[算法]详解关键路径算法

详解关键路径算法

#include <iostream>
#include <vector>
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;
}

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