leetcode 453. Minimum Moves to Equal Array Elements ( Python )

描述

Given a non-empty integer array of size n, find the minimum number of moves required to make all array elements equal, where a move is incrementing n - 1 elements by 1.

Example:

Input:
[1,2,3]

Output:
3

Explanation:
Only three moves are needed (remember each move increments two elements):

[1,2,3]  =>  [2,3,3]  =>  [3,4,3]  =>  [4,4,4]
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解析

根據題意，直接暴力算法會超時，換個思路，將這個數組中的元素，每次對 n-1 個數字加一，直到全部的數字都相等，計算總共操做了多少步，其實轉換一下思惟，要求結果，能夠每次對數組中的最大值減一，一直減到全部數字相等，操做的次數就是結果值，時間複雜度爲 O(1)，空間複雜度爲 O(1)。

解答

class Solution(object):
def minMoves(self, nums):
    """
    :type nums: List[int]
    :rtype: int
    """
    return sum(nums)-min(nums)*len(nums)                    	      
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運行結果

Runtime: 216 ms, faster than 98.21% of Python online submissions for Minimum Moves to Equal Array Elements.
Memory Usage: 12.9 MB, less than 57.89% of Python online submissions for Minimum Moves to Equal Array Elements.
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解析

根據題意，能夠經過觀察發現規律

長度 次數
 1  0
 2  1
 3  3
 4  6
 5  10
 6  15
 7  21
 8  28
 9  36
 10 45
 ...
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第 n 次的次數是第 n-1 次的次數加 n-1，時間複雜度爲 O(N)，空間複雜度爲 O(1)。

解答

class Solution:
    def minMoves(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        nums.sort()
        res = 0
        for num in nums:
            res += num - nums[0]
        return res
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運行結果

Runtime: 260 ms, faster than 14.85% of Python online submissions for Minimum Moves to Equal Array Elements.
Memory Usage: 12.9 MB, less than 71.05% of Python online submissions for Minimum Moves to Equal Array Elements.
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請做者吃狗果凍 支付寶

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