ACM模版

描述

题解

这个问题在 51Nod 的评论区 tangjz 大佬已经描述的十分详尽了，感觉没有什么需要多说的了，但是让人意外的是，用链表优化（代码 One）反而弄巧成拙，比直接循环判定（代码 Two）的时间消耗高很多……

代码

One：

#include <iostream>
#include <map>
#include <cmath>
#include <cstring>

using namespace std;

const int MAXN = 5e3 + 10;
const int MAXA = 1e6 + 10;

int N, K, maxA = 0, maxB;   // a 中最大元素，最多重复次数
int A[MAXA];
int B[MAXA];
int dif_cnt[MAXA];
int vis[MAXN];

struct lk
{
    short x, y;
    int next;
} LK[MAXN * MAXN / 2];

int key = 0;
int dif_head[MAXA];

map<int, int> m;

inline void add(short x, short y, int d)
{
    key++;
    LK[key].x = x;
    LK[key].y = y;
    LK[key].next = dif_head[d];
    dif_head[d] = key;
    dif_cnt[d]++;
}

int main(int argc, const char * argv[])
{
    cin >> N >> K;

    if (N == K)
    {
        cout << 1 << '\n';
        return 0;
    }

    maxB = K * (K + 1) / 2;
    for (short i = 0; i < N; i++)
    {
        scanf("%d", A + i);
        maxA = max(maxA, A[i]);
        for (short j = 0; j < i; j++)
        {
            add(i, j, abs(A[i] - A[j]));
        }
    }

    maxA += 2;
    int M = N - K;
    int temp;
    for (; M < maxA; M++)
    {
        int ct = 0;
        for (int i = M; i < maxA; i += M)
        {
            ct += dif_cnt[i];
        }
        if (ct > maxB)
        {
            continue;
        }
        ct = 0;
        for (int i = M; i < maxA && ct <= K; i += M)
        {
            for (int j = dif_head[i]; j != 0 && ct <= K; j = LK[j].next)
            {
                if (vis[LK[j].x] != M)
                {
                    temp = A[LK[j].x] % M;
                    if (B[temp] != M)
                    {
                        B[temp] = M;
                    }
                    else
                    {
                        ct++;
                    }
                    vis[LK[j].x] = M;
                }
                if (vis[LK[j].y] != M)
                {
                    temp = A[LK[j].y] % M;
                    if (B[temp] != M)
                    {
                        B[temp] = M;
                    }
                    else
                    {
                        ct++;
                    }
                    vis[LK[j].y] = M;
                }
            }
        }
        if (ct <= K)
        {
            break;
        }
    }

    cout << M << '\n';

    return 0;
}

Two：

#include <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long ll;

inline void read(int &x)
{
    x = 0;
    char ch;
    while (ch = getchar(), ch < '!') ;
    while (x = 10 * x + ch - '0', ch = getchar(), ch > '!') ;
}

const int MAXN = 1e6 + 10;

int N, K;
int a[MAXN], b[MAXN];
int dif[MAXN];

int main()
{
    read(N);
    read(K);

    for (int i = 1; i <= N; ++i)
    {
        read(a[i]);
    }
    sort(a + 1, a + N + 1);
    for (int i = 1; i <= N; ++i)
    {
        for (int j = i + 1; j <= N; ++j)
        {
            dif[a[j] - a[i]]++;
        }
    }

    int M = N - K - 1;
    int cnt_max = K * (K + 1) / 2;
    int cnt, ct;
    while (M++)
    {
        cnt = ct = 0;
        for (int i = M; i < MAXN; i += M)
        {
            cnt += dif[i];
        }
        if (cnt > cnt_max)
        {
            continue;
        }
        for (int i = 1; i <= N; ++i)
        {
            if (b[a[i] % M] == M)
            {
                ++ct;
                if (ct > K)
                {
                    break;
                }
            }
            b[a[i] % M] = M;
        }
        if (ct <= K)
        {
            break;
        }
    }

    printf("%d\n", M);

    return 0;
}