最大连续子序列

#include<stdio.h>
#include <malloc.h>
#include <string.h>
#include <string.h>
#include <iostream>
using namespace std;
int MaxSumSub_1(int a[],int n){
    //暴力法：算法复杂度为 n^3
    int max = 0;
    for (int i = 0; i < n; ++i) {
        for (int j = i; j < n; ++j) {
            int sum = 0;
            for (int k = i; k <= j; ++k) {
                sum += a[k];
            }
            if(max<sum) max=sum;
        }
    }
    return max;
}
int MaxSumSub_2(int a[],int n){
    //暴力法的优化：算法复杂度 n^2
    int max = 0;
    for (int i = 0; i < n; ++i) {
        int sum = 0;
        for (int j = i; j < n; ++j) {
            sum += a[j];
            if(max<sum) max = sum;
        }
    }
    return max;
}
int MAX(int a,int b){
    return a>=b? a:b;
}
int MaxSumSub_3(int a[],int n){
    //动态规划思想：dp状态转移方程为：  max(dp[i]) = max（ dp[i-1]+a[i] , a[i]);
    //时间复杂度为： n
    int max = 0;
    int *dp = (int*)malloc(sizeof(int)*(n+1));
    memset(dp,0, sizeof(dp));
    for (int i = 0; i < n; ++i) {
        dp[i+1] = MAX(dp[i]+a[i],a[i]);
        if(dp[i+1]>max)
            max = dp[i+1];
    }
    return max;
}
int MaxSumSub_4(int a[],int from,int to){
//当然
    //分治法：
    if(from==to)
        return a[from];
    int mid = (from+to)/2;
    int m1 = MaxSumSub_4(a,from,mid);
    int m2 = MaxSumSub_4(a,mid+1,to);
    int left = a[mid],now = a[mid];
    for (int i = mid-1; i >= from ; --i) {
        now += a[i];
        left = MAX(now,left);
    }
    int right = a[mid+1];
    now = a[mid+1];
    for (int i = mid+2; i <= to; ++i) {
        now += a[i];
        right = MAX(now,right);
    }
    int m3 = left + right;
    return MAX(m1,MAX(m2,m3));
}
int main()
{
    int n,a[20];
    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    cout << MaxSumSub_1(a,n) << endl;
    cout << MaxSumSub_2(a,n) << endl;
    cout << MaxSumSub_3(a,n) << endl;
    cout << MaxSumSub_4(a,0,n) << endl;
    return 0;
}
/*
 input:
 7
 1 4 -5 9 8 3 -6
 output: (9, 8, 3) 20
 8
 1 -2 3 10 -4 7 2 -5
 output: (3, 10, -4, 7, 2)  18
 */

来源：CSDN

作者：吴成伟

链接：https://blog.csdn.net/qq_43324779/article/details/104118697