Codeforces Round #335 (Div. 2) C. Sorting Railway Cars 最长连续上升子序列

C. Sorting Railway Cars

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

An infinitely long railway has a train consisting of n cars, numbered from 1 to n (the
numbers of all the cars are distinct) and positioned in arbitrary order. David Blaine wants to sort the railway cars in the order of increasing numbers. In one move he can make one of the cars disappear from its place and teleport it either to the beginning
of the train, or to the end of the train, at his desire. What is the minimum number of actions David Blaine needs to perform in order to sort the train?

Input

The first line of the input contains integer n (1 ≤ n ≤ 100 000) —
the number of cars in the train.

The second line contains n integers pi (1 ≤ pi ≤ n, pi ≠ pj if i ≠ j) —
the sequence of the numbers of the cars in the train.

Output

Print a single integer — the minimum number of actions needed to sort the railway cars.

Sample test(s)

input

5
4 1 2 5 3

output

2

input

4
4 1 3 2

output

2

题意：给你一个序列，你可以将序列中的任意一个数取出来放到序列的第一位或者最后一位，问你最少多少次就可以把该序列转换成一个递增的序列。

思路：从后向前遍历，假如现在遍历到了a[k],那么寻找a[k]+1,而[b]a[k]+1已经在之前做了类似操作[b]，依次类推就能找到以a[k]为起点的最长上升子序列了。[/b][/b]

代码：

#include <cstdio>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;
#define inf 0x3f3f3f3f
#define maxn 100011
typedef long long ll;
int a[maxn],dp[maxn];
//dp[k]代表以k为起点的最长连续上升子序列的长度
int main()
{
#ifdef CDZSC_June
freopen("t.txt","r",stdin);
#endif
int n;
while(~scanf("%d",&n))
{
for(int i = 1; i<= n; i++)
{
scanf("%d",&a[i]);
dp[i] = 0;
}
dp[n+1] = 0;
for(int i = n; i>= 1; i--)
{
dp[a[i]] = dp[a[i] + 1] +1;
}
sort(dp+1,dp+n+1);//排序找到最大值
printf("%d\n",n - dp
);
}
}