Find maximum possible stolen value from houses

There are n houses build in a line, each of which contains some value in it. A thief is going to steal the maximal value of these houses, but he can’t steal in two adjacent houses because owner of the stolen houses will tell his two neighbour left and right side. What is the maximum stolen value.
Examples:

Input  : hval[] = {6, 7, 1, 3, 8, 2, 4}
Output : 19
Thief will steal 6, 1, 8 and 4 from house.

Input  : hval[] = {5, 3, 4, 11, 2}
Output : 16
Thief will steal 5 and 11

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

While reaching house i thief has two options, either he robs it or leave it. Let dp[i] represents the maximum value stolen so far on reaching house i. We can calculate the value of dp[i] as following –

dp[i] = max (hval[i] + dp[i-2], dp[i-1])

hval[i] + dp[i-2] is the case when thief
decided to rob house i. In that situation 
maximum value will be the current value of
house + maximum value stolen till last 
robbery at house not adjacent to house 
i which will be house i-2.  
 
dp[i-1] is the case when thief decided not 
to rob house i. So he will check adjacent 
house for maximum value stolen till now.

Thief will consider both options and decide whether to rob or not and maximum of both values will be the maximum stolen value till reaching house i.

We can prepare dp in bottom up manner instead of recursively. Following is the program for that –

C++

// CPP program to find the maximum stolen value 
#include <iostream> 
using namespace std; 
  
// calculate the maximum stolen value 
int maxLoot(int *hval, int n) 
{ 
    if (n == 0) 
        return 0; 
    if (n == 1) 
        return hval[0]; 
    if (n == 2) 
        return max(hval[0], hval[1]); 
  
    // dp[i] represent the maximum value stolen 
    // so far after reaching house i. 
    int dp[n]; 
  
    // Initialize the dp[0] and dp[1] 
    dp[0] = hval[0]; 
    dp[1] = max(hval[0], hval[1]); 
  
    // Fill remaining positions 
    for (int i = 2; i<n; i++) 
        dp[i] = max(hval[i]+dp[i-2], dp[i-1]); 
  
    return dp[n-1]; 
} 
  
// Driver to test above code 
int main() 
{ 
    int hval[] = {6, 7, 1, 3, 8, 2, 4}; 
    int n = sizeof(hval)/sizeof(hval[0]); 
    cout << "Maximum loot possible : "
        << maxLoot(hval, n); 
    return 0; 
} 

Java

// Java program to find the maximum stolen value 
import java.io.*; 
  
class GFG  
{ 
    // Function to calculate the maximum stolen value 
    static int maxLoot(int hval[], int n) 
    { 
        if (n == 0) 
        return 0; 
        if (n == 1) 
            return hval[0]; 
        if (n == 2) 
            return Math.max(hval[0], hval[1]); 
   
        // dp[i] represent the maximum value stolen 
        // so far after reaching house i. 
        int[] dp = new int[n]; 
   
        // Initialize the dp[0] and dp[1] 
        dp[0] = hval[0]; 
        dp[1] = Math.max(hval[0], hval[1]); 
   
        // Fill remaining positions 
        for (int i = 2; i<n; i++) 
            dp[i] = Math.max(hval[i]+dp[i-2], dp[i-1]); 
   
        return dp[n-1]; 
    } 
      
    // Driver program 
    public static void main (String[] args)  
    { 
        int hval[] = {6, 7, 1, 3, 8, 2, 4}; 
        int n = hval.length; 
        System.out.println("Maximum loot value : " + maxLoot(hval, n)); 
    } 
} 
  
// Contributed by Pramod Kumar 

Python

# Python3 program to find the maximum stolen value 
  
# calculate the maximum stolen value 
def maximize_loot(hval, n): 
    if n == 0: 
        return 0
    if n == 1: 
        return hval[0] 
    if n == 2: 
        return max(hval[0], hval[1]) 
  
    # dp[i] represent the maximum value stolen so 
    # for after reaching house i. 
    dp = [0]*n 
  
    # Initialize the dp[0] and dp[1] 
    dp[0] = hval[0] 
    dp[1] = max(hval[0], hval[1]) 
      
    # Fill remaining positions 
    for i in range(2, n): 
        dp[i] = max(hval[i]+dp[i-2], dp[i-1]) 
  
    return dp[-1] 
  
