使用邻接矩阵（Python或伪代码）拓扑排序的无权有向无环图中的最短和最长路径

我正试图解决一个交给我做作业的问题，我真的觉得我对算法思考过度了，希望这里的人能把我推向正确的方向

我将得到一个输入txt文件，如下所示：

1    // n number of graphs
4    // n number of vertices for graph 1
4    // n number of edges for graph 1
1 2  // edges given in pairs
2 3
2 4
3 4 

我应该用这些数据来收集n个表示图的邻接矩阵。然后，我需要对邻接矩阵中的数据实施3种方法：

findLongestPath（），它将返回图形中最长的路径

findShortestPath（），它将返回图形中的最短路径

totalNumberPaths（），它将返回图形中不同数量的路径

我在执行前两部分时遇到了困难。这就是我到目前为止所做的：

def main():


numGraphs = input()

for x in xrange(0, numGraphs):
    numVerts = input()
    numEdges = input()
    adjMat = [[0 for x in xrange(numVerts)] for x in xrange(numVerts)] 
    for x in xrange(0, numEdges):
        edges = raw_input()
        i, padding, j = edges.rpartition(" ")

        i = int(i)
        j = int(j)

        i -= 1
        j -= 1

        adjMat[i][j] = 1


    numPaths = [0 for x in xrange(numVerts)]
    numPaths[0] = 1 

    longest_path = 1
    shortest_path = numVerts

    for i in xrange(0, numVerts):
        current_path = 0
        for j in xrange(0, numVerts):
            if adjMat[i][j] == 1:
                numPaths[j] += numPaths[i]
                current_path += 1

        if current_path > longest_path:
            longest_path = current_path
        if current_path < shortest_path:
            shortest_path = current_path

    print "shortest: %d, longest: %d, total %d" % (shortest_path, longest_path, numPaths[numVerts-1])

 if __name__ == "__main__":
     main()

---

我明白了。这是我的最终解决方案

numGraphs = input()

for x in xrange(0, numGraphs):
    numVerts = input()
    numEdges = input()
    adjMat = [[0 for x in xrange(numVerts)] for x in xrange(numVerts)] 
    for x in xrange(0, numEdges):
        edges = raw_input()
        i, padding, j = edges.rpartition(" ")

        i = int(i)
        j = int(j)

        i -= 1
        j -= 1

        adjMat[i][j] = 1


    numPaths = [0 for x in xrange(numVerts)]
    numPaths[0] = 1 

    currentPath = [0 for x in xrange(numVerts)]
    maxPath = 1
    minPath = numVerts -1

    for i in xrange(0, numVerts):
        for j in xrange(1, numVerts):
            if adjMat[i][j] == 1:
                numPaths[j] += numPaths[i]
                currentPath[j-i] += 1
            if (currentPath[j-i] is not 0):
                minPath = currentPath[j-i]
            maxPath = max(currentPath)

    print "shortest: %d, longest: %d, total %d" % (minPath, maxPath, numPaths[numVerts-1])

---

请将更新后的代码作为答案发布并接受。如果你确信它有效并且是你问题的正确解决方案，你应该回答你自己的问题(

numGraphs = input()

for x in xrange(0, numGraphs):
    numVerts = input()
    numEdges = input()
    adjMat = [[0 for x in xrange(numVerts)] for x in xrange(numVerts)] 
    for x in xrange(0, numEdges):
        edges = raw_input()
        i, padding, j = edges.rpartition(" ")

        i = int(i)
        j = int(j)

        i -= 1
        j -= 1

        adjMat[i][j] = 1


    numPaths = [0 for x in xrange(numVerts)]
    numPaths[0] = 1 

    currentPath = [0 for x in xrange(numVerts)]
    maxPath = 1
    minPath = numVerts -1

    for i in xrange(0, numVerts):
        for j in xrange(1, numVerts):
            if adjMat[i][j] == 1:
                numPaths[j] += numPaths[i]
                currentPath[j-i] += 1
            if (currentPath[j-i] is not 0):
                minPath = currentPath[j-i]
            maxPath = max(currentPath)

    print "shortest: %d, longest: %d, total %d" % (minPath, maxPath, numPaths[numVerts-1])