遇到一个算法题目,描述如下:
对图结构有了解的不难发现,这是经典的求图的最短路径问题。以下是python代码:
def findMin(row): minL = max(row) for i in row: if i != -1 and minL > i: minL = i return minL def initRow(row, plus): r = [] for i in row: if i != -1: i += plus r.append(i) return r def getMinLen(table, e, t): count = len(table) - 1 startPoint = 1 #记录原点到各点最短距离 初始值为-1,即不可达 lenRecord = list((-1 for i in range(count+1))) lenRecord[startPoint] = 0 #记录每次循环的起点 points = [startPoint] #已得到最短距离的点 visited = set() while len(points)>0: #当前起点 curPoint = points.pop() #原点到当前起点的距离 curLen = lenRecord[curPoint] #当前起点到各点的距离 curList = initRow(table[curPoint], t) #当前起点到各点的最短距离 curMin = findMin(curList) visited.add(curPoint) idx = 0 while idx<count: idx += 1 #当前点不可达或到当前点的最短距离已计算出 则跳过 if curList[idx] == -1 or idx in visited: continue #记录距离当前起点最近的点作为下次外层循环的起点 if curList[idx] == curMin: points.append(idx) #如果从原点经当前起点curPoint到目标点idx的距离更短,则更新 if lenRecord[idx] == -1 or lenRecord[idx] > (curLen+curList[idx]): lenRecord[idx] = curLen+curList[idx] return lenRecord[e] def processInput(): pointCnt, roadCnt, jobCnt = (int(x) for x in raw_input().split()) table = [] for i in range(pointCnt+1): table.append([-1] * (pointCnt+1)) for i in range(roadCnt): (x, y, w) = (int(n) for n in raw_input().split()) if table[x][y] == -1 or table[x][y] > w: table[x][y] = w table[y][x] = w res = [] for i in range(jobCnt): e, t = (int(x) for x in raw_input().split()) res.append(getMinLen(table, e, t)) for i in res: print(i) processInput()