CareerCup

dp

At i=0;
sum[0]=a[i];
sum[1]=max(a[0],a[1])
sum[i]=max(sum[i-2]+a[i],sum[i-1])
return sum[|a|-1)]

To solve these type of question, first thing is to find a recurring relation. In this case our recurring relation will tell the max sum till a given length. It means that we will get the max sum for running length of the array. If we denote the ith element as T(i) and max sum till ith element of the array as S(i), then


S(i) = MAX {S(i-1), S(i-2) + T(i) }

S(-1) = 0;
if i=0, S(i) = T(0);

Note: while developing this relationship, I assume array index is starting from 0.

Writing code for this problem is not a big deal now. Below is the code snippet for the same.

sum2 = 0;
sum = sum1 = array[0];

for(i=1; i<len; i++)
{
   sum = MAX(sum2 + array[i], sum1);
   sum2 = sum1;
   sum1 = sum;
}

For a detailed explanation, visit bit.ly/ReP5zl

Try this

for (int i=0;i<a.length-2;i++)
{
for(int j=i+2;j<a.length;j++)
{
sum = a[i]+a[j];
if (temp<sum)
{
temp = sum;
first = a[i];
second = a[j];
}
}
}

#include<iostream>

using namespace std;

main()
{


int SIZE=3;
int arr[]= {10,1,3,25};



int max_sum=0;

for(int i=0; i<SIZE-1; i++)
{
int sum=arr[i]+arr[i+2];
if(sum > max_sum)
{

max_sum=sum;

}



}

int sum1=arr[0] + arr[SIZE];
if(max_sum<sum1)
{

max_sum=sum1;
}
cout<<max_sum<<"is greatest";

}

import collections
'''
Problem :
Find the subsequences whose elements should not be adjacent and their sum should be maximum from the given array (contains only positive integers).
Eg: int[] A = {10, 1, 3, 25}
Sol: Sum: {10, 3} = 13
{1,25} = 26
{10,25} = 35
Here the Maximum subsequence is {10, 25}.

Approch :

compare the adj elements and find the max and keep them in the sum array
repeat until it's length is 2 (to form a pair)
'''
def findMaxNonAdj(array):
    sumList = []
    temp = array
    if len(array) < 2:
        print "Cannot form a pair"
        return
    while temp:
        for i in range(1,len(temp)):            
            sumList.append(max(temp[i-1],temp[i]))            
        temp = None
        temp = collections.OrderedDict.fromkeys(sumList).keys()#normal sets are unorderd
        print temp
        sumList = list()
        if len(temp) == 2:
            break

    print "Result "+str(temp)

def main():
    nums = [10,1,3,25]
    findMaxNonAdj(nums)

if __name__ == "__main__":main()

Simple and short implementation of Dynamic Programming idea mentioned here :

int sum_max_dp(int arr[], int n){
	int result[n];
	result[0]=arr[0];
	result[1]=max(arr[0],arr[1]);
	for(int i=2;i<n;i++) result[i]= max(result[i-2]+arr[i], result[i-1]);
	return result[n-1];
}