The All-purpose Zero

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 947    Accepted Submission(s): 453

Problem Description

?? gets an sequence S with n intergers(0 < n <= 100000,0<= S[i] <= 1000000).?? has a magic so that he can change 0 to any interger(He does not need to change all 0 to the same interger).?? wants you to help him to find out the length of the longest increasing (strictly) subsequence he can get.

Input

The first line contains an interger T,denoting the number of the test cases.(T <= 10)
For each case,the first line contains an interger n,which is the length of the array s.
The next line contains n intergers separated by a single space, denote each number in S.

Output

For each test case, output one line containing “Case #x: y”(without quotes), where x is the test case number(starting from 1) and y is the length of the longest increasing subsequence he can get.

Sample Input

2
7
2 0 2 1 2 0 5
6
1 2 3 3 0 0

Sample Output

Case #1: 5 Case #2: 5

Hint

In the first case,you can change the second 0 to 3.So the longest increasing subsequence is 0 1 2 3 5.

题意： 给你n个数字，你可以将其中的0变成任意数字，求最终能得到的最长严格递增子序列，

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <stdlib.h>
using namespace std;
typedef long long LL;
const int inf=0x3f3f3f3f;
const int mod=1e9+7;
const int N=1e5+10;

int a[N],ans[N];
int main()
{
    int cas,n,x,kk=0;
    scanf("%d",&cas);
    while(cas--){
        scanf("%d",&n);
        int cnt=0,num=0;
        for(int i=1;i<=n;i++){
            scanf("%d",&x);
            if(!x) cnt++;
            else a[++num]=x-cnt;
        }
        if(!num) {
            printf("Case #%d: %d\n",++kk,cnt);
            continue;
        }
        int len=1;
        ans[1]=a[1];
        for(int i=2;i<=num;i++){
            if(a[i]>ans[len]) ans[++len]=a[i];
            else {
              int pos=lower_bound(ans+1,ans+len,a[i])-ans;
              ans[pos]=a[i];
            }
        }
        printf("Case #%d: %d\n",++kk,len+cnt);
    }
    return 0;
}

　　0可以转化成任意整数，包括负数，显然求LIS时尽量把0都放进去必定是正确的。因此我们可以把0拿出来，对剩下的做O(nlogn)的LIS，统计结果的时候再算上0的数量。为了保证严格递增，我们可以将每个权值S[i]减去i前面0的个数，再做LIS，就能保证结果是严格递增的。