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Problem 1460 Make Two Arrays Equal by Reversing Subarrays

Problem Statement

Link - Problem 1460

Question

You are given two integer arrays of equal length target and arr. In one step, you can select any non-empty subarray of arr and reverse it. You are allowed to make any number of steps.

Return true if you can make arr equal to target or false otherwise.

Example 1

Input: target = [1,2,3,4], arr = [2,4,1,3]
Output: true
Explanation: You can follow the next steps to convert arr to target:
1- Reverse subarray [2,4,1], arr becomes [1,4,2,3]
2- Reverse subarray [4,2], arr becomes [1,2,4,3]
3- Reverse subarray [4,3], arr becomes [1,2,3,4]
There are multiple ways to convert arr to target, this is not the only way to do so.

Example 2

Input: target = [7], arr = [7]
Output: true
Explanation: arr is equal to target without any reverses.

Example 3

Input: target = [3,7,9], arr = [3,7,11]
Output: false
Explanation: arr does not have value 9 and it can never be converted to target.

Constraints

• target.length == arr.length
• 1 <= target.length <= 1000
• 1 <= target[i] <= 1000
• 1 <= arr[i] <= 1000

Solution

class Solution {
public:
    bool canBeEqual(vector<int>& target, vector<int>& arr) {
        vector<int> cnt1(1001);
        vector<int> cnt2(1001);
        for (int& v : target) {
            ++cnt1[v];
        }
        for (int& v : arr) {
            ++cnt2[v];
        }
        return cnt1 == cnt2;
    }
};

Complexity Analysis

| Algorithm | Time Complexity | Space Complexity |
| --------- | --------------- | ---------------- |
| Counting  | O(n)            | O(n)             |

Explanation

1. Intuition

We need to create subarrays of arr and reverse them to obtain target. But the key point is we can do this operation any number of times.

• This means we can take two element subarrays and reverse them to essentially generate the target array given that the elements are the same.
• Because of this we just need to check if the frequency of elements in both arrays is the same.
• If the frequency of elements is the same, we can generate the target array by reversing subarrays.
• If the frequency of elements is not the same, we cannot generate the target array by reversing subarrays.

2. Implementation

- Initialize two vectors `cnt1` and `cnt2` of size 1001 with 0.
- Iterate over the elements of `target` and increment the count of the element in `cnt1`.
- Iterate over the elements of `arr` and increment the count of the element in `cnt2`.
- Return whether the two vectors are equal.