[算法]详解关键路径算法

详解关键路径算法

#include 
#include 
using namespace std;
int eventsSize, activitiesSize;
int activitiesCostTimes[100][100];
pair<int, int> activities[100];
int eventEarlyBegin[100], eventLatestBegin[100];
int activityEarlyBegin[100], activityLatestBegin[100];

void init() {
    memset(eventLatestBegin, 0, sizeof(eventLatestBegin));
    memset(eventEarlyBegin, 0, sizeof(eventEarlyBegin));
    memset(activityEarlyBegin, 0, sizeof(eventEarlyBegin));
    memset(activityLatestBegin, 0, sizeof(activityLatestBegin));
}

void computeEventEarliestBegin() {
    eventEarlyBegin[1] = 0;
    int maxTimes;
    for (int i = 2; i <= eventsSize; ++i) {
        maxTimes = INT_MIN;
        for (int j = 1; j <= eventsSize; ++j) {
            if (activitiesCostTimes[j][i] != 0) {
                maxTimes = max(maxTimes, eventEarlyBegin[j] +
                                         activitiesCostTimes[j][i]);
            }
        }
        eventEarlyBegin[i] = maxTimes;
    }
}

void computeEventLatestBegin() {
    eventLatestBegin[eventsSize] = eventEarlyBegin[eventsSize];
    int minCostTimes;
    for (int i = eventsSize - 1; i >= 1; --i) {
        minCostTimes = INT_MAX;
        for (int j = i; j <= eventsSize; ++j) {
            if (activitiesCostTimes[i][j] != 0) {
                minCostTimes = min(minCostTimes, eventLatestBegin[j] -
                        activitiesCostTimes[i][j]);
            }
        }
        eventLatestBegin[i] = minCostTimes;
    }
}

void computeActivityEarlyBegin() {
    for (int i = 1; i <= activitiesSize; ++i) {
        activityEarlyBegin[i] = eventEarlyBegin[activities[i - 1].first];
    }
}

void computeActivityLatestBegin() {
    for (int i = 1; i <= activitiesSize; ++i) {
        activityLatestBegin[i] = eventLatestBegin[activities[i - 1].second] -
                activitiesCostTimes[activities[i - 1].first][activities[i -
                        1].second];
    }
}

vector<int> criticalPath() {
    init();
    computeEventEarliestBegin();
    computeEventLatestBegin();
    computeActivityEarlyBegin();
    computeActivityLatestBegin();
    vector<int> vec;
    for (int i = 1; i <= activitiesSize; ++i) {
        if (activityEarlyBegin[i] == activityLatestBegin[i]) {
            vec.push_back(i);
        }
    }
    return vec;
}

int main() {
    cin >> eventsSize >> activitiesSize;
    int start, end, last;
    for (int i = 0; i < activitiesSize; ++i) {
        cin >> start >> end >> last;
        activitiesCostTimes[start][end] = last;
        activities[i] = make_pair(start, end);
    }
    vector<int> ans = criticalPath();
    for (int j = 0; j < ans.size(); ++j) {
        cout << ans[j] << " ";
    }
    cout << endl;
    return 0;
}

测试样例：

9 11
1 2 6
1 3 4
1 4 5
2 5 1
3 5 1
4 6 2
5 7 7
5 8 5
6 8 4
7 9 2
8 9 4

详情见：

关键路径MBA
关键路径