花花酱 LeetCode 926. Flip String to Monotone Increasing

zxi — Sun, 21 Oct 2018 04:22:56 +0000

Problem

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

Solution: DP

l[i] := number of flips to make S[0] ~ S[i] become all 0s.

r[i] := number of flips to make S[i] ~ S[n – 1] become all 1s.

Try all possible break point, S[0] ~ S[i – 1] are all 0s and S[i] ~ S[n-1] are all 1s.

ans = min{l[i – 1] + r[i]}

Time complexity: O(n)

Space complexity: O(n)

C++

// Author: Huahua
class Solution {
public:
  int minFlipsMonoIncr(string S) {
    const int n = S.size();
    vector l(n + 1); // 1 -> 0
    vector r(n + 1); // 0 -> 1
    l[0] = S[0] - '0';
    r[n - 1] = '1' - S[n - 1];
    for (int i = 1; i < n; ++i)
      l[i] = l[i - 1] + S[i] - '0';
    for (int i = n - 2; i >= 0; --i)
      r[i] = r[i + 1] + '1' - S[i];
    int ans = r[0]; // all 1s.
    for (int i = 1; i <= n; ++i)
      ans = min(ans, l[i - 1] + r[i]);
    return ans;
  }
};

C++ v2

// Author: Huahua
class Solution {
public:
  int minFlipsMonoIncr(string S) {
    const int n = S.length();
    vector> dp(n + 1, vector(2));
    for (int i = 1; i <= n; ++i) {
      if (S[i - 1] == '0') {
        dp[i][0] = dp[i - 1][0];
        dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + 1;
      } else {
        dp[i][0] = dp[i - 1][0] + 1;
        dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]);
      }
    }
    return min(dp[n][0], dp[n][1]);
  }
};

C++ v2 / O(1) Space

// Author: Huahua
class Solution {
public:
  int minFlipsMonoIncr(string S) {
    const int n = S.length();
    int dp0 = 0;
    int dp1 = 0;
    for (int i = 1; i <= n; ++i) {
      int tmp0 = dp0 + (S[i - 1] == '1');
      dp1 = min(dp0, dp1) + (S[i - 1] == '0');
      dp0 = tmp0;
    }
    return min(dp0, dp1);
  }
};

The post 花花酱 LeetCode 926. Flip String to Monotone Increasing appeared first on Huahua's Tech Road.

two sides Archives - Huahua's Tech Road

花花酱 LeetCode 926. Flip String to Monotone Increasing

Problem

Solution: DP

C++

C++ v2

C++ v2 / O(1) Space