Ones and zeroes

Time: O(SxMxN); Space: O(MxN); medium

Given an array, strs, with strings consisting of only 0s and 1s. Also two integers m and n.

Now your task is to find the maximum number of strings that you can form with given m 0s and n 1s.

Each 0 and 1 can be used at most once.

Example 1:

Input: strs = [“10”,“0001”,“111001”,“1”,“0”], m = 5, n = 3

Output: 4

Explanation:

  • This are totally 4 strings can be formed by the using of 5 0s and 3 1s, which are “10”,“0001”,“1”,“0”.

Example 2:

Input: strs = [“10”,“0”,“1”], m = 1, n = 1

Output: 2

Explanation:

  • You could form “10”, but then you’d have nothing left. Better form “0” and “1”.

Constraints:

  • 1 <= len(strs) <= 600

  • 1 <= len(strs[i]) <= 100

  • strs[i] consists only of digits ‘0’ and ‘1’.

  • 1 <= m, n <= 100

[1]:

class Solution1(object):
    """
    Time: O(S*M*N), S is the size of the array
    Space: O(M*N)
    """
    def findMaxForm(self, strs, m, n):
        """
        :type strs: List[str]
        :type m: int
        :type n: int
        :rtype: int
        """
        dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]

        for s in strs:
            zero_count, one_count = 0, 0
            for c in s:
                if c == '0':
                    zero_count += 1
                elif c == '1':
                    one_count += 1

            for i in reversed(range(zero_count, m + 1)):
                for j in reversed(range(one_count, n + 1)):
                    dp[i][j] = max(dp[i][j], dp[i-zero_count][j-one_count]+1)

        return dp[m][n]

[2]:

s = Solution1()

strs = ["10","0001","111001","1","0"]
m = 5
n = 3
assert s.findMaxForm(strs, m, n) == 4

strs = ["10","0","1"]
m = 1
n = 1
assert s.findMaxForm(strs, m, n) == 2