12.贪心---分治

分治：
暴力最大子序列：

public static int maxSubarray(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        int max = Integer.MIN_VALUE;
        for (int begin = 0; begin < nums.length; begin++) {
            for (int end = begin; end < nums.length; end++) {
                //sum是子序列的和
                int sum = 0;
                for (int i = begin; i <= end; i++) {
                    sum += nums[i];
                }
                max = Math.max(max, sum);
            }
        }
        return max;
    }

分治2： 暴力优化2：

public static int maxSubarray2(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        int max = Integer.MIN_VALUE;
        for (int begin = 0; begin < nums.length; begin++) {
            int sum = 0;
            for (int end = begin; end < nums.length; end++) {
                //sum是子序列的和
                sum += nums[end];
                max = Math.max(max, sum);
            }
        }
        return max;
    }

分治：

public static int divideAndConquer(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        return divideAndConquer(nums, 0, nums.length);
    }
    /**
     * 求出begin到end中最大子序列的和
     */
    public static int divideAndConquer(int[] nums, int begin, int end) {
        if (end - begin < 2) {
            return nums[begin];
        }
        int mid = (begin + end) >> 1;
        int leftMax = Integer.MIN_VALUE;
        int leftSum = 0;
        int rightMax = Integer.MIN_VALUE;
        int rightSum = 0;
        for (int i = mid - 1; i >= begin; i--) {
            leftSum += nums[i];
            leftMax = Math.max(leftMax, leftSum);
        }
        for (int i = mid; i < end; i++) {
            rightSum += nums[i];
            rightMax = Math.max(rightMax, rightSum);
        }
        int max = leftMax + rightMax;
        return Math.max(max, Math.max(divideAndConquer(nums, begin, mid), divideAndConquer(nums, mid, end)));
    }