USACO 2009 Mar Silver 3.Look Up

最新推荐文章于 2020-10-31 16:43:17 发布

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#算法 #单调栈 #数据结构

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本文介绍使用单调栈解决寻找每个元素左侧最近且比其高的元素的问题。具体为：对于N头编号为1到N的奶牛，每头奶牛有一个高度H_i，需找出每头奶牛左侧第一头比其高的奶牛的编号。文章提供了完整的C语言实现代码。

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Description

Farmer John's N (1 <= N <= 100,000) cows, conveniently numbered
1..N, are once again standing in a row. Cow i has height H_i (1 <=
H_i <= 1,000,000).

Each cow is looking to her left toward those with higher index
numbers. We say that cow i 'looks up' to cow j if i < j and H_i <
H_j. For each cow i, FJ would like to know the index of the first
cow in line looked up to by cow i.

Note: about 50% of the test data will have N <= 1,000.

Input

* Line 1: A single integer: N

* Lines 2..N+1: Line i+1 contains the single integer: H_i

Output

* Lines 1..N: Line i contains a single integer representing the
smallest index of a cow up to which cow i looks. If no such
cow exists, print 0.

Sample Input

Sample Output

HINT

INPUT DETAILS:

FJ has six cows of heights 3, 2, 6, 1, 1, and 2.

OUTPUT DETAILS:

Cows 1 and 2 both look up to cow 3; cows 4 and 5 both look up to cow 6; and
cows 3 and 6 do not look up to any cow.

求距离此点最近且比它高的点

可以用单调栈维护

有高的点直接比较大小之后赋值编号

#include<stdio.h>
int a[100001],s[100001],ans[100001],i,top;
int main()
{
	int n;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
	for(i=n;i>=0;i--)
	{
		while(top&&a[s[top]]<=a[i])
			top--;
		ans[i]=s[top];
		s[++top]=i;
	}	
	for(i=1;i<=n;i++)
		printf("%d\n",ans[i]);
}