2010-5-25 Maximum Sum

Maximum Sum

 

今天有些无聊，就跑到jude online 上做做题，选的题目是 ：

Maximum Sum

Time Limit: 15 Sec  Memory Limit: 128 MB
Submissions: 523  Solved: 41

Description

Given an integer array, how will you find out the increasing subsequence which gives the largest sum. For example,
4, 2, 1, 5, 3
in this subsequence a few possible increasing subsequences are
1) 4
2) 2
3) 1
4) 5
5) 3
6) 4, 5
7) 2, 5
8) 2, 3
9) 1, 5
10) 1, 3

but 4, 5 gievs the maximum sum.

Your task is how to find such the maximum sum in a given integer array.

Input

Multiply Cases, For each case:
The first line contains N(0< N <=1000000), which is the number of the integer array.
The second line contains N integer numbers not exceeding 2000000 by the absolute value.

Output

For each case, output only one integer, which is the maximum sum of increasing subsequences.

Sample Input

5

4 2 1 5 3

Sample Output

9











写完后，修改了几次，每次都是超时，有些郁闷，不过欣慰的是 至少做对了，只是速度太慢了，我最后的代码如下：



#include <stdio.h>

#define N 1000000

int main(){

   int n = 0, i = 0, j = 0;
   int data[N], rec[N], tmp = 0, max, maxn;
   
    scanf("%d", &n);

    for(;i < n;i++){
      
      scanf("%d", &data[i]);
      rec[i] = data[i];
    }

    max = rec[0];
    maxn = 0;

    for(i = 1; i <n; i ++){
       for(j = i -1 ; j >= 0; j --){
          if(data[j] < data[i]){
             if(j == maxn){      
               rec[i] = max + data[i];
               max = rec[i];
               maxn = i;
               goto out;
             }
             else{
                 if((tmp = rec[j] + data[i]) > rec[i]){
                    rec[i] = tmp;
                 }
             }
          }
      }

       if(rec[i] > max){
          max = rec[i];
          maxn = i;
       }
out:  ;
    }

   printf("%d", max);

    return 0;
}





希望高手看到后可以指点下，谢啦！