CF Mike and Feet （求连续区间内长度为i的最小值）单调栈

Mike and Feet

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Mike is the president of country What-The-Fatherland. There are n bears living in this country besides Mike. All of them are standing
in a line and they are numbered from 1 to n from
left to right. i-th bear is exactly ai feet
high.

A group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strengthof
a group is the minimum height of the bear in that group.

Mike is a curious to know for each x such that 1 ≤ x ≤ n the
maximum strength among all groups of size x.

Input

The first line of input contains integer n (1 ≤ n ≤ 2 × 105),
the number of bears.

The second line contains n integers separated by space, a1, a2, ..., an (1 ≤ ai ≤ 109),
heights of bears.

Output

Print n integers in one line. For each x from 1 to n,
print the maximum strength among all groups of size x.

Sample test(s)

input

10
1 2 3 4 5 4 3 2 1 6

output

6 4 4 3 3 2 2 1 1 1

题意：给n个数。问连续区间长度为1,2,3,4,....n 所相应的区间长度最小值中的最大值是多少。

解题：单调栈。

#include<stdio.h>
const int N = 200005;
struct NODE
{
    int h,w;
}S[N];
int h[N],ans[N];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i=0; i<n; i++)
        scanf("%d",&h[i]),ans[i]=0;
    h[n++]=0;ans[n]=0;
    int sum,top=0;
    for(int i=0; i<n; i++){
        sum=0;
        while(top>0 && S[top].h>=h[i]){
            sum+=S[top].w;
            if(ans[sum]<S[top].h)
                ans[sum]=S[top].h;
            --top;
        }
        S[++top].h=h[i]; S[top].w=sum+1;
    }
    n--;

    /*
     长度为i 的连续数中ans[i]是这i个数的最小数，但却是全部长度为i 的连续数中
     最小中的最大数。

长度i能够依据长度i+1更新大小。原因是ans[i+1]比在此区间内
     的数都要小于等于，所以去掉边上的一个数答案不影响。对于假设要求区间内的
        最大值   ，仅仅需对以下的循环倒过来且比較符取反就可以。同理。
     */
    for(int i=n-1; i>=1; i--)
        if(ans[i]<ans[i+1])
        ans[i]=ans[i+1];

    for(int i=1; i<n; i++)
        printf("%d ",ans[i]);
    printf("%d\n",ans[n]);
}