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

Question

我正在尝试解决我在做作业时遇到的一个问题，感觉就像是我对算法的思考过多，希望这里的人可以将我推向正确的方向。

我将得到一个输入txt文件，它看起来像这样：

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 

我应该使用此数据来创建代表图形的n个邻接矩阵。 然后，我需要对邻接矩阵中的数据实现3种方法：

1. findLongestPath（）将返回图中的最长路径
2. findShortestPath（）将返回图中的最短路径
3. totalNumberPaths（）将返回图中的不同数量的路径

我很难很好地实现前两个部分。 这是我到目前为止的内容：

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()

显然，当它达到0时，shortest_path更新为0，并且不起作用。 另外，将其初始化为0时将不起作用。如果我可以获得一些伪代码，或者可能对较长或较短的方法有所帮助，我敢肯定我可以写相反的东西，或者我可能完全不合时宜。

感谢您的任何投入。

编辑：

所以我想通了。 如果有人遇到类似问题并需要帮助，这是我完成的代码。

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])

Answer 1

弄清楚了。 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])