51Nod-1217-Minimum Modular

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;
}