Find_Maximum_Subarray C++

Find_Maximum_Subarray

最大子数组一定在三种情况中：
A[low,mid] , A[mid+1,high] ,A[i,j]

Divide:
2分方式：

if (low == high)
		return { low,high,A[low] };
	else
	{
		int mid = (low + high) / 2;
		//vec_f = left_low,left_high,left_sum
		auto vec_f = Find_Maximum_Subarray(A, low, mid);
		//vec_r = right_low,right_high,right_sum
		auto vec_r = Find_Maximum_Subarray(A, mid + 1, high);

Conquer:
子问题找最大数组：
[i,j] 可以是 [low,mid], [mid+1,high]

std::vector<int> // v.front() = max_left,v[1]= max_right,v.back()=left_sum + right_sum
Find_Max_Crossing_Subarray(std::vector<int> A, int low, int mid, int high)
{
	int left_sum = INT_MIN;
	int sum = 0,max_left = mid, max_right=mid;
	for (auto i = mid; i >= low;--i)
	{
		sum += A[i];
		if (sum > left_sum)
		{
			left_sum = sum;
			max_left = i;
		}
	}
	int right_sum = INT_MIN;
	sum = 0;
	for (auto j = mid + 1;j <= high;++j)
	{
		sum += A[j];
		if (sum > right_sum)
		{
			right_sum = sum;
			max_right = j;
		}
	}
	return { max_left,max_right,left_sum + right_sum };
}

最后找到三者中最大的

if ((vec_f.back() >= vec_r.back()) && (vec_f.back() >= vec_c.back()))
			return { vec_f[0],vec_f[1],vec_f[2] };
		if ((vec_r.back() >= vec_f.back()) && (vec_r.back() >= vec_c.back()))
			return { vec_r[0],vec_r[1],vec_r[2] };
		else 
			return { vec_c[0],vec_c[1],vec_c[2] };

c++ code
#include"FIND_MAXIMUM_SUBARRAY .h"

#pragma once
#include<vector>
#include<limits>
#include<string>

std::vector<int> // v.front() = max_left,v[1]= max_right,v.back()=left_sum + right_sum
Find_Max_Crossing_Subarray(const std::vector<int> &A,const int &low,const int &mid,const int &high)
{
	int left_sum = INT_MIN;
	int sum = 0,max_left = mid, max_right=mid;
	for (auto i = mid; i >= low;--i)
	{
		sum += A[i];
		if (sum > left_sum)
		{
			left_sum = sum;
			max_left = i;
		}
	}
	int right_sum = INT_MIN;
	sum = 0;
	for (auto j = mid + 1;j <= high;++j)
	{
		sum += A[j];
		if (sum > right_sum)
		{
			right_sum = sum;
			max_right = j;
		}
	}
	return { max_left,max_right,left_sum + right_sum };
}

std::vector<int> //v.front() = low ,v[1] = high, v.back() = sum;
Find_Maximum_Subarray(const std::vector<int> &A,const int low,const int high)
{
	//一用Divide方式 ：带入子问题的下标(范围)
	if (low == high)
		return { low,high,A[low] };
	else
	{
		int mid = (low + high) / 2;
		//vec_f = left_low,left_high,left_sum
		auto vec_f = Find_Maximum_Subarray(A, low, mid);
		//vec_r = right_low,right_high,right_sum
		auto vec_r = Find_Maximum_Subarray(A, mid + 1, high);

		//Conquer部分：如何解决子问题
		//vec_c = cross_low,cross_high,cross_sum
		auto vec_c = Find_Max_Crossing_Subarray(A, low, mid, high);

		//子问题的答案如何让处理： 不影响每次带入Find_c 的下标
		if ((vec_f.back() >= vec_r.back()) && (vec_f.back() >= vec_c.back()))
			return { vec_f[0],vec_f[1],vec_f[2] };
		if ((vec_r.back() >= vec_f.back()) && (vec_r.back() >= vec_c.back()))
			return { vec_r[0],vec_r[1],vec_r[2] };
		else 
			return { vec_c[0],vec_c[1],vec_c[2] };
	}
}

main.cpp

#include"FIND_MAXIMUM_SUBARRAY .h"
void find_maximum_subarray()
{
    //13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7
    vector<int> arr = { 13,-3,-25,20,-3,-16,-23 };
    cout << " array is " << endl;
    for (auto const& i : arr)
        cout << i << " ";
    cout << endl;
    auto v_a = Find_Maximum_Subarray(arr, 0, arr.size()-1);
    cout << " Sum: " << v_a[2] << endl;
    cout << "  max subarray is " << endl;
    for (auto i = v_a[0];i <= v_a[1];++i)
        cout << arr[i] << " ";
    cout << endl;
}

int main()
{
    find_maximum_subarray();
}