2.16 求数组中最长递增子序列

问题：

如标题，求数组中最长递增子序列。

解法一：

动态规划

#include <stdio.h>
#include <stdlib.h>
#include<malloc.h>

int LIS(int* array, int num)
{
    int* temp = (int *)malloc(num*sizeof(int));
    int i = 0;
    int j = 0;
    int max = 0;
    for (i = 0; i < num; i++)
    {
        temp[i] = 1;
        for (j = 0; j < i; j++)
        {
            if (array[i] > array[j] && temp[j] + 1 > temp[i])
            {
                temp[i] = temp[j] + 1;
            }
        }
    }
    max = temp[0];
    for (i = 1; i < num; i++)
    {
        if (temp[i] > max)
            max = temp[i];
    }
    free(temp);
    return max;
}

int main()
{
    //printf("Hello world!\n");
    int array[] = {1,-1,2,-3,4,-5,6,-7};
    printf("%d\n", LIS(array, 8));
    return 0;
}

解法二：

#include <stdio.h>
#include <stdlib.h>
#include<malloc.h>

int Min(int* array, int num)
{
    int i = 0;
    int min = array[0];
    for (i = 1; i < num; i++)
    {
        if (array[i] < min)
            min = array[i];
    }
    return min;
}

int LIS(int* array, int num)
{
    int i = 0, j = 0;
    int* temp = (int *)malloc((num + 1) * sizeof(int));
    int* LIS = (int *)malloc(num * sizeof(int));
    temp[1] = array[0];
    temp[0] = Min(array, num) - 1;
    for (i = 0; i < num; i++)
    {
        LIS[i] = 1;
    }
    int nMaxLIS = 1;
    for(i = 1; i < num; i++)
    {
        for(j = nMaxLIS; j >= 0; j--)
        {
            if (array[i] > temp[j])
            {
                LIS[i] = j + 1;
                break;
            }
        }
        if (LIS[i] > nMaxLIS)
        {
            nMaxLIS = LIS[i];
            temp[LIS[i]] = array[i];
        }
        else if (temp[j] < array[i] && array[i] < temp[j + 1])
        {
            temp[j + 1] = array[i];
        }
    }
    return nMaxLIS;
}

int main()
{
    //printf("Hello world!\n");
    int array[] = {1,-1,2,-3,4,-5,6,-7};
    printf("%d\n", LIS(array, 8));
    return 0;
}