IOI '00 P5 - Post Office (3)

#include <bits/stdc++.h>

using namespace std;

const int INF = 1e9;

vector<int> x;
int A(int l, int r) {
    return (x[r]-x[r-(r-l+1)/2]) - (x[l+(r-l+1)/2-1]-x[l-1]);
}

vector<vector<int>> dp, pos;
void divideAndConquer(int i, int l, int r, int kl, int kr) {
    if (l > r) return;
    int j = (l+r)/2;
    for (int k = kl; k <= kr; ++k) {
        dp[i][j] = min(dp[i][j], dp[k][j-1] +  A(k+1, i));
    }
    for (int k = kl; k <= kr; ++k) {
        if (dp[i][j] == dp[k][j-1] + A(k+1, i)) pos[i][j] = k;
    }
    divideAndConquer(i, l, j-1, kl, pos[i][j]);
    divideAndConquer(i, j+1, r, pos[i][j], kr);
}

int main() {
    int n, m;
    cin >> n >> m;
    x.resize(1+n);
    for (int i = 1; i <= n; ++i) cin >> x[i], x[i] += x[i-1];

    dp = vector<vector<int>>(1+n, vector<int>(1+n, INF));
    pos = vector<vector<int>>(1+n, vector<int>(2+n));
    for (int i = 1; i <= n; ++i) {
        dp[i][1] = A(1, i);
        pos[i][i+1] = i-1;
    }

    for (int i = 2; i <= n; ++i) {
        int l = 2, r = i; // values for j
        int kl = 1, kr = i-1; // possible range of k (split) positions
        divideAndConquer(i, l, r, kl, kr);
    }

    cout << dp[n][m] << endl;
    vector<int> v;
    for (int i = n, j = m; j >= 1; i = pos[i][j--]) {
        int k = (i + pos[i][j]+1)/2;
        v.push_back(x[k]-x[k-1]);
    }
    for (int i = m-1; i >= 0; --i) cout << v[i] << ' ';
    cout << endl;
    return 0;
}