HDU 1231 最大连续子序列 &&HDU 1003Max Sum (区间dp问题)

C - 最大连续子序列
Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u
Appoint description:

Description

给定K个整数的序列{ N1, N2, ..., NK },其任意连续子序列可表示为{ Ni, Ni+1, ...,
Nj },其中 1 <= i <= j <= K。最大连续子序列是所有连续子序列中元素和最大的一个,
例如给定序列{ -2, 11, -4, 13, -5, -2 },其最大连续子序列为{ 11, -4, 13 },最大和
为20。
在今年的数据结构考卷中,要求编写程序得到最大和,现在增加一个要求,即还需要输出该
子序列的第一个和最后一个元素。
 

Input

测试输入包含若干测试用例,每个测试用例占2行,第1行给出正整数K( < 10000 ),第2行给出K个整数,中间用空格分隔。当K为0时,输入结束,该用例不被处理。
 

Output

对每个测试用例,在1行里输出最大和、最大连续子序列的第一个和最后一个元
素,中间用空格分隔。如果最大连续子序列不唯一,则输出序号i和j最小的那个(如输入样例的第2、3组)。若所有K个元素都是负数,则定义其最大和为0,输出整个序列的首尾元素。
 

Sample Input

6
-2 11 -4 13 -5 -2
10
-10 1 2 3 4 -5 -23 3 7 -21
6
5 -8 3 2 5 0
1
10
3
-1 -5 -2
3
-1 0 -2
0 

Sample Output

20 11 13
10 1 4
10 3 5
10 10 10
0 -1 -2
0 0 0 

Hint

Hint  Huge input, scanf is recommended.
        
        
 状态转移方程:sum = sum > 0 ? sum + a[i] : a[i] ; 第一个sum是前i个数的和,后面的两个sum是前(i-1)个是的和;如果i前面的和是小于0的,那么加上第i个数肯定比i要小,所以只取第i个数即 a[i],如果是大于0的,则就加上。
 
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
const int maxn=10005;
int a[maxn];
int main(){
    int n;
    while(scanf("%d",&n)!=EOF){
        if(!n)
            break;
        bool flag=true;
    //    memset(a,0,sizeof(a));
        for(int i=1;i<=n;i++){
            scanf("%d",&a[i]);
            if(a[i]>=0)
                flag=false;
        }
         if(flag){
             printf("0 %d %d
",a[1],a[n]);
             continue;
         }
        int ans,sum,head,tail,ans_head,ans_tail;
        ans=sum=a[1];
            ans_head=ans_tail=head=tail=1;
        for(int i=2;i<=n;i++){
              if(sum>0){
                  sum+=a[i];
                  tail=i;
              }
              if(sum<=0){
                   sum=a[i];
                   head=tail=i;
              }
              if(sum>ans){
                  ans=sum;
                  ans_head=head;
                  ans_tail =tail;
              }
        }

        printf("%d %d %d
",ans,a[ans_head],a[ans_tail]);

    }
    return 0;
}
D - Max Sum
Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u
Appoint description:

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
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
const int maxn=100005;
int a[maxn];
int main(){
    int n;
    int t;
    int cnt=0;
    scanf("%d",&t);
    while(t--){
      cnt++;
        scanf("%d",&n);
    //    bool flag=true;
    //    memset(a,0,sizeof(a));
        for(int i=1;i<=n;i++){
            scanf("%d",&a[i]);
        
        }
        int ans,sum,head,tail,ans_head,ans_tail;
        ans=sum=a[1];
            ans_head=ans_tail=head=tail=1;
        for(int i=2;i<=n;i++){
              if(sum>=0){
                  sum+=a[i];
                  tail=i;
              }
              if(sum<0){
                   sum=a[i];
                   head=tail=i;
              }
              if(sum>ans){

                  ans=sum;
                  ans_head=head;
                  ans_tail =tail;
              }
        }
            printf("Case %d:
",cnt);
        printf("%d %d %d
",ans,ans_head,ans_tail);

        if(t!=0)

        printf("
");

    }
    return 0;
}
 
原文地址:https://www.cnblogs.com/13224ACMer/p/4983978.html