子数组的最大和

public class SubarrayMax {
	
	
	public static void main(String[] args)
	{
		int[] a = {8,-1,-1,5,3,2,8,-9};
		
		System.out.println(method1(a,a.length));
		System.out.println(method2(a,a.length));
		System.out.println(method3(a,a.length));
		
		System.out.println(method4(a,0,a.length-1));
	}
	
	
	//分治思想
	public static int method4(int a[],int left,int right){  
	    if(left==right){  
	        return max(a[left],0);  
	    }  
	    int middle=(left+right)/2;  
	    //求(A[0],...A[n/2-1])中子数组包含A[n/2-1]的最大值  
	    int lmaximum=0;  
	    int lsum=0;  
	    for(int i=middle;i>=left;i--){  
	        lsum+=a[i];  
	        if(lsum>lmaximum)  
	            lmaximum=lsum;  
	    }  
	    //求(A[n/2],...,A[n-1])中子数组包含A[n/2]的最大值  
	    int rmaximum=0;  
	    int rsum=0;  
	    for(int i=middle+1;i<=right;i++){  
	        rsum+=a[i];  
	        if(rsum>rmaximum)  
	            rmaximum=rsum;  
	    }  
	    return max(lmaximum+rmaximum,max(method4(a,left,middle),method4(a,middle+1,right)));  
	} 
	
	
	public static int method3(int[] a,int n)
	{
		int nstart = a[n-1];
		int nall = a[n-1];
		
		
		for(int i=n-2;i>=0;i--)
		{
			
			if(nstart<0)
				nstart = 0;
			nstart +=a[i];
			
			if(nstart>nall)
				nall = nstart;
		}
		
		return nall;
	}
	
	//start 包含a[i]的最大值
	//all 最大值
	public static int method1(int a[],int n)
	{
		
		int[] start = new int[n];
		int[] all = new int[n];
		
		start[n-1] = a[n-1];
		all[n-1] = a[n-1];
		
		for(int i=n-2;i>=0;i--)
		{
			start[i] = max(a[i],a[i]+start[i+1]);
			all[i] = max(start[i],all[i+1]);
		}
		
		return all[0];
		
	}
	
	
	//节省空间
	public static int method2(int[] a,int n)
	{
		int nstart = a[n-1];
		int nall = a[n-1];
		
		for(int i=n-2;i>=0;i--)
		{
			nstart = max(a[i],nstart+a[i]);
			nall = max(nstart,nall);
		}
		
		return nall;
	}

	
	
	
	

	private static int max(int i, int j) {
		return i>j?i:j;
	}
}