# Driver to test above code  
def main(): 
  
    # Value of houses 
    hval = [6, 7, 1, 3, 8, 2, 4] 
  
    # number of houses 
    n = len(hval) 
    print("Maximum loot value : {}". 
        format(maximize_loot(hval, n))) 
  
if __name__ == '__main__': 
    main() 

C#

// C# program to find the  
// maximum stolen value 
using System; 
          
class GFG  
{ 
   // Function to calculate the  
   // maximum stolen value 
    static int maxLoot(int []hval, int n) 
    { 
        if (n == 0) 
        return 0; 
        if (n == 1) 
            return hval[0]; 
        if (n == 2) 
            return Math.Max(hval[0], hval[1]); 
  
        // dp[i] represent the maximum value stolen 
        // so far after reaching house i. 
        int[] dp = new int[n]; 
  
        // Initialize the dp[0] and dp[1] 
        dp[0] = hval[0]; 
        dp[1] = Math.Max(hval[0], hval[1]); 
  
        // Fill remaining positions 
        for (int i = 2; i<n; i++) 
            dp[i] = Math.Max(hval[i]+dp[i-2], dp[i-1]); 
  
        return dp[n-1]; 
    } 
      
    // Driver program 
    public static void Main ()  
    { 
        int []hval = {6, 7, 1, 3, 8, 2, 4}; 
        int n = hval.Length; 
        Console.WriteLine("Maximum loot value : " +  
                                 maxLoot(hval, n)); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to find  
// the maximum stolen value 
  
// calculate the maximum 
// stolen value 
function maxLoot($hval, $n) 
{ 
    if ($n == 0) 
        return 0; 
    if ($n == 1) 
        return $hval[0]; 
    if ($n == 2) 
        return max($hval[0],  
                   $hval[1]); 
  
    // dp[i] represent the maximum  
    // value stolen so far after  
    // reaching house i. 
    $dp = array(); 
  
    // Initialize the  
    // dp[0] and dp[1] 
    $dp[0] = $hval[0]; 
    $dp[1] = max($hval[0],  
                 $hval[1]); 
  
    // Fill remaining positions 
    for ($i = 2; $i < $n; $i++) 
        $dp[$i] = max($hval[$i] +  
                      $dp[$i - 2],  
                      $dp[$i - 1]); 
  
    return $dp[$n - 1]; 
} 
  
// Driver Code 
$hval = array(6, 7, 1,  
              3, 8, 2, 4); 
$n = sizeof($hval); 
echo "Maximum loot possible : ", 
             maxLoot($hval, $n); 
      
// This code is contributed by aj_36 
?> 

Output:

Maximum loot value : 19

Time complexity = $O(n)$
Space complexity = $O(n)$

We can optimize extra space, by using two variables to store value dp[i-1] and dp[i-2]. Following is the program for that –

C++

// C++ program to find the maximum stolen value 
#include <iostream> 
using namespace std; 
  
// calculate the maximum stolen value 
int maxLoot(int *hval, int n) 
{ 
    if (n == 0) 
        return 0; 
  
    int value1 = hval[0]; 
    if (n == 1) 
        return value1; 
  
    int value2 = max(hval[0], hval[1]); 
    if (n == 2) 
        return value2; 
  
    // contains maximum stolen value at the end 
    int max_val; 
  
    // Fill remaining positions 
    for (int i=2; i<n; i++) 
    { 
        max_val = max(hval[i]+value1, value2); 
        value1 = value2; 
        value2 = max_val; 
    } 
  
    return max_val; 
} 
  
// Driver to test above code 
int main() 
{ 
    // Value of houses 
    int hval[] = {6, 7, 1, 3, 8, 2, 4}; 
    int n = sizeof(hval)/sizeof(hval[0]); 
    cout << "Maximum loot possible : "
        << maxLoot(hval, n); 
    return 0; 
} 

