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