/**
* The importance of proper indentation:
* Proper indentation clearly shows the nesting relationship between the code blocks.
* It may help the programmer to debug the program when a syntax or logical error arises.
* Principle 1: Within a block, all statements should be indented.
* Principle 2: Two statements at the same level within a block should be indented the same.
* That is, all statements belonging to the same block should be indented the same way.
* The beginning brace and the ending brace of a block should be indented the same.
* In the following sample program (particularly in maxSubSum1( ) ), different levels are highlighted with different color.
* level 1
* level 2
* level 3
* level 4
* level 5
* level 6
**/
import java.util.Random;
public final class MaxSumTest
{
static private int seqStart = 0;
static private int seqEnd = -1;
/**
* Cubic maximum contiguous subsequence sum algorithm.
* seqStart and seqEnd represent the actual best sequence.
*/
public static int maxSubSum1( int [ ] a )
{
int maxSum = 0;
for( int i = 0; i < a.length; i++ )
for( int j = i; j < a.length; j++ )
{
int thisSum = 0;
for( int k = i; k <= j; k++ )
thisSum += a[ k ];
if( thisSum > maxSum )
{
maxSum = thisSum;
seqStart = i;
seqEnd = j;
}
}
return maxSum;
}
/**
* Quadratic maximum contiguous subsequence sum algorithm.
* seqStart and seqEnd represent the actual best sequence.
*/
public static int maxSubSum2( int [ ] a )
{
int maxSum = 0;
for( int i = 0; i < a.length; i++ )
{
int thisSum = 0;
for( int j = i; j < a.length; j++ )
{
thisSum += a[ j ];
if( thisSum > maxSum )
{
maxSum = thisSum;
seqStart = i;
seqEnd = j;
}
}
}
return maxSum;
}
/**
* Linear-time maximum contiguous subsequence sum algorithm.
* seqStart and seqEnd represent the actual best sequence.
*/
public static int maxSubSum3( int [ ] a )
{
int maxSum = 0;
int thisSum = 0;
for( int i = 0, j = 0; j < a.length; j++ )
{
thisSum += a[ j ];
if( thisSum > maxSum )
{
maxSum = thisSum;
seqStart = i;
seqEnd = j;
}
else if( thisSum < 0 )
{
i = j + 1;
thisSum = 0;
}
}
return maxSum;
}
/**
* Recursive maximum contiguous subsequence sum algorithm.
* Finds maximum sum in subarray spanning a[left..right].
* Does not attempt to maintain actual best sequence.
*/
private static int maxSumRec( int [ ] a, int left, int right )
{
int maxLeftBorderSum = 0, maxRightBorderSum = 0;
int leftBorderSum = 0, rightBorderSum = 0;
int center = ( left + right ) / 2;
if( left == right ) // Base case
return a[ left ] > 0 ? a[ left ] : 0;
int maxLeftSum = maxSumRec( a, left, center );
int maxRightSum = maxSumRec( a, center + 1, right );
for( int i = center; i >= left; i-- )
{
leftBorderSum += a[ i ];
if( leftBorderSum > maxLeftBorderSum )
maxLeftBorderSum = leftBorderSum;
}
for( int i = center + 1; i <= right; i++ )
{
rightBorderSum += a[ i ];
if( rightBorderSum > maxRightBorderSum )
maxRightBorderSum = rightBorderSum;
}
return max3( maxLeftSum, maxRightSum,
maxLeftBorderSum + maxRightBorderSum );
}
/**
* Return maximum of three integers.
*/
private static int max3( int a, int b, int c )
{
return a > b ? a > c ? a : c : b > c ? b : c;
}
/**
* Driver for divide-and-conquer maximum contiguous
* subsequence sum algorithm.
*/
public static int maxSubSum4( int [ ] a )
{
return a.length > 0 ? maxSumRec( a, 0, a.length - 1 ) : 0;
}
public static void getTimingInfo( int n, int alg )
{
int [] test = new int[ n ];
long startTime = System.currentTimeMillis( );;
long totalTime = 0;
int i;
for( i = 0; totalTime < 4000; i++ )
{
for( int j = 0; j < test.length; j++ )
test[ j ] = rand.nextInt( 100 ) - 50;
switch( alg )
{
case 1:
maxSubSum1( test );
break;
case 2:
maxSubSum2( test );
break;
case 3:
maxSubSum3( test );
break;
case 4:
maxSubSum4( test );
break;
}
totalTime = System.currentTimeMillis( ) - startTime;
}
System.out.println( "Algorithm #" + alg + "\t"
+ "N = " + test.length
+ "\ttime = " + ( totalTime * 1000 / i ) + " microsec" );
}
private static Random rand = new Random( );
/**
* Simple test program.
*/
public static void main( String [ ] args )
{
int a[ ] = { 4, -3, 5, -2, -1, 2, 6, -2 };
int maxSum;
maxSum = maxSubSum1( a );
System.out.println( "Max sum is " + maxSum + "; it goes"
+ " from " + seqStart + " to " + seqEnd );
maxSum = maxSubSum2( a );
System.out.println( "Max sum is " + maxSum + "; it goes"
+ " from " + seqStart + " to " + seqEnd );
maxSum = maxSubSum3( a );
System.out.println( "Max sum is " + maxSum + "; it goes"
+ " from " + seqStart + " to " + seqEnd );
maxSum = maxSubSum4( a );
System.out.println( "Max sum is " + maxSum );
// Get some timing info
for( int n = 10; n <= 1000000; n *= 10 )
for( int alg = 4; alg >= 1; alg-- )
{
if( alg == 1 && n > 50000 )
continue;
getTimingInfo( n, alg );
}
}
}