• Max Sum(dp)


    题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1003

    Max Sum

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
    Total Submission(s): 178388    Accepted Submission(s): 41628


    Problem 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
     
    Author
    Ignatius.L
     
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    题意 : 给出一个序列,输出最大子序列和,简单的dp
    dp数组储存的是以这个值结尾的最长的子序列和
    dp[i] = max(dp[i-1]+num[i] , num[i]);
    但是因为要保存起始和终止点的位置,所以可以用结构体来储存dp;
    下面是代码
     1 #include<cstdio>
     2 #include<cstring>
     3 #include<algorithm>
     4 using namespace std;
     5 #define N 100005
     6 #define ll long long
     7 struct DP{
     8     ll sum;
     9     int l;
    10     int r;
    11     bool operator < (const DP d) const
    12     {
    13         if(sum!=d.sum) return d.sum<sum;
    14         else if(l!=d.l) return l<d.l;
    15         else return r<d.r;
    16     }
    17 }dp[N];
    18 ll num[N];
    19 int main()
    20 {
    21     int T;
    22     scanf("%d",&T);
    23     for(int cnt = 0 ; cnt < T ; cnt++)
    24     {
    25         int n;
    26         scanf("%d",&n);
    27         for(int i = 0 ;i < n ;i++)
    28             dp[i].sum = 0, dp[i].l = i,dp[i].r = i;
    29         for(int i = 0 ;i < n ;i++)
    30         {
    31             scanf("%lld",&num[i]);
    32             if(i==0) dp[i].sum = num[0],dp[i].l = 0,dp[i].r = 0;
    33             
    34             else 
    35             {
    36                 if(dp[i-1].sum+num[i]>=num[i])
    37                 {
    38                     dp[i].sum = dp[i-1].sum+num[i];
    39                     dp[i].l = dp[i-1].l;
    40                     dp[i].r = i;
    41                 }
    42                 else 
    43                 {
    44                     dp[i].sum = num[i];
    45                     dp[i].l = i;
    46                     dp[i].r = i;
    47                 }
    48             }
    49         }
    50             sort(dp,dp+n);
    51             if(cnt!=0) puts("");
    52             printf("Case %d:
    ",cnt+1);
    53             printf("%lld %d %d
    ",dp[0].sum,dp[0].l+1,dp[0].r+1);
    54     }            
    55     return 0;
    56 }
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  • 原文地址:https://www.cnblogs.com/shanyr/p/4717363.html
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