Max Sum
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 281607 Accepted Submission(s): 66885
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
25 6 -1 5 4 -77 0 6 -1 1 -6 7 -5
Sample Output
Case 1:14 1 4Case 2:7 1 6
题目大意:在一个连续的序列中,求出和最大的子序列。
解题思路:我们从前往后遍历整个序列,用idx1表示子序列的头,idx2表示尾,sum1记录当前遍历到的项的前面的和(idx1~idx2-1),如果sum1<0就需要把idx1往后移一位,但是必须小于idx2,用一个sum2记录当前遍历所得到的最大和,然后用一个ans记录遍历过程的最优解即可,整个遍历过程有点类似于尺取法的思想.
AC代码:
#include<stdio.h> #include<iostream> #include<algorithm> #include<string.h> #include<math.h> #include<stdlib.h> #include<queue> #include<map> #define bug printf("*********\n"); #define mem(a, b) memset(a, b, sizeof(a)); #define in1(n) scanf("%d" ,&n); #define in2(a, b) scanf("%d%d", &a, &b); #define out(n) printf("%d\n", n); using namespace std; typedef pair<long long, int> par; const int mod = 1e9+7; const int INF = -1e9; const int N = 1000010; const double pi = 3.1415926; int T, n, a[100010]; int idx1, idx2, ans, sum1, sum2, l, r; int main() { int k = 1; scanf("%d", &T); int t = T; while(T --) { idx1 = idx2 = 1; //开始都指向序列的头 l = r = 1; sum1 = sum2 = 0; ans = INF; scanf("%d", &n); for(int i = 1; i <= n; i ++) scanf("%d", &a[i]); while(idx2 <= n) { sum1 = sum2; sum2 += a[idx2]; while(sum1 < 0 && idx1 < idx2) { //小于0的部分当然要去掉 sum2 -= a[idx1]; sum1 -= a[idx1]; idx1 ++; } if(sum2 > ans) { //最优解 l = idx1; r = idx2; ans = sum2; } idx2 ++; } printf("Case %d:\n", k ++); printf("%d %d %d\n", ans, l, r); if(k <= t) printf("\n"); //这里感觉是一大坑点,最后一组不输出 } return 0; }