1585. Check If String Is Transformable With Substring Sort Operations

Description

Given two strings s and t, transform string s into string t using the following operation any number of times:

• Choose a non-empty substring in s and sort it in place so the characters are in ascending order.
  • For example, applying the operation on the underlined substring in "14234" results in "12344".

Return true if it is possible to transform s into t. Otherwise, return false.

A substring is a contiguous sequence of characters within a string.

 

Example 1:

Input: s = "84532", t = "34852"
Output: true
Explanation: You can transform s into t using the following sort operations:
"84532" (from index 2 to 3) -> "84352"
"84352" (from index 0 to 2) -> "34852"

Example 2:

Input: s = "34521", t = "23415"
Output: true
Explanation: You can transform s into t using the following sort operations:
"34521" -> "23451"
"23451" -> "23415"

Example 3:

Input: s = "12345", t = "12435"
Output: false

 

Constraints:

• s.length == t.length
• 1 <= s.length <= 105
• s and t consist of only digits.

Solutions

Solution 1: Bubble Sort

The problem is essentially equivalent to determining whether any substring of length 2 in string $s$ can be swapped using bubble sort to obtain $t$.

Therefore, we use an array $pos$ of length 10 to record the indices of each digit in string $s$, where $pos[i]$ represents the list of indices where digit $i$ appears, sorted in ascending order.

Next, we iterate through string $t$. For each character $t[i]$ in $t$, we convert it to the digit $x$. We check if $pos[x]$ is empty. If it is, it means that the digit in $t$ does not exist in $s$, so we return false. Otherwise, to swap the character at the first index of $pos[x]$ to index $i$, all indices of digits less than $x$ must be greater than or equal to the first index of $pos[x]. If this condition is not met, we return false. Otherwise, we pop the first index from $pos[x]$ and continue iterating through string $t$.

After the iteration, we return true.

The time complexity is $O(n \times C)$, and the space complexity is $O(n)$. Here, $n$ is the length of string $s$, and $C$ is the size of the digit set, which is 10 in this problem.

Python3JavaC++Go

class Solution:
    def isTransformable(self, s: str, t: str) -> bool:
        pos = defaultdict(deque)
        for i, c in enumerate(s):
            pos[int(c)].append(i)
        for c in t:
            x = int(c)
            if not pos[x] or any(pos[i] and pos[i][0] < pos[x][0] for i in range(x)):
                return False
            pos[x].popleft()
        return True

class Solution {
    public boolean isTransformable(String s, String t) {
        Deque<Integer>[] pos = new Deque[10];
        Arrays.setAll(pos, k -> new ArrayDeque<>());
        for (int i = 0; i < s.length(); ++i) {
            pos[s.charAt(i) - '0'].offer(i);
        }
        for (int i = 0; i < t.length(); ++i) {
            int x = t.charAt(i) - '0';
            if (pos[x].isEmpty()) {
                return false;
            }
            for (int j = 0; j < x; ++j) {
                if (!pos[j].isEmpty() && pos[j].peek() < pos[x].peek()) {
                    return false;
                }
            }
            pos[x].poll();
        }
        return true;
    }
}

class Solution {
public:
    bool isTransformable(string s, string t) {
        queue<int> pos[10];
        for (int i = 0; i < s.size(); ++i) {
            pos[s[i] - '0'].push(i);
        }
        for (char& c : t) {
            int x = c - '0';
            if (pos[x].empty()) {
                return false;
            }
            for (int j = 0; j < x; ++j) {
                if (!pos[j].empty() && pos[j].front() < pos[x].front()) {
                    return false;
                }
            }
            pos[x].pop();
        }
        return true;
    }
};

func isTransformable(s string, t string) bool {
    pos := [10][]int{}
    for i, c := range s {
        pos[c-'0'] = append(pos[c-'0'], i)
    }
    for _, c := range t {
        x := int(c - '0')
        if len(pos[x]) == 0 {
            return false
        }
        for j := 0; j < x; j++ {
            if len(pos[j]) > 0 && pos[j][0] < pos[x][0] {
                return false
            }
        }
        pos[x] = pos[x][1:]
    }
    return true
}

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