01-複雜度2 Maximum Subsequence Sum （25 分)

題目地址：PTA

題目展示：

Given a sequence of K integers { N1, N2, …, NK }. A continuous subsequence is defined to be { Ni, Ni+1, …, Nj } where 1 <= i <= j <= K. The Maximum Subsequence is the continuous subsequence which has the largest sum of its elements. For example, given sequence { -2, 11, -4, 13, -5, -2 }, its maximum subsequence is { 11, -4, 13 } with the largest sum being 20.

Now you are supposed to find the largest sum, together with the first and the last numbers of the maximum subsequence.

Input Specification:

Each input file contains one test case. Each case occupies two lines. The first line contains a positive integer K (<= 10000). The second line contains K numbers, separated by a space.

Output Specification:

For each test case, output in one line the largest sum, together with the first and the last numbers of the maximum subsequence. The numbers must be separated by one space, but there must be no extra space at the end of a line. In case that the maximum subsequence is not unique, output the one with the smallest indices i and j (as shown by the sample case). If all the K numbers are negative, then its maximum sum is defined to be 0, and you are supposed to output the first and the last numbers of the whole sequence.

Sample Input:

10
-10 1 2 3 4 -5 -23 3 7 -21
Sample Output:

10 1 4

分析

1. 使用的是“在線處理”方法，時間複雜度只有 O(n)
2. 當序列全是負數的時候，輸出 0(最大子列和)，序列第一個數字，序列最後一個數字
3. 當序列只有 0 和負數時，輸出 0(最大子列和)，0 0
4. 注意最大子列和前面和後面爲0的情況
5. 有多個最大子列和時，輸出 i 和 j 最小的那個
6. 注意：舉例的輸出中 1 和 4 不是下標 而是數值

代碼

#include <stdio.h>
#define maxn 10005
#define INF 0x3f3f3f3f
int a[maxn];
int n;
void f() {
    int lsLeft=0, right=0, left=0;//lsLeft爲臨時左下標，left爲最大子序列最左邊下標，right爲最右邊下標
    int ThisSum=0, MaxSum=-INF;//首先ThisSum代表臨時子列和，MaxSum爲最大子列和
    for (int i = 0; i < n; i++) {
        ThisSum += a[i];
        if (ThisSum < 0) {
            ThisSum = 0;
            lsLeft = i+1;//更新臨時下標
        }
        else if (ThisSum > MaxSum) {
            MaxSum = ThisSum;
            left = lsLeft;//更新左下標
            right = i;//右下標
        }
    }
    if (MaxSum < 0) {
        printf("0 %d %d", a[0], a[n-1]);
    }
    else {
        printf("%d %d %d", MaxSum, a[left], a[right]);
    }
}
int main() {
    //freopen("data.txt", "r", stdin);
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        scanf("%d", &a[i]);
    }
    f();
    return 0;
}