08-图9 关键活动

最新推荐文章于 2024-10-11 16:33:59 发布

原创最新推荐文章于 2024-10-11 16:33:59 发布 · 1k 阅读

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#数据结构 #pat #c

中国大学MOOC-陈越、何钦铭-数据结构-2015秋专栏收录该内容

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本文介绍了一个使用C语言实现的关键路径算法程序，该程序通过输入节点数、边数及各边的权重来构建一个有向图，并计算出从起始节点到终点节点的最早开始时间和最晚结束时间，进而找出关键路径。

#include <stdio.h>

#define MAXINT 0x7fffffff
#define Max 101

int Graph[Max][Max], Indegree[Max], Outdegree[Max], Earliest[Max], Latest[Max];

int max(int a, int b)
{
	if (a > b)
		return a;
	else
		return b;	
}

int min(int a, int b)
{
	if (a < b)
		return a;
	else
		return b;
}

int Earliest_Time(int N);
void Latest_Time(int N, int res);

int main(int argc, char const *argv[])
{
	// freopen("test.txt", "r", stdin);
	int N, M;
	scanf("%d %d", &N, &M);
	for (int i = 1; i <= N; i++){
		for (int j = 0; j <= N; j++){
			Graph[i][j] = -1;
		}
		Indegree[i] = 0;
		Outdegree[i] = 0;
		Earliest[i] = 0;
		Latest[i] = MAXINT;
	}
	int s, e, c;
	for (int i = 0; i < M; i++){
		scanf("%d %d %d", &s, &e, &c);
		Graph[s][e] = c;
		Outdegree[s]++;
		Indegree[e]++;
	}
	int res = Earliest_Time(N);
	Latest_Time(N, res);
	if (res == -1)
		printf("0");
	else{
		printf("%d\n", res);
		for (int i = 1; i <= N; i++){
			if (Earliest[i] != Latest[i])
				continue;
			for (int j = N; j >= 1; j--){
				if (Graph[i][j] >= 0 && Earliest[j] == Latest[j] && (Latest[j] - Earliest[i] == Graph[i][j]))
					printf("%d->%d\n", i, j);
			}
		}
	}
	return 0;
}

int Earliest_Time(int N)
{
	int queue[N+1], front = 0, rear = 0;
	for (int i = 1; i <= N; i++){
		if (Indegree[i] == 0){
			queue[rear++] = i;
			Indegree[i]--;
		}
	}
	int cnt = 0, v;
	while (rear - front){
		v = queue[front++];
		cnt++;
		for (int i = 1; i <= N; i++){
			if (Graph[v][i] >= 0){
				Indegree[i]--;
				Earliest[i] = max(Earliest[i], Earliest[v] + Graph[v][i]);
			}
			if (Indegree[i] == 0){
				queue[rear++] = i;
				Indegree[i]--;
			}
		}
	}
	int res = 0;
	if (cnt != N)
		return -1;
	else {
		for (int i = 1; i <= N; i++){
			if (Outdegree[i] == 0)
				res = max(res, Earliest[i]);
		}
		return res;
	}
}

void Latest_Time(int N, int res)
{
	int queue[N+1], front = 0, rear = 0;
	for (int i = 1; i <= N; i++){
		if (Outdegree[i] == 0){
			queue[rear++] = i;
			Latest[i] = res;
			// Outdegree[i]--;
		}
	}
	int v;
	while (rear - front){
		v = queue[front++];
		for (int i = N; i >= 1; i--){
			if (Graph[i][v] >= 0){
				Outdegree[i]--;
				Latest[i] = min(Latest[i], Latest[v] - Graph[i][v]);
				if (Outdegree[i] == 0)
					queue[rear++] = i;
			}
		}
	}
}