Problem:
Score : 600 points

Problem Statement

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices.
In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.
The i-th operation is as follows:

The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i < R_i \leq N

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 C_1
:
L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.
If there is no shortest path, print -1 instead.

Sample Input 1

4 3
1 3 2
2 4 3
1 4 6

Sample Output 1

5

We have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.

Sample Input 2

4 2
1 2 1
3 4 2

Sample Output 2

-1

Sample Input 3

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3

Sample Output 3

28

Solution in C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
using pli=pair<int64_t, int>;
using mii=map<int, int>;

struct node {
    mii edge;
    bool done = false;
    int64_t cost = -1;

    bool operator<(const node &rhs) const {
        if (rhs.cost == -1 && this->cost == -1) {
            return false;
        } else if (rhs.cost == -1) {
            return true;
        } else if (this->cost == -1) {
            return false;
        }
        return this->cost < rhs.cost;
    }

    bool operator>(const node &rhs) const {
        return rhs < *this;
    }

    void update_cost(int64_t x) noexcept {
        if (x < 0) {
            cerr << "Illegal Argument in node.update_cost: x=" << x << endl;
            exit(1);
        }
        if (this->cost == -1 || this->cost > x) {
            this->cost = x;
        }
    }
};

int main() {
    int N, M;
    cin >> N >> M;

    vector<node> nodes(N);
    mii cover;
    for (auto i = 0; i < M; i++) {
        int L, R, C;
        cin >> L >> R >> C;
        if (cover.count(L - 1) == 0) {
            cover[L - 1] = R - 1;
        } else {
            cover[L - 1] = max(cover[L - 1], R - 1);
        }

        if (nodes.at(L - 1).edge.count(R - 1) == 0) {
            nodes.at(L - 1).edge[R - 1] = C;
        } else {
            nodes.at(L - 1).edge[R - 1] = min(nodes.at(L - 1).edge[R - 1], C);
        }

        if (nodes.at(R - 1).edge.count(L - 1) == 0) {
            nodes.at(R - 1).edge[L - 1] = C;
        } else {
            nodes.at(R - 1).edge[L - 1] = min(nodes.at(R - 1).edge[L - 1], C);
        }
    }

    if (cover.count(0) == 0) {
        cout << -1 << endl;
        return 0;
    }

    auto range = cover.at(0);
    for (auto i = 0; i < cover.size() && i < range; i++) {
        if(cover.count(i)==0){
            continue;
        }
        range = max(range, cover.at(i));
        if (range == N - 1) {
            break;
        }
    }

    if (range != N - 1) {
        cout << -1 << endl;
        return 0;
    }

    for (auto i = N - 1; i > 0; i--) {
        nodes.at(i).edge[i - 1] = 0;
    }

    priority_queue<pli, vector<pli>, greater<>> q;

    nodes.at(0).cost = 0;
    q.emplace(0, 0);

    do {
        auto top = q.top();
        q.pop();
        nodes.at(top.second).done = true;
        for (auto e:nodes.at(top.second).edge) {
            nodes.at(e.first).update_cost(top.first + e.second);
            if (!nodes.at(e.first).done) {
                q.emplace(nodes.at(e.first).cost, e.first);
            }
        }
    } while (!q.empty());

    cout << nodes.at(N - 1).cost << endl;
    return 0;
}