HDU-1024 Max Sum plus Plus (dp+ scrolling array optimization)

Title Link: http://acm.hdu.edu.cn/showproblem.php?pid=1024

Test instructions: Given n numbers, the maximum value of the M segment (no continuous between segments and segments, but continuous in a period)

For example:2 5 1-2 2 3-1 Five digits Select 2, choose 1 and 2 3 for each of the two paragraphs.

Puzzle: dp[i][j] Select I in the former J number, and then according to whether the number of J is independent into a paragraph, you can write

State transition equation:dp[i][j]=max (Dp[i][j-1]+num[j],max (dp[i-1][k)) +num[j])

Here Max (Dp[i-1][k]) stands for the maximum value of the I-1 segment, and then adds Num[j] as a separate paragraph.

But the problem does not give the range of M, it is possible to burst memory and explosion, you need to deal with.

For explosion-proof Memory: note dp[i][*] only and dp[i][*],dp[i-1][*], that is, the current state is only related to the previous state, you can use the scrolling array optimization (data).

For explosion protection: since Max (Dp[i-1][k] represents the maximum value of the i-1 segment, we can use an array pre to store the maximum value before

State transition equation: Dp[i][j]=max (dp[i][j-1]+num[j],pre[j-1]+num[j]) Find out what I'm doing, so

The final state transfer equation:dp[j]=max (Dp[j-1]+num[j],pre[j-1]+num[j])

1#include <iostream>2#include <algorithm>3 using namespacestd;4 5 Const intn=1000010;6 Const intinf=0x3f3f3f3f;7 intNum[n],pre[n],dp[n];8 9 intMain () {Ten     intn,m; One      while(SCANF ("%d%d", &m,&n)! =EOF) { A          for(intI=1; i<=n;i++) scanf ("%d", &num[i]), dp[i]=0, pre[i]=0; -          -         intMAX; thedp[0]=pre[0]=0; -          for(intI=1; i<=m;i++){ -max=-INF; -              for(intj=i;j<=n;j++) {//here starts with I, because I need to have at least I number to support I segment  +Dp[j]=max (dp[j-1]+num[j],pre[j-1]+num[j]); -pre[j-1]=MAX; +max=Max (max,dp[j]); A             } at         } -              -printf"%d\n", MAX);  -     }  -     return 0; -}

HDU-1024 Max Sum plus Plus (dp+ scrolling array optimization)