Formatted question description: https://leetcode.ca/all/1888.html
1888. Minimum Number of Flips to Make the Binary String Alternating
Level
Medium
Description
You are given a binary string s. You are allowed to perform two types of operations on the string in any sequence:
- Type-1: Remove the character at the start of the string
sand append it to the end of the string. - Type-2: Pick any character in
sand flip its value, i.e., if its value is'0'it becomes'1'and vice-versa.
Return the minimum number of type-2 operations you need to perform such that s becomes alternating.
The string is called alternating if no two adjacent characters are equal.
- For example, the strings
"010"and"1010"are alternating, while the string"0100"is not.
Example 1:
Input: s = “111000”
Output: 2
Explanation: Use the first operation two times to make s = “100011”.
Then, use the second operation on the third and sixth elements to make s = “101010”.
Example 2:
Input: s = “010”
Output: 0
Explanation: The string is already alternating.
Example 3:
Input: s = “1110”
Output: 1
Explanation: Use the second operation on the second element to make s = “1010”.
Constraints:
1 <= s.length <= 10^5s[i]is either'0'or'1'.
Solution
If only type-2 operations are performed, since the alternating string can either start with 0 or 1, the minimum number of flips can be calculated for the two cases. Use count0 and count1 to represent the minimum number of flips if the alternating string starts with 0 and with 1, respectively.
If the length of s is even, then any type-1 operation will not reduce the number of type-2 operations, so return the minimum of count0 and count1.
If the length of s is odd, then type-1 operations may reduce the number of type-2 operations. For 0 < i < s.length(), we may remove the first i characters at the start of s and append them to the end of s. Before performing type-1 operations, for each 0 < i < s.length(), calculate the minimum number of type-2 operations if s[i - 1] = s[i] = '0' and s[i - 1] = s[i] = '1' respectively. To do this in O(n) time, loop over s forward and backward, and for each 0 <= i < s.length(), calculate the minimum number of type-2 operations needed for both s[i] = 0 and s[i] = 1 in both directions. After the values are calculated, the minimum number of type-2 operations can be calculated.
class Solution {
public int minFlips(String s) {
int length = s.length();
int count0 = 0, count1 = 0;
for (int i = 0; i < length; i++) {
char c = s.charAt(i);
if (c == '0') {
if (i % 2 == 0)
count1++;
else
count0++;
} else {
if (i % 2 == 0)
count0++;
else
count1++;
}
}
if (length % 2 == 0)
return Math.min(count0, count1);
int[][] dpForward = new int[length][2];
if (s.charAt(0) == '0')
dpForward[0][1] = 1;
else
dpForward[0][0] = 1;
for (int i = 1; i < length; i++) {
if (s.charAt(i) == '0') {
dpForward[i][0] = dpForward[i - 1][1];
dpForward[i][1] = dpForward[i - 1][0] + 1;
} else {
dpForward[i][0] = dpForward[i - 1][1] + 1;
dpForward[i][1] = dpForward[i - 1][0];
}
}
int[][] dpBackward = new int[length][2];
if (s.charAt(length - 1) == '0')
dpBackward[length - 1][1] = 1;
else
dpBackward[length - 1][0] = 1;
for (int i = length - 2; i >= 0; i--) {
if (s.charAt(i) == '0') {
dpBackward[i][0] = dpBackward[i + 1][1];
dpBackward[i][1] = dpBackward[i + 1][0] + 1;
} else {
dpBackward[i][0] = dpBackward[i + 1][1] + 1;
dpBackward[i][1] = dpBackward[i + 1][0];
}
}
int minCount = Math.min(count0, count1);
for (int i = 1; i < length; i++) {
int curMin = Math.min(dpForward[i - 1][0] + dpBackward[i][0], dpForward[i - 1][1] + dpBackward[i][1]);
minCount = Math.min(minCount, curMin);
}
return minCount;
}
}