155 lines
4.4 KiB
C++
155 lines
4.4 KiB
C++
MaxSumTest.cpp - Various maximum subsequence sum algorithms
|
|
|
|
#include <iostream.h>
|
|
#include "vector.h"
|
|
|
|
/* START: Fig02_05.txt */
|
|
/**
|
|
* Cubic maximum contiguous subsequence sum algorithm.
|
|
*/
|
|
int maxSubSum1( const vector<int> & a )
|
|
{
|
|
/* 1*/ int maxSum = 0;
|
|
|
|
/* 2*/ for( int i = 0; i < a.size( ); i++ )
|
|
/* 3*/ for( int j = i; j < a.size( ); j++ )
|
|
{
|
|
/* 4*/ int thisSum = 0;
|
|
|
|
/* 5*/ for( int k = i; k <= j; k++ )
|
|
/* 6*/ thisSum += a[ k ];
|
|
|
|
/* 7*/ if( thisSum > maxSum )
|
|
/* 8*/ maxSum = thisSum;
|
|
}
|
|
|
|
/* 9*/ return maxSum;
|
|
}
|
|
/* END */
|
|
|
|
|
|
/* START: Fig02_06.txt */
|
|
/**
|
|
* Quadratic maximum contiguous subsequence sum algorithm.
|
|
*/
|
|
int maxSubSum2( const vector<int> & a )
|
|
{
|
|
/* 1*/ int maxSum = 0;
|
|
|
|
/* 2*/ for( int i = 0; i < a.size( ); i++ )
|
|
{
|
|
/* 3*/ int thisSum = 0;
|
|
/* 4*/ for( int j = i; j < a.size( ); j++ )
|
|
{
|
|
/* 5*/ thisSum += a[ j ];
|
|
|
|
/* 6*/ if( thisSum > maxSum )
|
|
/* 7*/ maxSum = thisSum;
|
|
}
|
|
}
|
|
|
|
/* 8*/ return maxSum;
|
|
}
|
|
/* END */
|
|
|
|
/**
|
|
* Return maximum of three integers.
|
|
*/
|
|
int max3( int a, int b, int c )
|
|
{
|
|
return a > b ? a > c ? a : c : b > c ? b : c;
|
|
}
|
|
|
|
/* START: Fig02_07.txt */
|
|
/**
|
|
* Recursive maximum contiguous subsequence sum algorithm.
|
|
* Finds maximum sum in subarray spanning a[left..right].
|
|
* Does not attempt to maintain actual best sequence.
|
|
*/
|
|
int maxSumRec( const vector<int> & a, int left, int right )
|
|
{
|
|
/* 1*/ if( left == right ) // Base case
|
|
/* 2*/ if( a[ left ] > 0 )
|
|
/* 3*/ return a[ left ];
|
|
else
|
|
/* 4*/ return 0;
|
|
|
|
/* 5*/ int center = ( left + right ) / 2;
|
|
/* 6*/ int maxLeftSum = maxSumRec( a, left, center );
|
|
/* 7*/ int maxRightSum = maxSumRec( a, center + 1, right );
|
|
|
|
/* 8*/ int maxLeftBorderSum = 0, leftBorderSum = 0;
|
|
/* 9*/ for( int i = center; i >= left; i-- )
|
|
{
|
|
/*10*/ leftBorderSum += a[ i ];
|
|
/*11*/ if( leftBorderSum > maxLeftBorderSum )
|
|
/*12*/ maxLeftBorderSum = leftBorderSum;
|
|
}
|
|
|
|
/*13*/ int maxRightBorderSum = 0, rightBorderSum = 0;
|
|
/*14*/ for( int j = center + 1; j <= right; j++ )
|
|
{
|
|
/*15*/ rightBorderSum += a[ j ];
|
|
/*16*/ if( rightBorderSum > maxRightBorderSum )
|
|
/*17*/ maxRightBorderSum = rightBorderSum;
|
|
}
|
|
|
|
/*18*/ return max3( maxLeftSum, maxRightSum,
|
|
/*19*/ maxLeftBorderSum + maxRightBorderSum );
|
|
}
|
|
|
|
/**
|
|
* Driver for divide-and-conquer maximum contiguous
|
|
* subsequence sum algorithm.
|
|
*/
|
|
int maxSubSum3( const vector<int> & a )
|
|
{
|
|
return maxSumRec( a, 0, a.size( ) - 1 );
|
|
}
|
|
/* END */
|
|
|
|
|
|
/* START: Fig02_08.txt */
|
|
/**
|
|
* Linear-time maximum contiguous subsequence sum algorithm.
|
|
*/
|
|
int maxSubSum4( const vector<int> & a )
|
|
{
|
|
/* 1*/ int maxSum = 0, thisSum = 0;
|
|
|
|
/* 2*/ for( int j = 0; j < a.size( ); j++ )
|
|
{
|
|
/* 3*/ thisSum += a[ j ];
|
|
|
|
/* 4*/ if( thisSum > maxSum )
|
|
/* 5*/ maxSum = thisSum;
|
|
/* 6*/ else if( thisSum < 0 )
|
|
/* 7*/ thisSum = 0;
|
|
}
|
|
|
|
/* 8*/ return maxSum;
|
|
}
|
|
/* END */
|
|
|
|
/**
|
|
* Simple test program.
|
|
*/
|
|
int main( )
|
|
{
|
|
vector<int> a( 8 );
|
|
a[ 0 ] = 4; a[ 1 ] = -3; a[ 2 ] = 5; a[ 3 ] = -2;
|
|
a[ 4 ] = -1; a[ 5 ] = 2; a[ 6 ] = 6; a[ 7 ] = -2;
|
|
int maxSum;
|
|
|
|
maxSum = maxSubSum1( a );
|
|
cout << "Max sum is " << maxSum << endl;
|
|
maxSum = maxSubSum2( a );
|
|
cout << "Max sum is " << maxSum << endl;
|
|
maxSum = maxSubSum3( a );
|
|
cout << "Max sum is " << maxSum << endl;
|
|
maxSum = maxSubSum4( a );
|
|
cout << "Max sum is " << maxSum << endl;
|
|
|
|
return 0;
|
|
}
|