Leetcode #474: Ones and Zeroes
In this guide, we solve Leetcode #474 Ones and Zeroes in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an array of binary strings strs and two integers m and n. Return the size of the largest subset of strs such that there are at most m 0's and n 1's in the subset.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, String, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: strs = ["10","0001","111001","1","0"], m = 5, n = 3
Output: 4
Explanation: The largest subset with at most 5 0's and 3 1's is {"10", "0001", "1", "0"}, so the answer is 4.
Other valid but smaller subsets include {"0001", "1"} and {"10", "1", "0"}.
{"111001"} is an invalid subset because it contains 4 1's, greater than the maximum of 3.
Python Solution
class Solution:
def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
sz = len(strs)
f = [[[0] * (n + 1) for _ in range(m + 1)] for _ in range(sz + 1)]
for i, s in enumerate(strs, 1):
a, b = s.count("0"), s.count("1")
for j in range(m + 1):
for k in range(n + 1):
f[i][j][k] = f[i - 1][j][k]
if j >= a and k >= b:
f[i][j][k] = max(f[i][j][k], f[i - 1][j - a][k - b] + 1)
return f[sz][m][n]
Complexity
The time complexity is , and the space complexity is , where is the length of the array , and and are the upper limits on the number of zeros and ones, respectively. The space complexity is , where is the length of the array , and and are the upper limits on the number of zeros and ones, respectively.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.