/**
*
* Source : https://oj.leetcode.com/problems/maximum-subarray/
*
* Created by lverpeng on 2017/7/18.
*
* Find the contiguous subarray within an array (containing at least one number)
* which has the largest sum.
*
* For example, given the array [−2,1,−3,4,−1,2,1,−5,4],
* the contiguous subarray [4,−1,2,1] has the largest sum = 6.
*
* More practice:
*
* If you have figured out the O(n) solution, try coding another solution using
* the divide and conquer approach, which is more subtle.
*
*/
public class MaxSubarray {
/**
* 找到所有子数组中最大的和
*
* 数组从前向后遍历,针对每个数组元素有两个选择,要么加入已经存在子数组,如果该元素的值大于该元素和前面数组总和的和还要大,
* 那就重新开始一个新的子数组,遍历完数组找到最大的和
*
*
* @param arr
* @return
*/
public int maxSubarray (int[] arr) {
int loopCount = 0;
int[] sum = new int[arr.length];
int max = 0;
sum[0] = arr[0];
for (int i = 1; i < arr.length; i++) {
sum[i] = Math.max(arr[i], sum[i - 1] + arr[i]);
max = Math.max(max, sum[i]);
loopCount ++;
}
System.out.println("maxSubarray-->" + loopCount);
return max;
}
public int maxSubarray1 (int[] arr) {
int loopCount = 0;
// 只记录上一个和
int sum = 0;
int max = 0;
for (int i = 1; i < arr.length; i++) {
if (sum < 0) {
sum = 0;
}
sum += arr[i];
max = Math.max(max, sum);
loopCount ++;
}
System.out.println("maxSubarray1-->" + loopCount);
return max;
}
/**
* 使用分治法
*
* @param arr
* @return
*/
int loopCount1 = 0;
public int maxSubarray2 (int[] arr) {
loopCount1 = 0;
return divide(arr, 0, arr.length - 1);
}
private int divide (int[] arr, int low, int high) {
if (low == high) {
return arr[low];
}
if (low == high - 1) {
return Math.max(arr[low] + arr[high], Math.max(arr[low], arr[high]));
}
int mid = (low + high) / 2;
int lmax = divide(arr, low, mid - 1);
int rmax = divide(arr, mid + 1, high);
int mmax = arr[mid];
int temp = mmax;
for (int i = mid - 1; i > 0; i--) {
temp += arr[i];
if (mmax < temp) {
mmax = temp;
}
loopCount1 ++;
}
temp = mmax;
for (int i = mid + 1; i < high; i++) {
temp += arr[i];
if (temp > mmax) {
mmax = temp;
}
loopCount1 ++;
}
System.out.println("maxSubarray2-->" + loopCount1);
return Math.max(mmax, Math.max(lmax, rmax));
}
public static void main(String[] args) {
MaxSubarray maxSubarray = new MaxSubarray();
int[] arr = new int[]{-2,1,-3,4,-1,2,1,-5,4};
System.out.println(maxSubarray.maxSubarray(arr));
System.out.println(maxSubarray.maxSubarray1(arr));
System.out.println(maxSubarray.maxSubarray2(arr));
int[] arr1 = new int[]{-2,1,-3,4,-1,2,1,-5,4,-2,1,-3,4,-1,2,1,-5,4,-2,1,-3,4,-1,2,1,-5,4,-2,1,-3,4,-1,2,1,-5,4};
System.out.println(maxSubarray.maxSubarray(arr1));
System.out.println(maxSubarray.maxSubarray1(arr1));
System.out.println(maxSubarray.maxSubarray2(arr1));
}
}