Java

// Java program to find the maximum stolen value 
import java.io.*; 
  
class GFG  
{ 
    // Function to calculate the maximum stolen value 
    static int maxLoot(int hval[], int n) 
    { 
        if (n == 0) 
        return 0; 
   
        int value1 = hval[0]; 
        if (n == 1) 
            return value1; 
   
        int value2 = Math.max(hval[0], hval[1]); 
        if (n == 2) 
            return value2; 
    
        // contains maximum stolen value at the end 
        int max_val = 0; 
   
        // Fill remaining positions 
        for (int i=2; i<n; i++) 
        { 
            max_val = Math.max(hval[i]+value1, value2); 
            value1 = value2; 
            value2 = max_val; 
        } 
   
        return max_val; 
    } 
      
    // driver program 
    public static void main (String[] args)  
    { 
        int hval[] = {6, 7, 1, 3, 8, 2, 4}; 
        int n = hval.length; 
        System.out.println("Maximum loot value : " + maxLoot(hval, n)); 
    } 
} 
  
// Contributed by Pramod kumar 

Python

# Python3 program to find the maximum stolen value 
  
# calculate the maximum stolen value 
def maximize_loot(hval, n): 
    if n == 0: 
        return 0
  
    value1 = hval[0] 
    if n == 1: 
        return value1 
  
    value2 = max(hval[0], hval[1]) 
    if n == 2: 
        return value2 
  
    # contains maximum stolen value at the end 
    max_val = None
  
    # Fill remaining positions 
    for i in range(2, n): 
        max_val = max(hval[i]+value1, value2) 
        value1 = value2 
        value2 = max_val 
  
    return max_val 
  
# Driver to test above code  
def main(): 
  
    # Value of houses 
    hval = [6, 7, 1, 3, 8, 2, 4] 
  
    # number of houses 
    n = len(hval) 
    print("Maximum loot value : {}".format(maximize_loot(hval, n))) 
  
if __name__ == '__main__': 
    main() 

C#

// C# program to find the  
// maximum stolen value 
using System; 
          
public class GFG  
{ 
    // Function to calculate the  
    // maximum stolen value 
    static int maxLoot(int []hval, int n) 
    { 
        if (n == 0) 
        return 0; 
  
        int value1 = hval[0]; 
        if (n == 1) 
            return value1; 
  
        int value2 = Math.Max(hval[0], hval[1]); 
        if (n == 2) 
            return value2; 
      
        // contains maximum stolen value at the end 
        int max_val = 0; 
  
        // Fill remaining positions 
        for (int i = 2; i < n; i++) 
        { 
            max_val = Math.Max(hval[i] + value1, value2); 
            value1 = value2; 
            value2 = max_val; 
        } 
  
        return max_val; 
    } 
      
    // Driver program 
    public static void Main ()  
    { 
        int []hval = {6, 7, 1, 3, 8, 2, 4}; 
        int n = hval.Length; 
        Console.WriteLine("Maximum loot value : " + 
                                 maxLoot(hval, n)); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to find  
// the maximum stolen value 
  
// calculate the  
// maximum stolen value 
function maxLoot($hval, $n) 
{ 
    if ($n == 0) 
        return 0; 
  
    $value1 = $hval[0]; 
    if ($n == 1) 
        return $value1; 
  
    $value2 = max($hval[0],  
                  $hval[1]); 
    if ($n == 2) 
        return $value2; 
  
    // contains maximum  
    // stolen value at the end 
    $max_val; 
  
    // Fill remaining positions 
    for ($i = 2; $i < $n; $i++) 
    { 
        $max_val = max($hval[$i] +  
                       $value1, $value2); 
        $value1 = $value2; 
        $value2 = $max_val; 
    } 
  
    return $max_val; 
} 
  
// Driver code 
$hval = array(6, 7, 1, 3, 8, 2, 4); 
$n = sizeof($hval); 
echo "Maximum loot value : ", 
          maxLoot($hval, $n); 
      
// This code is contributed by ajit 
?> 

Output:

Maximum loot value : 19

Time complexity = $O(n)$
Auxiliary Space = $O(1)$

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