Maximum Subarray Sum

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题目

https://leetcode.com/problems/maximum-subarray/description/

-w950

思路

很经典的一道题目，属于分治和DP的典型题目。

分治

时间复杂度应该是O(nlogn)，设计起来，如同题目中说的：subtle
TODO..

DP

DP推导式：
dp[i] = max(dp[i - 1] + nums[i], nums[i])

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class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        vector<int> dp(nums.size(), 0);
        for (int i = 0; i < nums.size(); i++) {
            dp[i] = max(nums[i], dp[i - 1] + nums[i]);
        }
        return *max_element(dp.begin(), dp.end());
    }
};

简化之后，用O(1)的时间复杂度就可以：

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class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int res = INT_MIN;
        int sum = 0;
        for (int n : nums) {
            sum = max(n, sum + n);
            res = max(sum, res);
        }
        return res;
    }
};

带下标（PAT-A 1007）

https://pintia.cn/problem-sets/994805342720868352/problems/994805514284679168

1007 Maximum Subsequence Sum (25)（25 分）
Given a sequence of K integers { N~1~, N~2~, …, N~K~ }. A continuous subsequence is defined to be { N~i~, N~i+1~, …, N~j~ } 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:

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-10 1 2 3 4 -5 -23 3 7 -21

Sample Output:

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10 1 4

思路

记录左右下标，当更新max的同时更新下标

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#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
int main() {
    int K;
    cin >> K;
    vector<int> num(K);
    for (int i = 0; i < K; i++) {
        cin >> num[i];
    }
    int res = -1;
    int resL = 0, resR = K - 1;
    int sum = 0;
    int l = 0;
    for (int i = 0; i < K; i++) {
        sum += num[i];
        if (sum < 0) {
            sum = 0;
            l = i + 1;
        } else if (sum > res) {
            res = sum;
            resL = l;
            resR = i;
        }
    }
    if (res < 0) {
        res = 0;
        resL = 0;
        resR = K - 1;
    }
    cout << res << " " << num[resL] << " " << num[resR];
    return 0;
}