题意:给定一个序列,找出包含1到k的元素的最短序列,序列定义是X0=1,X1=2,X2=3,Xk=(Xk-1+Xk-2+Xk-3)%m+1。
分析:滑动窗口,先找出包含这k个值的最大序列,然后将序列缩小,找到之后就取出一个先前加入的元素,寻找下一个。
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
const int N = 1000005;
int n, m, k, A[N], vis[N];
void init() {
memset(A, 0, sizeof(A));
memset(vis, 0, sizeof(vis));
scanf("%d%d%d", &n, &m, &k);
A[1] = 1; A[2] = 2; A[3] = 3;
for (int i = 4; i <= n; i++)
A[i] = (A[i-1] + A[i-2] + A[i-3]) % m + 1;
}
bool solve() {
int l = 1, r = 1, c = 0;
int ans = n + 1;
while (r <= n) {
int t = A[r++];
vis[t]++;
if (t <= k && vis[t] == 1) c++;
while (l < r && c == k) {
ans = min(ans, r - l);
t = A[l++];
vis[t]--;
if (t <= k && vis[t] == 0) c--;
}
}
if (ans <= n) {
printf("%d\n", ans);
return false;
}
return true;
}
int main() {
int cas;
scanf("%d", &cas);
for (int i = 1; i <= cas; i++) {
init();
printf("Case %d: ", i);
if (solve()) printf("sequence nai\n");
}
return 0;
}