300. Longest Increasing Subsequence

d[i] i为结尾的最长递增子序列，
d[0] = 1 ,
d[i] 算出 [0,i) 找出d[i] > d[[0,i)] ,同时d[[0,i)] 中的最大值加一

然后算出最大的d[]

int lengthOfLIS(int* nums, int numsSize) {
    int *lis, i, j, max = 0;
    lis = (int*) malloc ( sizeof( int ) * numsSize );
 
    /* Initialize LIS values for all indexes */
    for (i = 0; i < numsSize; i++ )
        lis[i] = 1;
 
    /* Compute optimized LIS values in bottom up manner */
    for (i = 1; i < numsSize; i++ )
        for (j = 0; j < i; j++ ) 
            if ( nums[i] > nums[j] &&  lis[j] + 1 > lis[i])
                lis[i] = lis[j] + 1;
 
    /* Pick maximum of all LIS values */
    for (i = 0; i < numsSize; i++ )
        if (max < lis[i])
            max = lis[i];
 
    /* Free memory to avoid memory leak */
    free(lis);
 
    return max;
    
}