关于计算最大子序列的四种方法

最新推荐文章于 2022-06-10 09:30:05 发布

iMISaD

最新推荐文章于 2022-06-10 09:30:05 发布

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分类专栏：算法学习

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本文详细介绍了四种不同时间复杂度的算法，从O(N^3)到O(N)，并着重探讨了第四种算法的高效率与简洁性。通过实际代码示例，深入解析算法原理，提供学习与实践指南。

亮瞎眼啊。还是努力学吧。

//一共四种算法，算法一时间复杂度为O(N^3),二为O(N^2),三为O(NlogN),四为O(N)
 
//The first Algorithm
int MaxSubsequenceSum ( const int A[ ], int N )
{
	int ThisSum, MaxSum, i, j, k;
	
	MaxSum = 0;
	for( i = 0; i < N;i++ )
		for( j = 1; j < N; j++ )
		{
			ThisSum =0;
			for( k = i; k <= j; k++ )
				ThisSum += A[ k ];
				
			if(ThisSum > MaxSum )
				MaxSum = ThisSum; 
		}
	return MaxSum; 
} 

//The second Algorithm
int MaxSubSequenceSum( const int A[ ], int N )
{
	int ThisSum, MaxSum, i, j;
	MaxSum = 0;
	for( i = 0; i < N; i++ )
	{
		ThisSum = 0;
		for( j = i; j < N; j++)
		{
			ThisSum += A[ j ];
			
			if(ThisSum > MaxSum )
				MaxSum = ThisSum;
		}
	}
	return MaxSum;
}

//The third Algorithm
static int MaxSubSum(const int A[ ], int Left, int Right )
{
	int MaxLeftSum,MaxRightSum;
	int MaxLeftBorderSum, MaxRightBorderSum;
	int LeftBorderSum, RightBorderSum;
	int Center, i;
	
	if( Left == Right )   //base case 
		if( A[ Left ] > 0)
			return A[ Left ];
		else
			return 0;
			
	Center = ( Left + Right ) / 2;
	MaxLeftSum = MaxSubSum( A, Left,Center );
	MaxRightSum = MaxSubSum( A, Center+1, Right );
	
	MaxLeftBorderSum = 0;LeftBorderSum = 0;
	for( i = Center; i >=Left; i-- )
	{
		LeftBorderSum += A[ i ];
		if( LeftBorderSum > MaxLeftBorderSum )
			MaxLeftBorderSum = LeftBorderSum;
	}
	
	MaxRightBorderSum = 0;RightBorderSum = 0;
	for( i = Center + 1; i <= Right; i++ )
	{
		RightBorderSum += A[ i ];
		if( RightBorderSum > MaxRightBorderSum )
			MaxRightBorderSum = RightBorderSum;

	}
	
	return Max3( MaxLeftSum, MaxRightSum,MaxLeftBorderSum + MaxRightBorderSum);
}

int MaxSubsequenceSum( const int A[ ],int N )
{
	return MaxSubSum( A, 0, N-1);
}

//The forth Algorithm
int MaxSubsequenceSum( const int A[ ], int N )
{
	int ThisSum, MaxSum, j;
	
	ThisSum = MaxSum = 0;
	for( j = 0; j < N; j++ )
	{
		ThisSum += A[ j ];
		
		if( ThisSum > MaxSum )
			MaxSum = ThisSum;
		else if ( ThisSum < 0 )
			ThisSum = 0; 
	}
	return MaxSum;
}

最后一种算法不仅短小精悍，而且效率很高。。。继续努力吧。