greedy won't work on 8,2,2,2,2,2,2...
On Sat, Aug 28, 2010 at 7:39 AM, Gene <gene.ress...@gmail.com> wrote:
> 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
>
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