C++ Programming Code Examples
C++ > Data Structures and Algorithm Analysis in C++ Code Examples
Various maximum subsequence sum algorithms
/* Various maximum subsequence sum algorithms */
#include <iostream.h>
#include "vector.h"
/**
* 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 */
/**
* 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;
}
/**
* 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 */
/**
* 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;
}
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