Maximum sum
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 40740 | Accepted: 12706 |
Description
Given a set of n integers: A={a1, a2,..., an}, we define a function d(A) as below:
Your task is to calculate d(A).![]()
Input
The input consists of T(<=30) test cases. The number of test cases (T) is given in the first line of the input.
Each test case contains two lines. The first line is an integer n(2<=n<=50000). The second line contains n integers: a1, a2, ..., an. (|ai| <= 10000).There is an empty line after each case.
Each test case contains two lines. The first line is an integer n(2<=n<=50000). The second line contains n integers: a1, a2, ..., an. (|ai| <= 10000).There is an empty line after each case.
Output
Print exactly one line for each test case. The line should contain the integer d(A).
Sample Input
1 10 1 -1 2 2 3 -3 4 -4 5 -5
Sample Output
13
Hint
In the sample, we choose {2,2,3,-3,4} and {5}, then we can get the answer.
Huge input,scanf is recommended.
Huge input,scanf is recommended.
Source
POJ Contest,Author:Mathematica@ZSU
题意://题目思路是从左到右分别求出它们所在位置的最大连续和,然后从右到左求出它们所在的最大连续和,从后往前求最大和,并加上在此位置之前的一个数的最大和,不断比较
#include <algorithm>
#include <iostream>
#include <cstring>
#include <string>
#include <cstdio>
#include <queue>
#include <vector>
#include <cmath>
#include <map>
#include <set>
using namespace std;
#define N 60000
#define INF 0x3f3f3f3f
int a[N];
int dp[N];
int main()
{
int T,n;
scanf("%d",&T);
while(T--) {
scanf("%d",&n);
for(int i=1;i<=n;i++) {
scanf("%d",&a[i]);
}
memset(dp,0,sizeof(dp));
dp[1]=a[1];
int sum=a[1];
int ans=a[1];
for(int i=2;i<=n;i++) {
if(sum<0)
sum=0;
sum+=a[i];
if(sum>ans)
ans=sum;
dp[i]=ans;
}
sum=a[n];
ans=a[n];
int maxi=dp[n-1]+sum;
for(int i=n-1;i>=2;i--) {
if(sum<0)
sum=0;
sum+=a[i];
if(sum>ans)
ans=sum;
maxi=max(maxi,dp[i-1]+ans);
}
printf("%d\n",maxi);
}
return 0;
}