#include <iostream>
#include <vector>
using namespace std;

/**
 * Cubic maximum contiguous subsequence sum algorithm.
 */
int maxSubSum1( const vector<int> & a )
{
    int maxSum = 0;

    for( int i = 0; i < a.size( ); i++ )
        for( int j = i; j < a.size( ); j++ )
        {
            int thisSum = 0;

            for( int k = i; k <= j; k++ )
                thisSum += a[ k ];

            if( thisSum > maxSum )
                maxSum   = thisSum;
        }

    return maxSum;
}


/**
 * Quadratic maximum contiguous subsequence sum algorithm.
 */
int maxSubSum2( const vector<int> & a )
{
    int maxSum = 0;

    for( int i = 0; i < a.size( ); i++ )
    {
        int thisSum = 0;
        for( int j = i; j < a.size( ); j++ )
        {
            thisSum += a[ j ];

            if( thisSum > maxSum )
                maxSum = thisSum;
        }
    }

    return maxSum;
}

/**
 * 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 )
{
    if( left == right )  // Base case
        if( a[ left ] > 0 )
            return a[ left ];
        else
            return 0;

    int center = ( left + right ) / 2;
    int maxLeftSum  = maxSumRec( a, left, center );
    int maxRightSum = maxSumRec( a, center + 1, right );

    int maxLeftBorderSum = 0, leftBorderSum = 0;
    for( int i = center; i >= left; i-- )
    {
        leftBorderSum += a[ i ];
        if( leftBorderSum > maxLeftBorderSum )
            maxLeftBorderSum = leftBorderSum;
    }

    int maxRightBorderSum = 0, rightBorderSum = 0;
    for( int j = center + 1; j <= right; j++ )
    {
        rightBorderSum += a[ j ];
        if( rightBorderSum > maxRightBorderSum )
            maxRightBorderSum = rightBorderSum;
    }

    return max3( maxLeftSum, maxRightSum,
                    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 );
}

/**
 * Linear-time maximum contiguous subsequence sum algorithm.
 */
int maxSubSum4( const vector<int> & a )
{
    int maxSum = 0, thisSum = 0;

    for( int j = 0; j < a.size( ); j++ )
    {
        thisSum += a[ j ];

        if( thisSum > maxSum )
            maxSum = thisSum;
        else if( thisSum < 0 )
            thisSum = 0;
    }

    return maxSum;
}

/**
 * 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;
}