Maximum sum of non consecutive elements

by

Dynamic programming? Given an array A[0..n], let M(i) be the optimal solution using the elements with indices 0..i. Then M(-1) = 0 (used in the recurrence), M(0) = A[0], and M(i) = max(M(i - 1), M(i - 2) + A[i]) for i = 1, ..., n. M(n) is the solution we want. This is O(n). You can use another array to store which choice is made for each subproblem, and so recover the actual elements chosen.

More Related Contents:

  1. maximize the top element of the stack after performing exactly K operations
  2. Algorithm for all subsets of Array
  3. How to sort in-place using the merge sort algorithm?
  4. Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing
  5. Finding three elements in an array whose sum is closest to a given number
  6. Given an array of numbers, return array of products of all other numbers (no division)
  7. How to find the kth smallest element in the union of two sorted arrays?
  8. Algorithm to find k smallest numbers in array of n items
  9. Can min/max of moving window achieve in O(N)?
  10. Weighted random selection from array
  11. Print two-dimensional array in spiral order
  12. Find the Smallest Integer Not in a List
  13. How to find a duplicate element in an array of shuffled consecutive integers?
  14. Find the majority element in array
  15. Given an array, find out the next smaller element for each element
  16. Binary Search algorithm implementations
  17. Algorithm to determine if array contains n…n+m?
  18. Find the 2nd largest element in an array with minimum number of comparisons
  19. Algorithm to rotate an array in linear time
  20. Find all subsets of length k in an array
  21. In-place array reordering?
  22. How to find max. and min. in array using minimum comparisons?
  23. Median of 5 sorted arrays
  24. find pair of numbers in array that add to given sum
  25. Interview question: three arrays and O(N*N)
  26. How to find repeating sequence of characters in a given array?
  27. Finding kth smallest number from n sorted arrays
  28. calculating the number of “inversions” in a permutation
  29. Algorithm to apply permutation in constant memory space
  30. Find the first element in a sorted array that is greater than the target

Leave a Comment