53.Maximum Subarray

原题

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [-2,1,-3,4,-1,2,1,-5,4],
the contiguous subarray [4,-1,2,1] has the largest sum = 6.

More practice:
If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

思路

非常典型的DP问题。

子数组只会有两种操作:

  1. 如果总和比之前大就不停的添加新成员
  2. 如果总和比之前一次变小了就清空成员重新计数

于是只用记住历史最大值和数组总和最大值就好

代码

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class Solution {
public:
int maxSubArray(vector<int>& nums) {
int maxValue = INT_MIN;
int tempMax = 0;
for(int x:nums){
tempMax = max(tempMax + x,x);
maxValue = max(maxValue,tempMax);
}
return maxValue;
}
};