2.Dynamic Programming on Stolen Values【dp】

Problem: There are  n houses built in a line, each of which contains some value in it. A thief is going to steal the maximal value in these houses, but he cannot steal in two adjacent houses because the owner of a stolen house will tell his two neighbors on the left and right side. What is the maximal stolen value?

For example, if there are four houses with values {6, 1, 2, 7}, the maximal stolen value is 13 when the first and fourth houses are stolen.

My Code:

#include <iostream>

#include <string.h>

using namespace std;





int dp[100];



int main()

{

	memset(dp,0,sizeof(dp));

	const int len=6;

	int a[len]={6,1,33,7,11,13};



	for(int i=0;i<len;i++)

	{

		if(i<2)

		{

			if(i==0)

				dp[i]=a[i];

			else if(i==1)

				dp[i]=a[i]>a[i-1]?a[i]:a[i-1];

		}

		else

		{

			dp[i]=dp[i-2]+a[i]>dp[i-1]?dp[i-2]+a[i]:dp[i-1];

		}



	}

	cout<<dp[len-1]<<endl;

	return 0;

}

Harry He:

Analysis: A function  f( i) is defined to denote the maximal stolen value from the first house to the  i^thhouse, and the value contained in the  i^th house is denoted as  v_i. When the thief reaches the  i^thhouse, he has two choices: to steal or not. Therefore,  f( i) can be defined with the following equation:

It would be much more efficient to calculate in bottom-up order than to calculate recursively. It looks like a 1D array with size  n is needed, but actually it is only necessary to cache two values for  f( i-1) and  f( i-2) to calculate  f( i).

This algorithm can be implemented with the following C++ code:

int maxStolenValue( const vector< int>& values)

{

     int length = values.size();

     if(length == 0)

         return 0;

     int value1 = values[0];

     if(length == 1)

         return value1;

     int value2 = max< int>(values[0], values[1]);

     if(length == 2)

         return value2;

     int value;

     for( int i = 2; i < length; ++i)

    {

        value = max< int>(value2, value1 + values[i]);

        value1 = value2;

        value2 = value;

    }

     return value;

}

More coding interview questions are discussed in my book <Coding Interviews: Questions, Analysis & Solutions>. You may find the details of this book on  Amazon.com, or  Apress.

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