(CodeForces
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(CodeForces - 455A)Boredom
time limit per test:1 second
memory limit per test:256 megabytes
input:standard input
output:standard output
Alex doesn’t like boredom. That’s why whenever he gets bored, he comes up with games. One long winter evening he came up with a game and decided to play it.
Given a sequence a consisting of n integers. The player can make several steps. In a single step he can choose an element of the sequence (let’s denote it ak) and delete it, at that all elements equal to ak + 1 and ak - 1 also must be deleted from the sequence. That step brings ak points to the player.
Alex is a perfectionist, so he decided to get as many points as possible. Help him.
Input
The first line contains integer n (1 ≤ n ≤ 105) that shows how many numbers are in Alex’s sequence.
The second line contains n integers a1, a2, …, an (1 ≤ ai ≤ 105).
Output
Print a single integer — the maximum number of points that Alex can earn.
Examples
input
2
1 2
output
2
input
3
1 2 3
output
4
input
9
1 2 1 3 2 2 2 2 3
output
10
Note
Consider the third test example. At first step we need to choose any element equal to 2. After that step our sequence looks like this [2, 2, 2, 2]. Then we do 4 steps, on each step we choose any element equals to 2. In total we earn 10 points.
题目大意:一个有n个数的数字串,当你将这个数字串中的ak这个数删除时,这个数字串中所有的ak-1和ak+1都将会被删除(注意这不是数组下标,即不是这个数的相邻两个数,因为这样wa了几发),相应的你会得到ak分数,问当你把所有数字都删除的时候所能获得的最大分数是多少。
思路:可从dp角度考虑。设f[i]表示i这个数字删或者不删时所能得到分数的最大值。当i这个数字不删时,那么必定i-1会删除,此时f[i]=f[i-1];当i这个数字删除时,则f[i]=f[i-2]+i*num[i](num[i]记录数字i出现的个数)。
综上所述,f[i]=max(f[i-1],f[i-2]+i*num[i])。
(其中初值为f[0]=0,f[1]=num[1])
显然答案是,f[mx] (mx表示数字串中最大的那个数)。
ps:最大的情况是
#include<cstdio>#include<algorithm>#include<cstring>using namespace std;typedef long long LL;const int maxn=100005;LL f[maxn],num[maxn];int main(){ int n; while(scanf("%d",&n)!=EOF) { int x,mx=0; memset(num,0,sizeof(num)); for(int i=0;i<n;i++) { scanf("%d",&x); if(mx<x) mx=x; num[x]++; } f[0]=0; f[1]=num[1]; for(int i=2;i<=mx;i++) f[i]=max(f[i-1],f[i-2]+i*num[i]); printf("%lld\n",f[mx]); } return 0;}
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