POJ #2479

Hi, I'm back.

This is a realy classic DP problem to code. 

1. You have to be crystal clear about what you are going to solve.
2. Apparently there are 2 DP sections
3. Think carefully about recurrence relations
5. Details: take care of indices boundaries - it costed me 1hr to find an indexing bug!
6. Again: think crystal clear before you code!

And, #2593 is exactly the same. 

Here is my AC code:

#include <stdio.h>

#define MAX_INX 50010
#define Max(a,b) (a)>(b)?(a):(b)

int max_sum2(int *pData, int cnt)
{
    //    DP: Max sum of sub-sequence: dp[i] = MAX(num[i], dp[i-1] + num[i])

    //    Left -> Right
    int  lt[MAX_INX] = { 0 };    
    lt[0] = pData[0];
    for (int i = 1; i < cnt; i ++)
    {
        lt[i] = Max(pData[i], lt[i - 1] + pData[i]);
    }
    
    //    Right -> Left
    int   rt[MAX_INX] = { 0 };
    int     rtm[MAX_INX] = { 0 };
    rt[cnt-1] = pData[cnt-1];
    for (int i = cnt-2; i >= 0; i--)
    {
        rt[i] = Max(pData[i], rt[i + 1] + pData[i]);
    }
    rtm[cnt-1] = rt[cnt-1];
    for (int i = cnt-2; i >=0; i--)
    {        
        rtm[i] = Max(rtm[i+1], rt[i]);
    }

    //    O(n) to find real max
    int ret = -10010;
    for (int i = 0; i < cnt - 1; i ++)
    {
        ret = Max(ret, lt[i] + rtm[i+1]);
    }

    return ret;
}

int main()
{    
    int nTotal = 0; 
    scanf("%d", &nTotal);

    while (nTotal--)
    {
        int num[MAX_INX] = { 0 };
        
        //    Get Input
        int nCnt = 0; scanf("%d", &nCnt);        
        for (int i = 0; i < nCnt; i ++)
        {
            scanf("%d", num + i);
        }
        
        printf("%d
", max_sum2(num, nCnt));
    }

    return 0;
}