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Copy pathMaxSubArray_Recursive.java
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79 lines (68 loc) · 2.61 KB
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package sort;
import java.util.Arrays;
/**
* 4.1-3 最大子数组递归解法。Θ(n*lgn)
*
* @author 周何圳 2018年05月28日 新建
*/
public class MaxSubArray_Recursive {
public MaxSubArrayBean findMaxSubArray(int[] src) {
if (src.length <= 2) {
System.out.println("Error: Array length must be >= 2!");
return null;
}
MaxSubArrayBean m = findMaxSubArray(src, 0, src.length - 1);
System.out.println(m);
return m;
}
// 递归程序,主要是分解和合并部分
private MaxSubArrayBean findMaxSubArray(int[] src, int start, int end) {
if (start == end) {
return new MaxSubArrayBean(start, end, src[start]);
}
int mid = (start + end) / 2;
// 左边最大值
MaxSubArrayBean leftMax = findMaxSubArray(src, start, mid);
// 右边最大值
MaxSubArrayBean rightMax = findMaxSubArray(src, mid + 1, end);
// 左右两边合并后集合的最大值
MaxSubArrayBean crossMidMax = findMaxSubArrayCrossMid(src, start, end);
if (leftMax.sumValue >= rightMax.sumValue && leftMax.sumValue >= crossMidMax.sumValue) {
return leftMax;
} else if (rightMax.sumValue >= leftMax.sumValue && rightMax.sumValue >= crossMidMax.sumValue) {
return rightMax;
} else
return crossMidMax;
}
// 处理部分，这部分是核心逻辑。这部分的时间复杂度应该是Θ(n)
private MaxSubArrayBean findMaxSubArrayCrossMid(int[] src, int start, int end) {
int mid = (start + end) / 2;
int leftSumTemp = 0, rightSumTemp = 0;
int leftSum = Integer.MIN_VALUE, rightSum = Integer.MIN_VALUE;
int leftIndex = 0, rightIndex = 0;
// 从mid往前最大
for (int i = mid; i >= start; i--) {
leftSumTemp += src[i];
if (leftSum < leftSumTemp) {
leftSum = leftSumTemp;
leftIndex = i;
}
}
// 从mid往后最大
for (int i = mid; i <= end; i++) {
rightSumTemp += src[i];
if (rightSum < rightSumTemp) {
rightSum = rightSumTemp;
rightIndex = i;
}
}
return new MaxSubArrayBean(leftIndex, rightIndex, leftSum + rightSum - src[mid]);
}
public static void main(String[] args) {
MaxSubArray_Recursive m = new MaxSubArray_Recursive();
for (int[] testData : TestData.MaxSubArrayTestData()) {
System.out.println("Test: " + Arrays.toString(testData));
m.findMaxSubArray(testData);
}
}
}