求最大子段和的一些算法

public class MaxSubSeqSum {
/**
* 算法1，穷举搜索
*/
public static final int maxSubSeqSum1(int seq[]) {
int length = seq.length;
int sum = 0;
for (int i = 0; i < length; i++) {
for (int j = i; j < length; j++) {
int theSum = 0;
for (int k = i; k <= j; k++) {
theSum += seq[k];
}
if (sum < theSum) sum = theSum;
}
}
return sum;
}

/**
* 算法2。改进算法1
*/
public static final int maxSubSeqSum2(int seq[]) {
int length = seq.length;
int sum = 0;
for (int i = 0; i < length; i++) {
int theSum = 0;
for (int j = i; j < length; j++) {
theSum += seq[j];
if (theSum > sum) {
sum = theSum;
}
}
}
return sum;
}

/**
* 算法3：分治法
*/
public static final int maxSubSeqSum3(int seq[]) {
return maxSubSeqSum31(seq, 0, seq.length - 1);
}

private static int max(int... args) {
int max = Integer.MIN_VALUE;
for (int i : args) {
if (i > max) max = i;
}
return max;
}

private static final int maxSubSeqSum31(int[] seq, int left, int right) {
if (right - left == 1) { // 仅仅剩下两个了：
return max(seq[left], seq[right], seq[left] + seq[right], 0);
} else if (left == right) {
return max(seq[left], 0);
} else {
int middle = (left + right) / 2;
int maxLeft = maxSubSeqSum31(seq, left, middle);
int maxRight = maxSubSeqSum31(seq, middle + 1, right);
int maxMiddle = maxSubSeqMiddle(seq, left, right, middle);
return max(maxLeft, maxRight, maxMiddle);
}
}

private static final int maxSubSeqMiddle(int[] seq, int left, int right, int middle) {
int maxLeft = 0, maxRight = 0;
int temp = 0;
for (int i = middle; i >= left; i--) {
temp += seq[i];
if (maxLeft < temp) {
maxLeft = temp;
}
}
temp = 0;
for (int i = middle + 1; i <= right; i++) {
temp += seq[i];
if (maxRight < temp) {
maxRight = temp;
}
}
return max(maxLeft, maxRight, maxLeft + maxRight);
}

/**
* 最快的计算方式
* @param seq
* @return
*/
public static final int maxSubSeqSum4(int seq[]) {
int sum = 0, theSum = 0;
int length = seq.length;
for (int i = 0; i < length; i++) {
theSum = max(theSum + seq[i], 0);
if (sum < theSum) {
sum = theSum;
}
}
return sum;
}

public static void main(String[] args) throws Exception {
int length = 100000;
int[] arr = new int[length];
Random rand = new Random(10);
for (int i = 0; i < length; i++) {
arr[i] = rand.nextInt(11) - 5;
}
long t = System.currentTimeMillis();
//		int ret1 = maxSubSeqSum1(arr);
//		System.out.println("算法1耗时：" + (System.currentTimeMillis() - t));
//		System.out.println("结果1：" + ret1);
//
t = System.currentTimeMillis();
int ret2 = maxSubSeqSum2(arr);
System.out.println("算法2耗时：" + (System.currentTimeMillis() - t));
System.out.println("结果2：" + ret2);

t = System.currentTimeMillis();
int ret3 = maxSubSeqSum3(arr);
System.out.println("算法3耗时：" + (System.currentTimeMillis() - t));
System.out.println("结果3：" + ret3);

t = System.currentTimeMillis();
int ret4 = maxSubSeqSum4(arr);
System.out.println("算法4耗时：" + (System.currentTimeMillis() - t));
System.out.println("结果4：" + ret4);
}
}