*[codility]AscendingPaths

https://codility.com/programmers/challenges/magnesium2014

图形上的DP，先按照路径长度排序，然后依次遍历，状态是使用到当前路径为止的情况；每个节点记录以该节点结束的最长路径，这样加入新的路径时去更新。注意路径是双向的~

#include <vector>

#include <algorithm>

using namespace std;

 

struct Road {

    int start;

    int end;

    int val;

};

 

bool cmp(const Road &a, const Road &b) {

    return a.val < b.val;

}

 

int solution(int N, vector<int> &A, vector<int> &B, vector<int> &C) {

    int M = A.size();

    vector<Road> roads(M);

    for (int i = 0; i < M; i++) {

        roads[i].start = A[i];

        roads[i].end = B[i];

        roads[i].val = C[i];

    }

    sort(roads.begin(), roads.end(), cmp);

    vector<pair<int, int>> dp(N); // first: the longest length ends with this node; second: the last path val to this node;

    int result = 0;

    for (int i = 0; i < M; i++) {

        int x2y_len = dp[roads[i].end].first;

        int x2y_val = dp[roads[i].end].second;

        if (roads[i].val > dp[roads[i].start].second &&

            dp[roads[i].start].first + 1 > dp[roads[i].end].first) {

            x2y_len = dp[roads[i].start].first + 1;

            x2y_val = roads[i].val;

            result = max(x2y_len, result);

        }

        // the other side

        int y2x_len = dp[roads[i].start].first;

        int y2x_val = dp[roads[i].start].second;

        if (roads[i].val > dp[roads[i].end].second &&

            dp[roads[i].end].first + 1 > dp[roads[i].start].first) {

            y2x_len = dp[roads[i].end].first + 1;

            y2x_val = roads[i].val;

            result = max(y2x_len, result);

        }

        dp[roads[i].end].first = x2y_len;

        dp[roads[i].end].second = x2y_val;

        dp[roads[i].start].first = y2x_len;

        dp[roads[i].start].second = y2x_val;

    }

    return result;

}