474. Ones and Zeroes

Description

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 mostm0's and n1's in the subset.

A set x is a subset of a set y if all elements of x are also elements of y.

 

Example 1:

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.

Example 2:

Input: strs = ["10","0","1"], m = 1, n = 1
Output: 2
Explanation: The largest subset is {"0", "1"}, so the answer is 2.

 

Constraints:

• 1 <= strs.length <= 600
• 1 <= strs[i].length <= 100
• strs[i] consists only of digits '0' and '1'.
• 1 <= m, n <= 100

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(strs.length*mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {string[]} strs
 * @param {number} m
 * @param {number} n
 * @return {number}
 */
const findMaxForm = function (strs, m, n) {
  const len = strs.length;
  const strOnesAndZeros = Array.from({ length: len }, () => [0, 0]);
  const dp = Array.from({ length: m + 1 }, () => new Array(n + 1).fill(0));

  for (let index = 0; index < len; index++) {
    for (const char of strs[index]) {
      strOnesAndZeros[index][char] += 1;
    }
  }

  for (let index = 0; index < len; index++) {
    const [zeros, ones] = strOnesAndZeros[index];

    for (let a = m; a >= zeros; a--) {
      for (let b = n; b >= ones; b--) {
        const size = 1 + dp[a - zeros][b - ones];

        dp[a][b] = Math.max(size, dp[a][b]);
      }
    }
  }

  return dp[m][n];
};