Almost Sorted Array

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 7942 Accepted Submission(s): 1848

Problem Description

We are all familiar with sorting algorithms: quick sort, merge sort, heap sort, insertion sort, selection sort, bubble sort, etc. But sometimes it is an overkill to use these algorithms for an almost sorted array.

We say an array is sorted if its elements are in non-decreasing order or non-increasing order. We say an array is almost sorted if we can remove exactly one element from it, and the remaining array is sorted. Now you are given an array a1,a2,…,an, is it almost sorted?

Input

The first line contains an integer T indicating the total number of test cases. Each test case starts with an integer n in one line, then one line with n integers a1,a2,…,an.

1≤T≤2000
2≤n≤105
1≤ai≤105
There are at most 20 test cases with n>1000.

Output

For each test case, please output "`YES`" if it is almost sorted. Otherwise, output "`NO`" (both without quotes).

Sample Input

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2 1 7

3 2 1

3 1 4 1 5

Sample Output

YES

Source

2015ACM/ICPC亚洲区长春站-重现赛（感谢东北师大）

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Statistic | Submit | Discuss | Note

题意：给定长度的数列，去掉一个数字后，能否让数列变成为递增或递减。

思路：先正着LIS，再把数列翻转，再求一次LIS。判断 lis >= n-1 是否成立即可。

#pragma GCC optimize(2)
#include <bits/stdc++.h>
using namespace std;
#define clr(a) memset(a,0,sizeof(a))
#define line cout<<"-----------------"<<endl;

typedef long long ll;
const int maxn = 1e5+10;
const int MAXN = 1e6+10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9+7;
const int N = 1010;

int n;
int a[maxn],b[maxn];
bool check(){
    int top = 0;
    for(int i=0;i<n;i++){
        int pos = upper_bound(b, b+top, a[i]) - b;
        b[pos] = a[i];
        top = max(top, pos+1);
    }
    if(top >= n-1) return true;
    return false;
}

int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        for(int i=0;i<n;i++)
            scanf("%d",&a[i]);
        bool flag = check();
        reverse(a, a+n);
        flag |= check();
        if(flag) puts("YES");
        else puts("NO");
    }
    return 0;
}

HDU 5532 - Almost Sorted Array（LIS）

Almost Sorted Array

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