标签：blog sel div ati style stream spec sequence 思路
hdu1024 Max Sum Plus Plus
Now I think you have got an AC in Ignatius.L‘s "Max Sum" problem. To be a brave ACMer, we always challenge ourselves to more difficult problems. Now you are faced with a more difficult problem.
Given a consecutive number sequence S 1, S 2, S 3, S 4 ... S x, ... S n (1 ≤ x ≤ n ≤ 1,000,000, -32768 ≤ S x ≤ 32767). We define a function sum(i, j) = S i + ... + S j (1 ≤ i ≤ j ≤ n).
Now given an integer m (m > 0), your task is to find m pairs of i and j which make sum(i 1, j 1) + sum(i 2, j 2) + sum(i 3, j 3) + ... + sum(i m, j m) maximal (i x ≤ iy ≤ j x or i x ≤ j y ≤ j x is not allowed).
But I`m lazy, I don‘t want to write a special-judge module, so you don‘t have to output m pairs of i and j, just output the maximal summation of sum(i x, j x)(1 ≤ x ≤ m) instead. ^_^
Input
Each test case will begin with two integers m and n, followed by n integers S 1, S2, S 3 ... S n.
Process to the end of file.
Output
Output the maximal summation described above in one line.
Sample Input
1 3 1 2 3
2 6 -1 4 -2 3 -2 3
Sample Output
6
8
Hint
Huge input, scanf and dynamic programming is recommende
解题思路：
首先定义各个数组，尽量易懂，
a[i] 储存输入的数据
now[j]，表示以第j个元素为结尾的i个子段的最大和，必须包含a[j]。
pre[j]，表示前j个元素i个子段的最大和，不一定包含a[j]。
dp[i][j]，表示前j个元素i个子段的最大和，包含a[j]。
原始状态转移方程：
dp[i][j]=max(dp[i][j-1]+a[j]，dp[i-1][k]+a[j]) (i-1<=k<=j-1)
有两种情况：
1.直接将第j个元素加在第i个子段之后。
2.第j个元素单独作为一个子段，那么前面必须是i-1个子段。
状态转移方程就是比较这两种情况较大值
实现代码：
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
#define M 1000002
int a[M],now[M],pre[M];
int main()
{
int m,n,i,j,Max;
while(scanf("%d%d",&m,&n)==2)
{
for(i=1;i<=n;i++)
scanf("%d",&a[i]);
memset(now,0,sizeof(now));
memset(pre,0,sizeof(pre));
for(i=1;i<=m;i++)
{
Max = -999999999; //此处max值尽量开大，max是和，开小了就WA,
for(j=i;j<=n;j++)
{
now[j]=max(now[j-1]+a[j],pre[j-1]+a[j]);
//now[j]有两种来源，一种是直接在第i个子段之后添加a[j]
//一种是是a[j]单独成为1个子段
pre[j-1]=Max; //更新pre使得pre是前j-1个中最大子段和
if(now[j]>Max)
Max=now[j];
}
}
printf("%d\n",Max);
}
return 0;
}
hdu1024 Max Sum Plus Plus (Dp)
标签：blog sel div ati style stream spec sequence 思路
原文地址：http://www.cnblogs.com/kls123/p/6804434.html
