LeetCode 453题解法输出偏差1问题排查——使数组所有元素相等的最小操作次数

安全阿岳

2026-4-27

LeetCode 453: Min Moves to Equal Array Elements - Debugging Off-by-One Error

Hey there, let's break down what's going wrong with your solution and fix it. First, let's recap your situation: you've written a Python solution for LeetCode 453 that works for most test cases, but fails on a large input with an off-by-one error.

Your Current Code

Here's the code you shared:

class Solution(object):
    def minMoves(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        max_number = max(nums)
        min_number = min(nums)
        total_count = max_number - min_number
        _nums = nums[:]
        while max_number - min_number != 1 and (max_number - min_number != 0):
            diff = max_number - min_number
            max_list = []
            for i, n in enumerate(_nums):
                if n != max_number:
                    _nums[i] += diff
                else:
                    max_list.append(i)
            if len(max_list) > 1:
                # if there are duplicate max_numbers
                for i in max_list[1:]:
                    _nums[i] += diff
            max_number = max(_nums)
            min_number = min(_nums)
        if max_number - min_number == 1:
            total_count += 1
        else:
            total_count += (max_number - min_number)
        return total_count

The Failing Test Case

You mentioned this large input causes an off-by-one error:

[83,-14,77,15,93,35,86,-8,-51,-79,62,-73,-10,-41,63,26,40,-74,72,36,-89,68,67,-71,82,30,-38,23,-33,35,29,-98,-78,-42,-31,67,93,-44,-89,-58,-71,73,-79,19,84,37,98,24,15,70,-87,26,-9,80,56,-27,-38,70,96,-19,5,25,-16,27,36,5,-54,29,13,-43,24,-5,82,45,-86,67,-66,64,-57,50,-13,-92,-24,78,88,84,-97,-49,54,99,32,-40,-24,68,39,-88,-74,86,-6,39,95,70,-66,78,-33,-99,-3,2,17,-8,-48,56,1,-20,-14,-59,-35,-11,-56,-81,-60,29,-69,17,-3,71,-19,-25,9,27,67,-44,-3,53,86,65,6,-17,-81,-76,28,-29,32,-71,3,-81,-30,68,8,15,40,49,96,23,-82,-55,-54,-49,21,55,79,-12,64,-72,-59,50,93,0,-66,64,24,14,87,-44,43,-9,-73,65,-41,36,-68,51,-63,-72,-25,-93,-26,21,-42,95,-71,-63,-65,93,-82,-72,43,-89,28,29,76,-96,-57,63,-87,38,-94,-60,4,-82,28,-12,69,17,17,96,24,43,-30,83,-10,-1,72,25,-56,90,5,39,54,86,-31,-18,42,-36,97,7,55,-96,48,-89,-78,-72,-1,43,46,68,40,-78,11,-90,-95,-99,-39,30,-22,5,20,36,-56,-74,22,-35,8,-84,-18,-42,24,-63,-38,-76,-100,-64,-48,-1,79,50,-32,-29,73,31,-19,30,33,-6,-40,63,99,81,-1,96,59,73,-87,-32,90,-5,26,-34,-16,40,-10,-16,76,42,36,7,-55,56,79,-82,-13,-88,48,72,-41,-91,36,-90,42,87,-94,1,13,72,21,-45,-81,99,21,4,39,-89,40,-33,5,-72,27,50,84,-42,20,-76,-78,-31,96,-19,-70,-16,-8,72,-28,-50,-75,85,-78,-1,-60,-58,-2,13,-2,90,24,90,-91,81,-81,36,32,55,94,-96,79,69,-27,76,-50,-45,-40,42,79,-16,93,-95,-79,67,4,-87,61,54,26,-41,44,-98,-98,6,84,-79,-58,-32,28,89,-28,8,58,-2,-64,-92,53,-52,3,33,33,-52,-10,54,67,46,68,29,0,-54,88,97,-51,90,3,-67,63,-3,-47,-8,-14,25,52,96,75,88,57,29,-64,-40,-86,21,-40,4,-72,-73,-50,48,56,2,94,-3,-1,-57,-61,-98,-72,-97,0,-19,-53,38,59,51,35,34,39,-8,-85,27,4,-71,-51,64,-15,-71,43,35,77,0,-62,71,49,-11,67,88,-8,95,43,44,-71,90,-18,40,41,69,-74,-68,-39,-58,60,17,-77,61,-19,9,90,-75,96,67,-23,-66,-10,-74,24,-43,-86,68,-95,58,12,86,0,46,26,94,16,52,78,29,46,-10,-53,70,-49,-20,-69,93,-43,-73,12,-14,-86,55,12,-10,-88,-21,-90,69,89,-26,55,-59,-80,-67,87,-12,38,66,70,-16,-44,-83,-94,-40,-51,-63,-95,-41,-83,18,45,83,-27,-42,-27,-63,-11,-17,-93,-22,57,14,-29,29,0,-41,-82,-62,-75,88,-26,-67,57,-19,-7,58,-30,-1,-83,-61,69,63,-78,94,73,-53,-69,-38,-18,90,-8,91,-43,15,21,57,74,-9,47,51,-69,-79,37,40,-46,-70,-2,25,-19,16,16,-98,-69,39,96,-96,38,80,-82,-79,70,-38,-88,79,77,-15,36,4,76,-17,-93,59,-43,44,-1,11,27,50,-64,60,-82,5,63,-51,-56,11,-95,34,-9,75,55,-86,89,68,93,18,-95,-18,-78,82,17,-70,-7,74,26,93,-14,-47,43,-26,-86,13,79,77,62,75,-12,19,10,32,-6,-83,46,-65,37,-9,53,43,73,28,25,-9,10,-82,-83,-64,63,-45,-10,-42,30,4,71,-39,-67,-15,89,-27,-96,-49,-95,-50,-32,3,-15,-94,95,-61,49,20,67,-74,63,-23,96,81,-35,60,-64,55,70,18,-89,42,32,96,79,21,-30,84,72,-73,-66,-60,-17,-28,98,-70,-37,47,50,-70,73,14,-41,22,-53,24,-18,-65,-68,-96,54,-57,-2,-14,-60,-22,59,-38,-38,-17,-59,-52,23,24,-28,22,54,35,-79,-43,65,47,71,76,-31,-82,1,3,-47,33,7,59,28,-94,97,20,-16,8,34,-2,91,76,-2,15,-48,71,89,59,6,-90,-84,-76,9,39,-100,78,9,-47,-19,14,38,89,-74,-33,47,-77,87,-69,32,22,-19,-25,-50,79,90,-46,50,31,-87,-43,-6,81,-19,-97,20,-67,82,81,-13,-85,-4,-75,-96,22,-8,51,-3,-68,34,81,6,-85,-43,8,95,99,62,-3,-17,76,54,77,9,87,32,82,-79,-34,63,-40,-18,-89,-15,-14,-15,30,90,83,14,-24,16,-80,-8,25,28,-61,25,-10,36,60,-82,-57,37,28,82,-79,10,55,-12,-75,-85,70,-63,-47,-92,22,83,50,-43,-3,-73,26,-31,-29,-49,49,10,28,-61,98,-12,-90,93,77,-10,76,99,52,31,-13,77,-1,-43,66,52,-83,-59,35,68,-2,84,95,76,-95,-34,-72,54,28,8,93,-22,97,55,-28,74,-55,-100,25,97,-17,-88,27,82,-79]

