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;
}