最大子列和问题-4种解法

1.暴力求解

#include <bits/stdc++.h>
using namespace std;
int main()
{
	int n;
	int a[100001];
	int maxsum=0,sum;
	int i,j,k;
	cin>>n;
	for(i=0;i<n;i++)
		cin>>a[i];
	for(i=0;i<n;i++)
		for(j=i;j<n;j++)
		{
			sum=0;
			for(k=i;k<=j;k++)
			{
				sum+=a[k];	
			}
			if(sum>maxsum)
				maxsum=sum;
		}
	cout<<maxsum<<endl;
	return 0;
} 

2.稍稍改进

//稍稍改进 
#include <bits/stdc++.h>
using namespace std;
int main()
{
	int n;
	int a[100001];
	int maxsum=0,sum;
	int i,j,k;
	cin>>n;
	for(i=0;i<n;i++)
		cin>>a[i];
	for(i=0;i<n;i++)
	{
		sum=0;
		for(j=i;j<n;j++)
		{
			
			sum+=a[j];         //避免重复计算 
			
			if(sum>maxsum)
				maxsum=sum;
		}
	}
	cout<<maxsum<<endl;
	return 0;
} 

3.分治法

//分治法
#include <iostream>
using namespace std;

int maxcross(int a[],int left,int mid,int right)
{
	
	int leftsum=0,rightsum=0,sum=0;
	int i;
	for(i=mid;i>=left;i--)
	{
		sum+=a[i];
		if(sum>leftsum)
			leftsum=sum;
	}
	sum=0;
	for(i=mid+1;i<=right;i++)
	{
		sum+=a[i];
		if(sum>rightsum)
			rightsum=sum;
	}
	return rightsum+leftsum;
}
int max(int x,int y,int z)
{
	if(x>=y&&x>=z)
		return x;
	else if(y>=x&&y>=z)
		return y;
	else if(z>=y&&z>=x)
		return z;

}
int maxsubsequencesum(int a[],int left,int right)
{

	if(left==right)
	{	
		if(a[left]>0) return a[left];	
		else return 0;
	}

	int mid=(left+right)/2;
	int x,y,z;
	x=maxsubsequencesum(a,left,mid);
	y=maxsubsequencesum(a,mid+1,right);
	z=maxcross(a,left,mid,right);
	return max(x,y,z);

}


int main()
{
	int n;
	int i;
	int a[100001];
	cin>>n;
	for(i=0;i<n;i++)
		cin>>a[i];
	cout<<maxsubsequencesum(a,0,n-1)<<endl;
	return 0;
} 

4.在线处理

#include <stdio.h>
int main()
{
	int n;
	int a[100001];
	int sum=0;
	int max=0;
	int i;
	scanf("%d",&n);
	for(i=0;i<n;i++)
	{
		scanf("%d",&a[i]);
	}
	for(i=0;i<n;i++)
	{
		sum+=a[i];
		if(sum<0)
			sum=0;
		if(sum>max)
			max=sum;
		
	}
	printf("%d",max);
	return 0;
}