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:
class Solution {
public int minFlipsMonoIncr(String S) {
int n = S.length();
int[][] dp = new int[n + 1][2];
for (int i = 1; i <= n; i ++) {
int curr = S.charAt(i - 1) - '0';
if (curr == 0) {
dp[i][0] = dp[i - 1][0];
dp[i][1] = Math.min(dp[i - 1][0], dp[i - 1][1]) + 1;
} else {
dp[i][1] = Math.min(dp[i - 1][1], dp[i - 1][0]);
dp[i][0] = dp[i - 1][0] + 1;
}
}
return Math.min(dp[n][0], dp[n][1]);
}
}