# 最大子段和问题的四种算法（暴力法、优化后的暴力法、分治算法、动态规划算法）

``````import java.util.Random;
import java.util.Scanner;

public class maxSum {
public static void main(String[] args){

Scanner scan = new Scanner(System.in);
Random rd = new Random();

System.out.println("请输入数据规模n（10的倍数）：");
int n = scan.nextInt();
int[] a = new int[n];
for(int i=0; i<n; i++){
a[i] = rd.nextInt(20)-10;
}//初始化数组，生成-10~10的随机数

/*
* test暴力法
*/
long startMili1 = System.currentTimeMillis();
maxSum ms1 = new maxSum();
System.out.println("最大子序列和：" + ms1.maxSum(a));
long endMili1 = System.currentTimeMillis();
System.out.println("暴力法总耗时："+ (endMili1 - startMili1));

/*
* test优化后的暴力法
*/
long startMili2 = System.currentTimeMillis();
maxSum ms2 = new maxSum();
System.out.println("最大子序列和：" + ms2.maxSumBF(a));
long endMili2 = System.currentTimeMillis();
System.out.println("总耗时："+ (endMili2 - startMili2));

/*
* test分治算法
*/
long startMili3 = System.currentTimeMillis();
maxSum ms3 = new maxSum();
System.out.println("最大子序列和：" + ms3.maxSumFZ(a));
long endMili3 = System.currentTimeMillis();
System.out.println("总耗时："+ (endMili3 - startMili3));

/*
* test动态规划算法
*/
long startMili4 = System.currentTimeMillis();
maxSum ms4 = new maxSum();
System.out.println("最大子序列和：" + ms4.MaxSumDynamic(a));
long endMili4 = System.currentTimeMillis();
System.out.println("总耗时："+ (endMili3 - startMili3));

}

//暴力法(O(n^3))
public static int maxSum(int a[]){
int n = a.length - 1;
int sum = 0;
for(int i=1; i<=n; i++){
for(int j=1; j<=n; j++){
int thissum = 0;
for(int k=i; k<=j; k++){
thissum += a[k];
}
if(thissum>sum){
sum = thissum;
}
}
}
return sum;
}

//优化后的暴力法 (O(n^2))
public int maxSumBF(int a[]){
int n = a.length - 1;
int sum = 0;
for(int i=1; i<=n; i++){
int thissum = 0;
for(int j=i; j<=n; j++){
thissum += a[j];
if(thissum>sum){
sum = thissum;
}
}
}
return sum;
}

//分治算法(n log(n))
private static int maxSubSum(int a[], int left, int right){
int sum = 0;
if(left == right){
sum = a[left]>0?a[left]:0;
}else{
int center = (left + right)/2;
int leftsum = maxSubSum(a,left,center);
int rightsum = maxSubSum(a,center+1,right);
int s1 = 0;
int lefts = 0;
for(int i=center; i>=left; i--){
lefts += a[i];
if(lefts>s1){
s1 = lefts;
}
}
int s2 = 0;
int rights = 0;
for(int i=center+1; i<=right; i++){
rights += a[i];
if(rights>s2){
s2 = rights;
}
}
sum = s1 + s2;
f(sum<leftsum){
sum = leftsum;
}
if(sum<rightsum){
sum = rightsum;
}
}
return sum;
}

public static int maxSumFZ(int a[]){
return maxSubSum(a,1,a.length-1);
}

//动态规划算法(O(n))
public static int MaxSumDynamic(int a[]){
int n = a.length-1;
int sum = 0,b = 0;
for(int i=1; i<=n; i++){
if(b>0){
b += a[i];
}else{
b = a[i];
}
if(b>sum){
sum = b;
}
}
return sum;
}
}
``````