Max Array Sum
Problem Statement :
Given an array of integers, find the subset of non-adjacent elements with the maximum sum. Calculate the sum of that subset. It is possible that the maximum sum is 0, the case when all elements are negative. For example, given an array arr = [ -2, 1 , 3, -4, 5 ] we have the following possible subsets. These exclude the empty subset and single element subsets which are also valid. Subset Sum [-2, 3, 5] 6 [-2, 3] 1 [-2, -4] -6 [-2, 5] 3 [1, -4] -3 [1, 5] 6 [3, 5] 8 Our maximum subset sum is 8. Note that any individual element is a subset as well. Function Description Complete the maxSubsetSum function in the editor below. It should return an integer representing the maximum subset sum for the given array. maxSubsetSum has the following parameter(s): arr: an array of integers Input Format The first line contains an integer, n. The second line contains n space-separated integers arr[ i ]. Constraints 1 <= n <= 10^5 - 10^4 <= arr[ i ] <= 10^4 Output Format Return the maximum sum described in the statement. Sample Input 0 5 3 7 4 6 5 Sample Output 0 13
Solution :
Solution in C :
int dp[100005];
int maxSubsetSum(vector<int> arr) {
dp[0]=max(0,arr[0]);
if(arr.size()==1)
return dp[0];
for(int i=1;i<arr.size();i++)
{
dp[i]=max(dp[i-2],max(dp[i-1],dp[i-2]+arr[i]));
}
int n=arr.size();
return max(dp[n-1],dp[n-2]);
}
View More Similar Problems
Costly Intervals
Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the
View Solution →The Strange Function
One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting
View Solution →Self-Driving Bus
Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever
View Solution →Unique Colors
You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti
View Solution →Fibonacci Numbers Tree
Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in is associated with some positive integer value (all values are initially ). Let's define Fk as the Kth Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T
View Solution →Pair Sums
Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v
View Solution →