This is a nice problem. It looks like a trivial matroid, so a greedy algorithm will work fine. The obvious greedy algorithm is to work left-to-right and incorporate elements into the sorted order one-by- one. In each case, you have 2 choices. The first is to decrement elements to the left by the amount needed to restore non-decreasing order. The second is to delete the new element. The cost of each is easy to calculate. Pick the choice with least cost and continue. This algorithm is O(n^2). There may be a faster way to do it, but I can't see one.
#include <stdio.h> int make_nondecreasing(int *a, int n) { int i, j, dec, dec_cost, total_cost; total_cost = 0; for (i = 0; i < n - 1; i++) { // If we find a decrease... if (a[i] > a[i + 1]) { // Find cost of decrementing all to the left. dec_cost = dec = a[i] - a[i + 1]; for (j = i - 1; j >= 0; j--) { // Find decrement that would be needed. dec += a[j] - a[j + 1]; // If no decement, we're done. if (dec <= 0) break; // Count cost of decrement. dec_cost += dec; } // Compare decrement cost with deletion cost. if (dec_cost < a[i + 1]) { // Decrement is cheaper. Do it. for (j = i; j >= 0; j--) { if (a[j] > a[i + 1]) a[j] = a[i + 1]; } total_cost += dec_cost; } else { // Deletion is cheaper. Do it. total_cost += a[i + 1]; for (j = i + 1; j < n - 1; j++) a[j] = a[j + 1]; --n; } } } return total_cost; } int main(void) { int a[] = { 14, 15, 16, 13, 11, 18 }; //int a[] = { 4, 3, 5, 6}; //int a[] = { 10, 3, 11, 12 }; int cost = make_nondecreasing(a, sizeof a / sizeof a[0]); printf("cost=%d\n", cost); return 0; } On Aug 27, 12:15 pm, jagadish <jagadish1...@gmail.com> wrote: > You are given an array of positive integers. Convert it to a sorted > array with minimum cost. Only valid operation are > 1) Decrement -> cost = 1 > 2) Delete an element completely from the array -> cost = value of > element > > For example: > 4,3,5,6, -> cost 1 > 10,3,11,12 -> cost 3 -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.