Flip String to Monotone Increasing

Description

A string of '0's and '1's is monotone increasing if it consists of some number of '0's (possibly 0), followed by some number of '1's (also possibly 0.)

We are given a string S of '0's and '1's, and we may flip any '0' to a '1' or a '1' to a '0'.

Return the minimum number of flips to make S monotone increasing.

 

Example 1:

Input: "00110"
Output: 1
Explanation: We flip the last digit to get 00111.

Example 2:

Input: "010110"
Output: 2
Explanation: We flip to get 011111, or alternatively 000111.

Example 3:

Input: "00011000"
Output: 2
Explanation: We flip to get 00000000.

 

Note:

1. 1 <= S.length <= 20000
2. S only consists of '0' and '1' characters.

Solution(javascript)

/** DP
 * @param {string} S
 * @return {number}
 */
const minFlipsMonoIncr = function (S) {
  const memo = {}
  const aux = (index, prev) => {
    memo[index] = memo[index] || {}
    if (memo[index][prev] !== undefined) {
      return memo[index][prev]
    }
    if (index >= S.length) {
      return 0
    }
    if (prev === '0') {
      if (S[index] === '0') {
        memo[index][prev] = Math.min(aux(index + 1, '0'), aux(index + 1, '1') + 1)
      } else {
        memo[index][prev] = Math.min(aux(index + 1, '1'), aux(index + 1, '0') + 1)
      }
    } else if (S[index] === '0') {
      memo[index][prev] = aux(index + 1, '1') + 1
    } else {
      memo[index][prev] = aux(index + 1, '1')
    }
    return memo[index][prev]
  }
  return aux(0, '0')
}