t cost; std::tie(y, cost) = edge;
if ((dist[x] == INT64_MIN ? INT64_MIN : dist[x] + cost) < dist[y]) {
dist[y] = (iteration >= n - 1 ? INT64_MIN : dist[x] + cost);
if (not pushed[y]) {
if (not nxt.empty() and dist[y] < dist[nxt.front()]) {
// Small Label First
nxt.push_front(y);
} else {
nxt.push_back(y);
}
pushed[y] = true;
}
}
}
}
if (nxt.empty()) break;
}

return dist;
}



#line 2 "graph/shortest_path_faster_algorithm.hpp"
#include <cassert>
#include <climits>
#include <cstdint>
#include <deque>
#include <tuple>
#include <utility>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 10 "graph/shortest_path_faster_algorithm.hpp"

/**
* @brief Shortest Path Faster Algorithm
* @note the interface is same to one of Bellman Ford
*/
std::vector<int64_t> shortest_path_faster_algorithm(int root, std::vector<std::vector<std::pair<int, int64_t> > > const & g) {
assert (not g.empty());
int n = g.size();
std::vector<int64_t> dist(n, INT64_MAX);
std::deque<int> cur, nxt;
std::vector<bool> pushed(n);
dist[root] = 0;
nxt.push_back(root);
pushed[root] = true;

REP (iteration, 2 * n - 2) {
cur.swap(nxt);
while (not cur.empty()) {
int x = cur.front();
cur.pop_front();
pushed[x] = false;
for (const auto & edge : g[x]) {
int y; int64_t cost; std::tie(y, cost) = edge;
if ((dist[x] == INT64_MIN ? INT64_MIN : dist[x] + cost) < dist[y]) {
dist[y] = (iteration >= n - 1 ? INT64_MIN : dist[x] + cost);
if (not pushed[y]) {
if (not nxt.empty() and dist[y] < dist[nxt.front()]) {
// Small Label First
nxt.push_front(y);
} else {
nxt.push_back(y);
}
pushed[y] = true;
}
}
}
}
if (nxt.empty()) break;
}

return dist;
}