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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