动态规划_leetcode64

#coding=utf-8

# 按递归的逆顺序 从底向上
class Solution1(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """

        self.m = len(grid)
        self.n = len(grid[0])


        self.nextDirection = [[0,-1],[-1,0]]

        self.visit = [[False for i in range(self.n)] for i in range(self.m)]

        self.dp(grid)

        return grid[0][0]


    def inArea(self,x,y):
        return x >= 0 and x < self.m and y >= 0 and y < self.n

    def getDownValue(self,grid,x,y):
        downX = x +1
        downY  = y

        if self.inArea(downX,downY):
            return grid[downX][downY]

        return None

    def getrightValue(self,grid,x,y):
        rightX = x
        rightY = y + 1

        if self.inArea(rightX, rightY):
            return grid[rightX][rightY]

        return None

    # grid[x][y] 表示grid[x][y] 到 grid[m][n]的最短路径
    def dp(self,grid):

        sX = self.m-1
        sY = self.n-1



        queue = []
        queue.append([sX,sY])

        while queue:
            x, y = queue.pop(0)

            if not self.visit[x][y]:

                self.visit[x][y] = True

                downValue = self.getDownValue(grid,x,y)
                rightValue = self.getrightValue(grid,x,y)

                if downValue != None  and rightValue != None:
                    grid[x][y] = min(downValue,rightValue) + grid[x][y]

                if  downValue != None  and rightValue == None:
                    grid[x][y] = downValue + grid[x][y]

                if  downValue == None and  rightValue != None:
                    grid[x][y] = rightValue + grid[x][y]


                for item in self.nextDirection:
                    nextX = x + item[0]
                    nextY = y + item[1]

                    if self.inArea(nextX,nextY):
                        queue.append([nextX,nextY])


        print grid[0][0]



# 递归的逆顺序可以优化为 一直向上和一直向左回溯
class Solution2(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """

        self.m = len(grid)
        self.n = len(grid[0])


        for x in range(self.m-1,-1,-1):
            for y in range(self.n-1,-1,-1):

                if x == self.m-1 and y == self.n-1:
                    continue
                if x == self.m-1:
                    grid[x][y] = grid[x][y] + grid[x][y+1]
                    continue

                if y == self.n-1:
                    grid[x][y] = grid[x+1][y] + grid[x][y]
                    continue

                grid[x][y] = min(grid[x+1][y],grid[x][y+1]) + grid[x][y]

        print grid[0][0]
        return grid[0][0]















s = Solution2()

g = [
  [1,3,1],
  [1,5,1],
  [4,2,1]
]


g1 = [
        [9,9,0,8,9,0,5,7,2,2,7,0,8,0,2,4,8],        [4,4,2,7,6,0,9,7,3,2,5,4,6,5,4,8,7],        [4,9,7,0,7,9,2,4,0,2,4,4,6,2,8,0,7],        [7,7,9,6,6,4,8,4,8,7,9,4,7,6,9,6,5],        [1,3,7,5,7,9,7,3,3,3,8,3,6,5,0,3,6],        [7,1,0,7,5,0,6,6,5,3,2,6,0,0,9,5,7],        [6,5,6,3,8,1,8,6,4,4,3,4,9,9,3,3,1],        [1,0,2,9,7,9,3,1,7,5,1,8,2,8,4,7,6],        [9,6,7,7,4,1,4,0,6,5,1,9,0,3,2,1,7],        [2,0,8,7,1,7,4,3,5,6,1,9,4,0,0,2,7],        [9,8,1,3,8,7,1,2,8,3,7,3,4,6,7,6,6],        [4,8,3,8,1,0,4,4,1,0,4,1,4,4,0,3,5],        [6,3,4,7,5,4,2,2,7,9,8,4,5,6,0,3,9],        [0,4,9,7,1,0,7,7,3,2,1,4,7,6,0,0,0]]g2 = [    [9,9,0,8,9],    [4,4,2,7,6],    [4,9,7,0,7],    [7,7,9,6,6],    [1,3,7,5,7]]g3 = [    [9,9,0,8],    [4,4,2,7],    [4,9,7,0],    [7,7,9,6],]s.minPathSum(g1)