PTA数据结构-01-复杂度2 Maximum Subsequence Sum

最新推荐文章于 2021-04-20 16:08:35 发布

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本文介绍了一种解决最大连续子序列求和问题的算法，通过详细解析输入输出规格，提供了一个Java实现案例，该算法能够找出具有最大元素和的连续子序列及其范围。

一、题目

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

二、解答

import java.util.Scanner;

//21:40
public class Main {
    public static void main(String[] args) {
        //get arrs
        Scanner sc = new Scanner(System.in);
        String lenStr = sc.nextLine();
        String arrsStr = sc.nextLine();
        sc.close();

        //processing arrs
        int len = Integer.parseInt(lenStr.trim());
        int[] arrs = new int[len];
        String[] arrsStrs = arrsStr.split(" ");
        for (int i = 0; i < len; i++) {arrs[i] = Integer.parseInt(arrsStrs[i].trim());}

        //start to end
        printArrs(getMaxSubSeqSum(arrs));

    }
    public static int[] getMaxSubSeqSum(int[] arrs){
        int tempFirst = arrs[0];
        int tempLast = tempFirst;
        int tempSum = tempFirst;
        int maxSum = tempFirst < 0 ? -1 : tempFirst;
        int maxFirst = tempFirst;
        int maxLast = tempFirst;

        for (int i = 1; i < arrs.length; i++) {
            if (tempSum < 0) {
                tempFirst = arrs[i];
                tempSum = tempFirst;
            } else {
                tempLast = arrs[i];
                tempSum += tempLast;
            }
            if (tempSum > maxSum) {
                maxSum = tempSum;
                maxFirst = tempFirst;
                maxLast = tempFirst > tempLast ? tempFirst : tempLast;
            }
        }

        int[] result;
        if (maxSum < 0) result = new int[]{0, arrs[0], arrs[arrs.length-1]};
        else result = new int[]{maxSum, maxFirst, maxLast};
        return result;
    }
    public static void printArrs (int[] arrs){
        String result = "";
        for (int arr : arrs) {
            result += arr + " ";
        }
        System.out.println(result.trim());
    }
}