查找最长子数组的方法

查找最长子数组的方法,是算法导论里一道很有趣的题目。

比如,给定一个数组{13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7},找出这里面最长的子数组是什么?

因为最长子数组必定是:
1)处于mid左边;
2)处于mid右边;
3)跨过mid
三种情况。

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#include "common.h"

class Solution {
public:

int CrossMidSubArray(vector<int> arr, int mid, int left, int right) {
int left_sum = -10000;
int left_pos = -1;
int pos = mid-1;
int sum = 0;
for (; pos >= left; --pos) {
sum += arr[pos];
if (sum > left_sum) {
left_sum = sum;
left_pos = pos;
}
}
pos = mid + 1;
int right_sum = -10000;
int right_pos = -1;
sum = 0;
for (; pos <= right; ++pos) {
sum += arr[pos];
if (sum > right_sum) {
right_sum = sum;
right_pos = pos;
}
}
sum = left_sum + arr[mid] + right_sum;
cout << " arr[" << mid << "] : ( " << left_pos << ", " << right_pos << "), sum = " << sum << endl;
return sum;
}

int FindMaxSubArray(vector<int> arr, int left, int right) {
if (left == right) return arr[right];
if (left > right) return arr[right];
if (right < left) return arr[left];
int mid = (left + right) / 2;
int left_sum = FindMaxSubArray(arr, left, mid-1);
int right_sum = FindMaxSubArray(arr, mid+1, right);
int mid_sum = CrossMidSubArray(arr, mid, left, right);
return max(left_sum + arr[mid], max(right_sum + arr[mid], mid_sum));
}

int LongestContinueArray(vector<int> arr) {
return FindMaxSubArray(arr, 0, arr.size()-1);
}
};

int main() {
vector<int> arr{13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7};
Solution sol;
cout << sol.LongestContinueArray(arr) << endl;
return 0;
}

算法导论最后给出了另一种思路(习题:4.1-5),如果知道arr[1,j]的最大子数组,那么arr[1,j+1]的最大子数组有两种情况:
1)即:arr[1,j]的最大子数组;
2)或:arr[i,j+1]的最长连续子数组。