使用鄰接矩陣（Python或偽代碼）在拓撲排序的未加權有向無環圖中的最短和最長路徑

Question

我正在嘗試解決我在做作業時遇到的一個問題，感覺就像是我對算法的思考過多，希望這里的人可以將我推向正確的方向。

我將得到一個輸入txt文件，它看起來像這樣：

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 

我應該使用此數據來創建代表圖形的n個鄰接矩陣。 然后，我需要對鄰接矩陣中的數據實現3種方法：

1. findLongestPath（）將返回圖中的最長路徑
2. findShortestPath（）將返回圖中的最短路徑
3. totalNumberPaths（）將返回圖中的不同數量的路徑

我很難很好地實現前兩個部分。 這是我到目前為止的內容：

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()

顯然，當它達到0時，shortest_path更新為0，並且不起作用。 另外，將其初始化為0時將不起作用。如果我可以獲得一些偽代碼，或者可能對較長或較短的方法有所幫助，我敢肯定我可以寫相反的東西，或者我可能完全不合時宜。

感謝您的任何投入。

編輯：

所以我想通了。 如果有人遇到類似問題並需要幫助，這是我完成的代碼。

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。 這是我的最終解決方案。

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])