文章目录
题目描述
给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。
示例:
输入: [-2,1,-3,4,-1,2,1,-5,4],
输出: 6
解释: 连续子数组 [4,-1,2,1] 的和最大，为 6。
进阶:
如果你已经实现复杂度为 O(n) 的解法，尝试使用更为精妙的分治法求解。
来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/maximum-subarray
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
解题思路
本题目和之前的一篇《LeetCode系列6：求乘积最大子数组》基本类似，把求解乘积换成了求和。同样解法多样。
暴力破解
通过求出所有子数组，然后逐个求和。这是最初的解题思想，事实证明，有很大缺陷，时间复杂度O(n^2)，在leetcode上超时，将代码贴出来如下。
class Solution {
public:
int maxSubArray(vector<int>& nums) {
vector<vector<int>> v1;
for (int i = 0; i < nums.size(); i++)
{
vector<int> v2;
for (int j = i; j < nums.size(); j++)
{
v2.push_back(nums[j]);
v1.push_back(v2);
}
}
int intMax = INT_MIN;
for (int i = 0; i < v1.size(); i++)
{
intMax=max(accumulate(v1[i].begin(), v1[i].end(),0),intMax);
}
return intMax;
}
};
超时测试用例
[-64,78,56,10,-8,26,-18,47,-31,75,89,13,48,-19,-69,36,-39,55,-5,-4,-15,-37,-27,-8,-5,35,-51,83,21,-47,46,33,-91,-21,-57,0,81,1,-75,-50,-23,-86,39,-98,-29,69,38,32,24,-90,-95,86,-27,-23,-22,44,-88,3,27,9,55,-50,-80,40,5,-61,-82,-14,40,-58,35,93,-68,-26,94,3,-79,9,-88,21,19,-84,7,91,-8,84,12,-19,-13,-83,66,-80,-34,62,59,48,-98,53,-66,18,94,46,11,-73,96,-18,6,-83,91,17,38,10,9,-78,-22,77,83,89,-42,-30,-94,-98,-34,-51,63,-97,96,64,55,-93,-41,27,52,69,53,26,-71,-64,42,-80,52,-43,6,-62,-21,83,-85,-38,49,-50,8,55,-72,74,80,90,53,53,32,-15,36,90,-88,-34,37,41,91,65,76,33,61,5,90,-33,42,-54,-73,34,-16,75,83,91,7,-89,42,-36,77,-5,-83,9,80,53,-23,68,-81,90,10,-90,55,-14,19,-7,91,-14,59,33,31,62,-33,-85,37,-73,83,-78,-86,25,-15,91,97,2,-23,54,-68,53,22,-73,43,-68,-87,-25,18,31,67,-14,94,3,-81,25,-35,-37,17,79,-34,-23,-99,-43,-98,-38,-52,75,63,1,29,71,-68,-71,74,51,-40,86,-73,54,-5,70,-60,-11,-49,-64,90,-8,-25,-16,-52,40,60,-75,96,39,-13,-79,14,-73,22,-79,75,30,-51,49,-19,-15,36,-16,-60,-69,-68,-21,-4,-18,-9,-14,50,65,70,75,-17,30,99,-44,-31,-14,-46,60,-10,52,80,-35,-18,-94,-86,62,-10,49,-53,6,56,-45,62,-48,36,-47,15,-37,-81,-15,-62,-22,91,-85,33,-62,-23,86,97,66,15,54,-69,96,36,-55,36,-97,70,82,9,4,-63,-29,32,49,23,-53,88,18,8,-96,72,-23,-82,6,14,-6,-31,-12,-39,61,-58,-32,57,77,12,-7,56,-40,-48,-35,40,-35,12,-28,90,-87,-4,79,30,80,82,-20,-43,76,62,70,-30,-92,-42,7,68,-24,75,26,-70,-36,95,86,0,-52,-49,-60,12,63,-11,-20,75,84,-41,-18,41,-82,61,98,70