Your Approach

You tried to simulate the operations by incrementing n-1 elements to close the gap between min and max values, using the example [1,2,3,100] to walk through your logic:

Step 1: Add 99 to all elements except 1 → [100,101,102,100], total moves = 99
Step 2: Add 2 to all elements except one 100 → [102,103,102,102], total moves = 99+2=101
Step3: Add 1 to make all elements equal → total moves=102

While this example works, your simulation approach has two big issues:

Efficiency: For large arrays (like your failing test case), this loop runs many times, leading to slow performance.
Logic Errors: Your handling of multiple max values and the final condition (max_number - min_number ==1) can lead to off-by-one mistakes, especially in edge cases with duplicates or negative numbers.

The Correct Mathematical Insight

Here's the key trick you're missing: Incrementing n-1 elements by 1 is equivalent to decrementing 1 element by 1.

Think about it: if you have array [a,b,c] and you increment two elements by 1, the relative difference between elements is the same as if you'd decremented the largest element by 1. Instead of making all elements equal to the max, you can make all elements equal to the min, and count how many decrements (equivalent to your increments) are needed.

The total number of moves is simply the sum of the differences between each element and the minimum value in the array. Mathematically, that's:
sum(nums) - min(nums) * len(nums)

For your example [1,2,3,100]:
sum = 1+2+3+100=106, min=1, len=4 → 106 - 1*4 = 102, which matches your manual calculation.

The Fixed Solution

This approach is O(n) time, O(1) space, and completely avoids simulation errors:

class Solution(object):
    def minMoves(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        min_num = min(nums)
        return sum(num - min_num for num in nums)
        # Or the more efficient version (avoids creating a temporary list):
        # return sum(nums) - min_num * len(nums)

Why Your Code Failed

Your simulation logic has a flaw in how it handles multiple max values and the final loop condition. For example:

When you have multiple max values, your code adds diff to all non-max elements, then adds diff to all but one max element. This changes the relative gaps in a way that doesn't perfectly align with the equivalent decrement approach, leading to an off-by-one error in large, complex arrays.
The final check for max_number - min_number ==1 assumes you only need one more move, but in some cases, this might not account for how the previous loop iterations altered the array.

By switching to the mathematical approach, you eliminate all these edge case issues and get a much cleaner solution.

内容的提问来源于stack exchange，提问作者Suhail Gupta

LeetCode 453题解法输出偏差1问题排查——使数组所有元素相等的最小操作次数

Your Current Code #

The Failing Test Case #

Your Approach #

The Correct Mathematical Insight #

The Fixed Solution #