动态规划_leetcode474

# coding=utf8

# 递归
# 递归过程是错的，求子集过程错误
class Solution1(object):
    def findMaxForm(self, strs, m, n):
        """
        :type strs: List[str]
        :type m: int
        :type n: int
        :rtype: int
        """


        return self.tryFindMaxForm(strs, 0, m, n)


    def ZeroAndOne(self,str):

        length = len(str)
        zeroCount = 0

        for item in str:
            if item == "0":
                zeroCount += 1

        return zeroCount,length-zeroCount


    def tryFindMaxForm(self,strs,index,m,n):


        # if m < 0 or n < 0:
        #     return 0

        res = 0
        for i in range(index,len(strs)):

            zeroNums,oneNums = self.ZeroAndOne(strs[i])

            if m-zeroNums >= 0 and  n-oneNums >= 0 :

                res = max(self.tryFindMaxForm(strs,index+1,m,n),1 + self.tryFindMaxForm(strs,index+1,m-zeroNums,n-oneNums))

        return res



# A1= ["11110", "00011", "11100"]
# m1 = 2
# n1 = 2
#
# A2 = ["10", "0", "1"]
# m2 =1
# n2 = 1
#
# A3 = ["10", "0001", "111001", "1", "0"]
# m3 = 5
# n3 = 3
#
# s = Solution1()


# print  s.findMaxForm(A3,m3,n3)


# 记忆化递归
class Solution2(object):
    def findMaxForm(self, strs, m, n):
        """
        :type strs: List[str]
        :type m: int
        :type n: int
        :rtype: int
        """
        length = len(strs)

        self.memo = [[[-1 for i in range(n+1)] for i in range(m+1)] for i in range(length+1)]


        return self.tryFindMaxForm(strs, 0, m, n)


    def ZeroAndOne(self,str):

        length = len(str)
        zeroCount = 0

        for item in str:
            if item == "0":
                zeroCount += 1

        return zeroCount,length-zeroCount


    def tryFindMaxForm(self,strs,index,m,n):

        if self.memo[index][m][n] != -1:
            return self.memo[index][m][n]

        if m < 0 or n < 0:
            return 0

        res = 0
        for i in range(index,len(strs)):

            zeroNums,oneNums = self.ZeroAndOne(strs[i])

            if not (m-zeroNums < 0  or  n-oneNums < 0) and index < len(strs):

                res = max(res,1 + self.tryFindMaxForm(strs,index+1,m-zeroNums,n-oneNums))


        self.memo[index][m][n] = res
        return res


# A1= ["11110", "00011", "11100"]
# m1 = 2
# n1 = 2
#
# A2 = ["10", "0", "1"]
# m2 =1
# n2 = 1
#
# A3 = ["10", "0001", "111001", "1", "0"]
# m3 = 5
# n3 = 3
#
# s = Solution2()
#
#
# print  s.findMaxForm(A3,m3,n3)



# F(i,m,n) = max(F(i+1,m,n), F(i+1,m-a,n-b))

class Solution3(object):
    def findMaxForm(self, strs, m, n):
        """        :type strs: List[str]        :type m: int        :type n: int        :rtype: int        """        return self.tryFindMaxForm(strs, 0, m, n)    def ZeroAndOne(self,str):        length = len(str)        zeroCount = 0        for item in str:            if item == "0":                zeroCount += 1        return zeroCount,length-zeroCount    def tryFindMaxForm(self,strs,index,m,n):        if m < 0 or n < 0 or index >= len(strs):            return 0        res = 0        zeroNums,oneNums = self.ZeroAndOne(strs[index])        if m-zeroNums >= 0 and n-oneNums >= 0:            res = max(self.tryFindMaxForm(strs,index+1,m,n),1 + self.tryFindMaxForm(strs,index+1,m-zeroNums,n-oneNums))        else:            res = self.tryFindMaxForm(strs,index+1,m,n)        return res# A1= ["11110", "00011", "11100"]# m1 = 2# n1 = 2## A2 = ["10", "0", "1"]# m2 =1# n2 = 1## A3 = ["10", "0001", "111001", "1", "0"]# m3 = 5# n3 = 3## s = Solution3()### print  s.findMaxForm(A2,m2,n2)class Solution4(object):    def findMaxForm(self, strs, m, n):        """        :type strs: List[str]        :type m: int        :type n: int        :rtype: int        """        # self.memo = [[-1 for i in range(n + 1)] for i in range(m+1)] for i in range(len(strs))]        self.memo = [[[-1 for i in range(n+1)] for i in range(m+1)] for i in range(len(strs) + 1)]        self.tryFindMaxForm(strs, 0, m, n)        return self.memo[0][m][n]    def ZeroAndOne(self,str):        length = len(str)        zeroCount = 0        for item in str:            if item == "0":                zeroCount += 1        return zeroCount,length-zeroCount    def tryFindMaxForm(self,strs,index,m,n):        if self.memo[index][m][n] != -1:            return self.memo[index][m][n]        if m < 0 or n < 0 or index >= len(strs):            return 0        res = 0        zeroNums,oneNums = self.ZeroAndOne(strs[index])        if m-zeroNums >= 0 and n-oneNums >= 0:            res = max(self.tryFindMaxForm(strs,index+1,m,n),1 + self.tryFindMaxForm(strs,index+1,m-zeroNums,n-oneNums))        else:            res = self.tryFindMaxForm(strs,index+1,m,n)        self.memo[index][m][n] = res        return res# A1= ["11110", "00011", "11100"]# m1 = 2# n1 = 2## A2 = ["10", "0", "1"]# m2 =1# n2 = 1## A3 = ["10", "0001", "111001", "1", "0"]# m3 = 5# n3 = 3## s = Solution4()### print  s.findMaxForm(A2,m2,n2)# 动归class Solution5(object):    def findMaxForm(self, strs, m, n):        """        :type strs: List[str]        :type m: int        :type n: int        :rtype: int        """        # self.memo = [[-1 for i in range(n + 1)] for i in range(m+1)] for i in range(len(strs))]        length = len(strs)        self.memo = [[[0 for i in range(n+1)] for i in range(m+1)] for i in range(length+1)]        # F(i,m,n) = max(F(i+1,m,n),F(i+1,m-a,n-b))        # for i in range(m+1):        #     for j in range(n+1):        #         self.memo[length][i][j] = 0        for index in range(length-1,-1 ,-1):            for mIndex in range(m+1):                for nIndex in range(n+1):                    zeroNums, oneNums = self.ZeroAndOne(strs[index])                    if mIndex - zeroNums >= 0 and nIndex - oneNums >= 0:                        self.memo[index][mIndex][nIndex]= max(self.memo[index+1][ mIndex][nIndex],1+self.memo[index+1][mIndex-zeroNums][nIndex-oneNums])                    else:                        self.memo[index][mIndex][nIndex] = self.memo[index+1][mIndex][nIndex]        return self.memo[0][m][n]    def ZeroAndOne(self,str):        length = len(str)        zeroCount = 0        for item in str:            if item == "0":                zeroCount += 1        return zeroCount,length-zeroCountA1= ["11110", "00011", "11100"]m1 = 2n1 = 2A2 = ["10", "0", "1"]m2 =1n2 = 1A3 = ["10", "0001", "111001", "1", "0"]m3 = 5n3 = 3s = Solution4()A4 = ["1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101","1101","0101"]m4 = 100n4 = 100print  s.findMaxForm(A4,m4,n4)