Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
A subarray is a contiguous part of an array.
中文翻譯
給予一個整數陣列 nums,尋找一個值加總最大的相鄰子陣列 (至少包含一個數字) 並回傳其加總
一個子陣列指的是一個陣列中相連的部分
範例及題目限制
解題思路
這題最重要的就是相鄰這兩個字
所以我們的解決方法肯定是用迴圈來處理,而如何僅在一次迴圈中完成就很重要了 (壓低時間複雜度)
C# 解決方案
方案1
public class Solution {
public int MaxSubArray(int[] nums) {
int max = nums[0];
int tmp =0;
for(int i = 0;i<nums.Length;i++)
{
tmp+=nums[i];
if(tmp>max)
{
max = tmp;
}
if(tmp<0)
{
tmp = 0;
}
}
return max;
}
}
時間複雜度 : O(n)
在這個解決方法,我們用了陣列中的第一個數字來當一個暫定的變數 ➡ max,用來進行後續的比較
然後正常跑著遞迴,若tmp值大於當前max則取代
若tmp小於 0 則設為 0,意思其實就是加總值根本對最大值沒有幫助,故從下一個索引繼續判斷
Java解決方案
方案1
class Solution {
public int maxSubArray(int[] nums) {
int max = nums[0];
int tmp =0;
for(int i = 0;i<nums.length;i++)
{
tmp+=nums[i];
if(tmp>max)
{
max = tmp;
}
if(tmp<0)
{
tmp = 0;
}
}
return max;
}
}
Python3 解決方案
方案1
class Solution:
def maxSubArray(self, nums: List[int]) -> int:
max = nums[0]
tmp =0
for i in range(0,len(nums)):
tmp+=nums[i]
if(tmp>max):
max = tmp
if(tmp<0):
tmp = 0
return max
JavaScript 解決方案
方案1
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
var max = nums[0];
var tmp =0;
for(var i = 0;i<nums.length;i++)
{
tmp+=nums[i];
if(tmp>max)
{
max = tmp;
}
if(tmp<0)
{
tmp = 0;
}
}
return max;
};
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