2.16 求数组中最长递增子序列

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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;}