import math

class Graph:
    
    def __init__(self, N = 0): # a graph with Node 0,1,...,N-1
        self.N = N
        self.W = [[math.inf for j in range(0,N)] for i in range(0,N)] # adjacency matrix for weight
        self.dp = [[math.inf for j in range(0,N)] for i in range(0,N)] # dp[i][j] stores minimum distance from i to j

    def addEdge(self, u, v, w):
        self.dp[u][v] = w

    def floyd_warshall(self):
        for k in range(0,self.N):
            for i in range(0,self.N):
                for j in range(0,self.N):
                    self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j])

    def showMin(self, u, v):
        return self.dp[u][v]
    
if __name__ == '__main__':
    graph = Graph(5)
    graph.addEdge(0,2,9)
    graph.addEdge(0,4,10)
    graph.addEdge(1,3,5)
    graph.addEdge(2,3,7)
    graph.addEdge(3,0,10)
    graph.addEdge(3,1,2)
    graph.addEdge(3,2,1)
    graph.addEdge(3,4,6)
    graph.addEdge(4,1,3)
    graph.addEdge(4,2,4)
    graph.addEdge(4,3,9)
    graph.floyd_warshall()
    graph.showMin(1,4)
    graph.showMin(0,3)