三種算法實現最大子段和問題(Java實現)

分別用簡單實現（比較容易理解但時間複雜度較高）、分治法、動態規劃法實現

 

public class MaxSum {
	// 最大子段和簡單算法
	public static void maxSumSimp(int arr[], int bestx, int besty) {
		int n = arr.length, sum = 0;
		for (int i = 1; i <= n; i++) {
			int thissum = 0;
			for (int j = i; j <= n; j++) {
				thissum += arr[j - 1];
				if (thissum > sum) {
					sum = thissum;
					bestx = i;
					besty = j;
				}
			}
		}
		System.out.println("簡單算法最優值：" + sum);
		System.out.println("最優解：" + bestx + "-->" + besty);
	}

	// 最大子段和分治實現

	public static int maxSumDiv(int[] arr, int left, int right) {
		int sum = 0;
		if (left == right) {
			sum = arr[left] > 0 ? arr[left] : 0;
		} else {
			int center = (left + right) / 2;
			int leftSum = maxSumDiv(arr, left, center);
			int rightSum = maxSumDiv(arr, center + 1, right);
			int s1 = 0;
			int lefts = 0;
			for (int i = center; i >= left; i--) {
				lefts += arr[i];
				if (lefts > s1) {
					s1 = lefts;
				}
			}
			int s2 = 0;
			int rights = 0;
			for (int i = center + 1; i <= right; i++) {
				rights += arr[i];
				if (rights > s2) {
					s2 = rights;
				}
			}
			sum = s1 + s2;
			if (sum < leftSum) {
				sum = leftSum;
			}
			if (sum < rightSum) {
				sum = rightSum;
			}
		}
		return sum;
	}

	// 最大子段和動態規劃法實現
	public static void maxSumDp(int[] arr) {
		int sum = 0, b = 0, n = arr.length, bestx = 0, besty = 0;
		for (int i = 1; i <= n; i++) {
			if (b > 0) {
				b += arr[i - 1];
			} else {
				b = arr[i - 1];
				bestx = i;
			}
			if (b > sum) {
				sum = b;
				besty = i;
			}
		}
		System.out.println("動態規劃算法最優值：" + sum);
		System.out.println("最優解：" + bestx + "-->" + besty);
	}

	public static void main(String[] args) {
		int[] arr = { 2,5,-3,4,-9,44,32,22,11,-30 };
		for (int i : arr) {
			System.out.print(i + " ");
		}
		System.out.println();
		System.out.println("最大子段和：");
		System.out.println("分治算法最優值：" + maxSumDiv(arr, 0, arr.length - 1));
		System.out.println("====================");
		maxSumDp(arr);
		System.out.println("====================");
		maxSumSimp(arr, 0, 0);
	}
}