Leetcode#53 Maximum Subarray

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

.

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DIfficulty:Medium

非常经典的问题

解法一，用分治法做，复杂度较高，可AC

int gen(vector<int>& nums,int start,int en){
int temp = nums[start],sum = 0,temp1 = start;

if(start==en)
{
return nums[start];
}

if(start>en)
return -2147483648;
for(int i = start;i<=en;i++)
{
sum = sum + nums[i];
if(nums[i]<temp)
{
temp = nums[i];
temp1 = i;
}
}
int ans;
int leftMax = -2147483648, rightMax = -2147483648;
int sum1 = 0;
for (int i = temp1; i >= start; i--)
{
sum1 += nums[i];
if (sum1 > leftMax)
leftMax = sum1;
}
sum1 = 0;
for (int i = temp1+1; i <=en; i++)
{
sum1 += nums[i];
if (sum1 > rightMax)
rightMax = sum1;
}

if (leftMax < 0 || rightMax < 0)
sum1 = max(leftMax, rightMax);
else
sum1 = leftMax + rightMax;
ans = max(gen(nums,start,temp1-1),gen(nums,temp1+1,en));
ans = max(sum,ans);
ans = max(ans,sum1);
return ans;
}

int maxSubArray(vector<int>& nums) {
int len = nums.size();
int ans;
ans = gen(nums,0,len-1);
return ans;

}

解法二：DP作法，看了题解才理解，十分牛逼。
其中Sum表示之前的数组值之和，若这个值小于0的则说明对后面无贡献，因此清0.

int maxSubArray(vector<int>& nums) {
int len = nums.size();
int sum = nums[0] , maxSum = nums[0];
for(int i = 1; i < len; i++){
if(sum < 0) sum = 0;
sum += nums[i];
maxSum = max(maxSum, sum);
}
return maxSum;
}