,0,45,-83,8,-96,24,-24,-44,-24,-98,-14,39,97,-51,-60,-78,-24,-44,10,-84,44,89,67,5,-75,-73,-53,-81,64,-55,88,-35,89,-94,72,69,29,-52,-97,81,-73,-35,20,-99,13,36,98,65,69,8,81,13,-25,25,95,-1,51,-58,-5,16,-37,-17,57,-71,-35,29,75,70,53,77,51,79,-58,-51,56,31,84,54,-27,30,-37,-46,-56,14,56,-84,89,7,-43,-16,99,19,67,56,24,-68,-38,-1,-97,-84,-24,53,71,-6,-98,28,-98,63,-18,-25,-7,21,5,13,-88,-39,28,-98,68,61,-15,44,-43,-71,1,81,-39,62,-20,-60,54,33,69,26,-96,48,-69,-94,11,-11,-20,80,87,61,-29,98,-77,75,99,67,37,-38,11,93,-10,88,51,27,28,-68,66,-41,41,36,84,44,-16,91,49,71,-19,-94,28,-32,44,75,-57,66,51,-80,10,-35,-19,97,-65,70,63,86,-2,-9,94,-59,26,35,76,11,-21,-63,-21,-94,84,59,87,13,-96,31,-35,-53,-26,-84,-34,60,-20,23,58,15,-7,21,-22,67,88,-28,-91,14,-93,61,-98,-38,75,-19,-56,59,-83,-91,-51,-79,16,14,-56,90,6,-14,27,63,-91,-15,-22,-22,82,32,-54,47,-96,-69,-61,86,91,-60,-75,43,-3,-31,3,-9,-23,28,11,69,-81,31,59,25,-83,-36,-12,-75,48,42,-21,8,-26,24,-68,-23,31,-30,-60,0,-13,-36,-57,60,32,22,-49,85,-49,38,55,-54,-31,-9,70,-38,54,-65,-37,-20,76,42,64,-73,-57,95,-20,74,-57,19,-49,29,83,-7,-11,-8,-84,40,-45,-57,-45,86,-12,24,-46,-64,62,-91,-30,-74,-35,-76,44,-94,-73,86,77,7,37,-80,-74,87,48,85,-19,-85,-45,-27,31,9,-8,85,-28,79,-14,25,91,-51,10,-61,-49,74,-38,94,56,-12,57,34,71,-5,53,74,-18,-21,59,39,-30,90,-88,-99,-24,3,62,47,-40,-51,-27,-49,-26,82,-11,1,34,27,-5,-10,92,-48,-99,63,23,31,14,-94,-90,-49,44,-44,-59,33,-44,17,-64,-82,-36,-28,-57,13,0,-7,-4,88,70,-93,-7,-35,-4,-15,-6,-26,-75,93,-95,39,98,90,66,20,-54,-93,-47,-22,0,-35,-28,41,14,-8,-46,-86,84,26,-98,55,32,-29,96,-94,32,-33,-21,57,-39,-17,-27,-64,-50,-61,55,-28,-78,84,49,22,-73,-79,-37,40,12,-7,53,-26,-80,31,-94,51,-97,-98,56,34,-54,-88,-32,-17,-29,17,18,20,32,-49,91,54,-65,40,-47,-39,38,-8,-99,-73,84,30,0,-96,-38,5,32,-36,-16,-35,74,29,-23,-80,-88,47,36,29,-32,-54,79,-64,76,91,53,-71,-71,-9,-3,-93,17,-19,36,94,-38,97,-1,70,-62,82,-65,-87,11,11,-68,-1,-41,44,-71,3,89]
贪心法
遍历数组，逐个相加，如果遇到和为负数，置0，继续往下加.
class Solution
{
public:
int maxSubArray(vector<int> &nums)
{
int re = INT_MIN;
int numsSize = int(nums.size());
int sum = 0;
for (int i = 0; i < numsSize; i++)
{
sum += nums[i];
re = max(re, sum);
//如果sum < 0，重新开始找子序串
if (sum < 0)
{
sum = 0;
}
}
return re;
}
};
动态规划
另外还可以通过动态规划求解，后续继续补充。