【Ivan and Powers of Two】【CodeForces - 305C】（思维）（Set 应用)

题目：

Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorted in the non-decreasing order.

Ivan wrote out integers 2a1, 2a2, ..., 2an on a piece of paper. Now he wonders, what minimum number of integers of form 2b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2v - 1 for some integer v (v ≥ 0).

Help Ivan, find the required quantity of numbers.

Input

The first line contains integer n (1 ≤ n ≤ 105). The second input line contains nspace-separated integers a1, a2, ..., an (0 ≤ ai ≤ 2·109). It is guaranteed that a1 ≤ a2 ≤ ... ≤ an.

Output

Print a single integer — the answer to the problem.

Examples

Input

4
0 1 1 1

Output

Input

1
3

Output

Note

In the first sample you do not need to add anything, the sum of numbers already equals 23 - 1 = 7.

In the second sample you need to add numbers 20, 21, 22.

解题报告：首先咱们需要的数学储备知识，(2^a+2^a)=2^(a+1) ,2^1+2^2……+2^n=2^(n+1)-1;接下来咱们可以开始了，所求的是满足题意的：将所有的数组元素进行2的幂数操作，然后求和，问再添加几位数可以使和满足2^v-1，因为题目没有要求是否最小添加，所以利用set，将数组元素相同的进行合并操作，然后找出最大的数字，之前的用数补齐，那么所补数的数目就是输出的数值。

ac代码：

#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<set>
using namespace std;
typedef long long ll;set<int > ss;
int main()
{int n,a;while(scanf("%d",&n)!=EOF){ss.clear();int maxx=0;for(int i=0;i<n;i++){scanf("%d",&a);while(ss.count(a)){ss.erase(a);a++;}ss.insert(a);maxx=max(maxx,a); }printf("%d\n",maxx-ss.size()+1);}return 0;
}

【Ivan and Powers of Two】【CodeForces - 305C】（思维）（Set 应用)相关推荐

Ivan and Powers of Two CodeForces - 305C（set）
Ivan has got an array of n non-negative integers a1, a2, -, an. Ivan knows that the array is sorted ...
【CodeForces - 305C】Ivan and Powers of Two（思维）
C. Ivan and Powers of Two time limit per test 0.5 seconds memory limit per test 256 megabytes input ...
【CodeForces - 305C】Ivan and Powers of Two（思维，STL，set，优先队列）
题干: Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is s ...
CodeForces 305C Ivan and Powers of Two【set】
这个题啊,纠结了本公举一中午,知道如果出现了重复的,就要往后移,差点就把自己想的恶心的bool 数组付诸实现了,== 既然是思维的题,借助了STL的特性是再正常不过的了,既然想写数组,先应该想想Set ...
Codeforces Round #594 (Div. 2) C. Ivan the Fool and the Probability Theory 思维 + dp
文章目录题意: 思路题意: 思路一开始找规律,表都打好了,没找出来.. 找规律还是适合让队友来. 先考虑第一行,我们先计算第一行的方案数,设f[i][j]f[i][j]f[i][j]表示到了ii ...
CodeForces 798D 思维,贪心
CodeForces 798D 题意:长度为 n的两个数组 a[]和 b[],要找出 k ( k<=n/2+1 )个下标,使得在两个数组中这 k个数的和乘上 2 要大于所有数的和. tags: ...
codeforces - 1315C - 思维题
原题链接:https://codeforces.com/problemset/problem/1315/C 翻译: 这是一个猜谜游戏,你需要猜中一个序列,谜题是一个序列,我们设为b,长度为n.你需要根 ...
Balanced Substring CodeForces - 873B (思维+前缀和)
Balanced Substring CodeForces - 873B You are given a string s consisting only of characters 0 and 1. ...
Ivan and Powers of Two
Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorte ...

【Ivan and Powers of Two】【CodeForces - 305C】（思维）（Set 应用)

【Ivan and Powers of Two】【CodeForces - 305C】（思维）（Set 应用)相关推荐

最新文章

热门文章