【1】【数学】CodeForces 588C Duff and Weight Lifting

C. Duff and Weight Lifting

time limit per test：1 second
memory limit per test：256 megabytes
input：standard input
output：standard output

Recently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of i-th of them is 2wi pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there’s no more weight left. Malek asked her to minimize the number of steps.

Duff is a competitive programming fan. That’s why in each step, she can only lift and throw away a sequence of weights 2a1, …, 2ak if and only if there exists a non-negative integer x such that 2a1 + 2a2 + … + 2ak = 2x, i. e. the sum of those numbers is a power of two.

Duff is a competitive programming fan, but not a programmer. That’s why she asked for your help. Help her minimize the number of steps.

Input
The first line of input contains integer n (1 ≤ n ≤ 10^6), the number of weights.

The second line contains n integers w1, …, wn separated by spaces (0 ≤ wi ≤ 10^6 for each 1 ≤ i ≤ n), the powers of two forming the weights values.

Output
Print the minimum number of steps in a single line.

Examples
input
5
1 1 2 3 3
output
2

input
4
0 1 2 3
output
4

Note
In the first sample case: One optimal way would be to throw away the first three in the first step and the rest in the second step. Also, it’s not possible to do it in one step because their sum is not a power of two.

In the second sample case: The only optimal way is to throw away one weight in each step. It’s not possible to do it in less than 4 steps because there’s no subset of weights with more than one weight and sum equal to a power of two.

链接
CodeForces 588C

题意
扔东西。给出的是2^k中的指数k，相加和为2的几次幂的数可以一次性扔掉，问最少要扔几次。

分析
16/8/10首先2^m+2^n=2^a当m!=n时不成立（胡乱证了一通），然后要预估最多会到多少，由于10^6<2^20，所以差不多加到10^6+32，本来想要一点点扩大数组，wa了，不知道原因= =。