sum max(hdu 1003)
观察可以发现,0,1,2,……,n结尾的分组中,
maxsum a[0] = a[0]
maxsum a[1] = max( a[0] + a[1] ,a[1]) = max( maxsum a[0] + a[1] ,a[1])
maxsum a[2] = max( max ( a[0] + a[1] + a[2],a[1] + a[2] ),a[2])
= max( max( a[0] + a[1] ,a[1]) + a[2] , a[2])
= max( maxsum a[1] + a[2] , a[2])
……
依此类推,可以得出通用的式子。
maxsum a[i] = max(maxsum a[i-1] + a[i],a[i])
//#define LOCAL #include<cstdio> const int INF=-1000000; int sum,sum_max,begin,end,temp,T,N,conn; void solve() { scanf("%d",&N); int a; sum_max=INF,sum=0,temp=1,begin=1; for(int i=0;i<N;i++) { scanf("%d",&a); sum=sum+a; if(sum_max<sum) { sum_max=sum; begin=temp; end=i+1; } if(sum<0) { sum=0; temp=i+2; } } printf("Case %d:\n%d %d %d\n",(conn-T),sum_max,begin,end); if(T!=0) { printf("\n"); } } int main() { #ifdef LOCAL freopen("1003.in","r",stdin); freopen("1003.out","w",stdout); #endif scanf("%d",&T); conn=T; while(T--) { solve(); } return 0; }
Max Sum
Time
Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K
(Java/Others)
Total Submission(s): 136354 Accepted Submission(s):
31568
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