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sum max(hdu 1003)

2024-07-04 07:49:35   231人阅读

 

观察可以发现，0，1，2，……，n结尾的分组中，

maxsum a[0] = a[0]

maxsum a[1] = max( a[0] + a[1] ，a[1])  = max( maxsum a[0] + a[1] ，a[1]) 

maxsum a[2] = max( max ( a[0] + a[1] + a[2]，a[1] + a[2] )，a[2])  

   = max(  max( a[0] + a[1] ，a[1]) + a[2] ， a[2]) 

   = max(  maxsum a[1] + a[2] ， a[2])

……

依此类推，可以得出通用的式子。

maxsum a[i] = max(maxsum a[i-1] + a[i]，a[i])

//#define LOCAL
#include<cstdio>
const int INF=-1000000;
int sum,sum_max,begin,end,temp,T,N,conn;
void solve()
{
    scanf("%d",&N);
    int a;
    sum_max=INF,sum=0,temp=1,begin=1;
    for(int i=0;i<N;i++)
    {
        scanf("%d",&a);
        sum=sum+a;
        if(sum_max<sum)
        {
            sum_max=sum;
            begin=temp;
            end=i+1;
        }
        if(sum<0)
        {
            sum=0;
            temp=i+2;
        }
    }
    printf("Case %d:\n%d %d %d\n",(conn-T),sum_max,begin,end);
    if(T!=0)
    {
        printf("\n");
    }
}
int main()
{
#ifdef LOCAL
    freopen("1003.in","r",stdin);
    freopen("1003.out","w",stdout);
#endif    
    scanf("%d",&T);
    conn=T;
    while(T--)
    {
        solve();
    }
    return 0;
}

 

 

Max Sum

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 136354    Accepted Submission(s): 31568


Problem Description
Given a sequence a[1],a[2],a[3]......a[n], your job is to calculate the max sum of a sub-sequence. For example, given (6,-1,5,4,-7), the max sum in this sequence is 6 + (-1) + 5 + 4 = 14.
 

 

Input
The first line of the input contains an integer T(1<=T<=20) which means the number of test cases. Then T lines follow, each line starts with a number N(1<=N<=100000), then N integers followed(all the integers are between -1000 and 1000).
 

 

Output
For each test case, you should output two lines. The first line is "Case #:", # means the number of the test case. The second line contains three integers, the Max Sum in the sequence, the start position of the sub-sequence, the end position of the sub-sequence. If there are more than one result, output the first one. Output a blank line between two cases.
 

 

Sample Input
2 5 6 -1 5 4 -7 7 0 6 -1 1 -6 7 -5
 

 

Sample Output
Case 1: 14 1 4 Case 2: 7 1 6
 

 

Author
Ignatius.L


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