Submission #599058

#	Time	Username	Problem	Language	Result	Execution time	Memory
599058		jophyyjh	Aliens (IOI16_aliens)	C++14	12 / 100	34 ms	2260 KiB

aliens

/**
 * I don't feel like fully solving this, so maybe i'll just score some partials.
 * 
 * [S1] Too trivial
 * [S2] Each point lies on the main diagonal. Clearly, no two squares should have
 *      common squares, which means the points are partitioned into contiguous
 *      segments. O(n^2 * k) dp kills it.
 * [S3] Maybe we can somehow sort the points based on their columns, then apply [S2]?
 *      Yep, pretty much analagous to [S2]. The key here is that if (2,5), (3,5),
 *      the square that covers (2,5) must cover (3,5).
 * 
 * Time Complexity: O(n^2 * k)
 * Implementation 1     ([S3] hold, only solves the first two)
*/

#include <bits/stdc++.h>
#include "aliens.h"

typedef long long   ll;

const int N_MAX = 500;
const ll INF = 0x3f3f3f3f3f3f;

inline ll sqr(int k)    { return ll(k) * ll(k); }


ll cover[N_MAX + 1][N_MAX + 1];

struct point_t {
    int i, j;
};

inline bool operator<(const point_t& p1, const point_t& p2) { return p1.i < p2.i || (p1.i == p2.i && p1.j < p2.j); }
inline bool operator==(const point_t& p1, const point_t& p2)    { return p1.i == p2.i && p1.j == p2.j; }

ll take_photos(int n, int m, int max_sqr, std::vector<int> row, std::vector<int> col) {
    if (max_sqr == n) {
        std::vector<point_t> values(n);
        for (int i = 0; i < n; i++)
            values[i].i = row[i], values[i].j = col[i];
        std::sort(values.begin(), values.end());
        return std::unique(values.begin(), values.end()) - values.begin();
    }
    std::sort(row.begin(), row.end());
    n = std::unique(row.begin(), row.end()) - row.begin();
    cover[0][0] = 0;
    for (int s = 1; s <= max_sqr; s++)
        cover[0][s] = INF;
    for (int k = 0; k < n; k++) {
        cover[k + 1][0] = INF;
        for (int s = 1; s <= max_sqr; s++) {
            cover[k + 1][s] = INF;
            for (int m = 0; m <= k; m++) {  // [m,k]
                cover[k + 1][s] = std::min(
                    cover[k + 1][s],
                    cover[m][s - 1] + sqr(row[k] - row[m] + 1)
                );
            }
        }
    }
    ll ans = INF;
    for (int s = 1; s <= max_sqr; s++)
        ans = std::min(ans, cover[n][s]);
    return ans;
}

• Subtask 1: 0 / 4
• Subtask 2: 12 / 12
• Subtask 3: 0 / 9
• Subtask 4: 0 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40