IOI '00 P5 - Post Office

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int INF = 1e9;

int main() {
    int n, m;
    cin >> n >> m;
    vector<int> x(n);
    for (int &a : x) cin >> a;
    auto d = [&x](int i, int j) {
        return abs(x[i]-x[j]);
    };

    vector<vector<int>> dp(1+m, vector<int>(n, INF));
    vector<vector<int>> prev(1+m, vector<int>(n, -1)); // previous post office used
    // one post office
    for (int i = 0; i < n; ++i) {
        dp[1][i] = 0;
        for (int j = 0; j < n; ++j) dp[1][i] += d(i, j);
    }

    // more post offices
    for (int k = 2; k <= m; ++k) { // number of post offices
        for (int i = k-1; i < n; ++i) { // position of last post office
            int firstCloser = i; // leftmost village closer to i than to j
            int sumDistToI = 0; // sum of distances to i for all in range [firstCloser, i]
            for (int j = i-1; j >= k-2; --j) { // position of previous post office
                // update firstCloser
                while (firstCloser && d(firstCloser-1, i) <= d(firstCloser-1, j)) {
                    sumDistToI += d(--firstCloser, i);
                }

                int deltaCost = 2*sumDistToI - (n-firstCloser) * d(i, j);
                int totalCost = dp[k-1][j] + deltaCost;
                if (totalCost < dp[k][i]) {
                    dp[k][i] = totalCost;
                    prev[k][i] = j;
                }
            }
        }
    }

    int i = 0;
    for (int j = 1; j < n; ++j) {
        if (dp[m][j] < dp[m][i]) i = j;
    }
    cout << dp[m][i] << endl;
    vector<int> v;
    for (int k = m; k > 0; i=prev[k--][i]) v.push_back(i);
    for (int p = m-1; p >= 0; --p) cout << x[v[p]] << ' ';
    cout << endl;
    return 0;
}