Check whether it is possible to make both arrays equal by modifying a single element in Python

Suppose we have two arrays nums1 and nums2 and another value k. We have to check whether both arrays can be made equal by modifying any one element from nums1 in the following way (only once): We can add any value from the range [-k, k] to any element of nums1.

So, if the input is like nums1 = [5,7,11], nums2 = [5,5,11], k = 8, then the output will be True as we can add -2 (in range [-8,8]) with nums1[1] to make it 5 then it will be same as nums2.

Algorithm

To solve this, we will follow these steps ?

• Sort both arrays nums1 and nums2
• Initialize temp := False and idx := -1
• For each index i from 0 to length of nums1 ? 1, do:
  • If nums1[i] is not same as nums2[i], then:
    • If temp is true, return False (more than one difference)
    • Set temp := True and idx := i
• If idx is -1 (no differences) or |nums1[idx] - nums2[idx]| ? k, return True
• Otherwise, return False

Implementation

Let us see the following implementation to get better understanding ?

def solve(nums1, nums2, k):
    nums1.sort()
    nums2.sort()
    
    temp = False
    idx = -1
    
    for i in range(len(nums1)):
        if nums1[i] != nums2[i]:
            if temp:
                return False
            temp = True
            idx = i
    
    if idx == -1 or abs(nums1[idx] - nums2[idx]) <= k:
        return True
    return False

# Test the function
nums1 = [5, 7, 11]
nums2 = [5, 5, 11]
k = 8
print(solve(nums1, nums2, k))

The output of the above code is ?

True

Example Walkthrough

Let's trace through the example step by step:

def solve_with_debug(nums1, nums2, k):
    print(f"Original: nums1 = {nums1}, nums2 = {nums2}")
    
    nums1.sort()
    nums2.sort()
    print(f"After sorting: nums1 = {nums1}, nums2 = {nums2}")
    
    temp = False
    idx = -1
    
    for i in range(len(nums1)):
        if nums1[i] != nums2[i]:
            print(f"Difference found at index {i}: {nums1[i]} != {nums2[i]}")
            if temp:
                return False
            temp = True
            idx = i
    
    difference = abs(nums1[idx] - nums2[idx]) if idx != -1 else 0
    print(f"Required change: {difference}, allowed range: {k}")
    
    return idx == -1 or difference <= k

# Test with example
nums1 = [5, 7, 11]
nums2 = [5, 5, 11]
k = 8
result = solve_with_debug(nums1, nums2, k)
print(f"Result: {result}")

Original: nums1 = [5, 7, 11], nums2 = [5, 5, 11]
After sorting: nums1 = [5, 7, 11], nums2 = [5, 5, 11]
Difference found at index 1: 7 != 5
Required change: 2, allowed range: 8
Result: True

Key Points

• Sorting ensures we compare elements in the same relative positions
• We can only modify one element from nums1
• The modification range is [-k, k], so the absolute difference must be ? k
• If arrays are already equal, no modification is needed

Conclusion

This solution efficiently checks if two arrays can be made equal by modifying a single element within a given range. The key insight is sorting both arrays first and ensuring only one difference exists that can be resolved within the allowed range.