[Luogu] P1886 滑动窗口

Posted 2020-10-27 MZQ667

Luogu P1886 滑动窗口

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传送门

此题为单调队列入门题。单调队列，可以\(O(n)\)求一段数列中区间极值。记录队列中元素大小与该元素在原数组中的位置。当队首元素超出当前求值区间时，头指针加一；当当前将入队元素大于或小于尾元素时，尾指针减一，直到不符合上一条件时，将当前元素入队。然后要求极值只需输出队首元素即可。

#include <cstdio>
const int MAXN = 1000001;
int n, k;
int a[MAXN], que[MAXN], id[MAXN], head, tail;
int main() {
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; ++i)
        scanf("%d", &a[i]);
    head = 1; tail = 0;
    for (int i = 1; i <= n; ++i) {
        while(head <= tail && id[head] <= i - k) head++;
        while(head <= tail && que[tail] >= a[i]) tail--;
        que[++tail] = a[i]; id[tail] = i;
        if(i >= k) printf("%d ", que[head]);
    }
    printf("\n");
    head = 1; tail = 0;
    for (int i = 1; i <= n; ++i) {
        while(head <= tail && id[head] <= i - k) head++;
        while(head <= tail && que[tail] <= a[i]) tail--;
        que[++tail] = a[i]; id[tail] = i;
        if(i >= k) printf("%d ", que[head]);
    }
    printf("\n");
    return 0;
}