查找给定序列最长的递增子序列的C ++程序
最长增加子序列是一个项目大于前一个项目的子序列。
在这里，我们将尝试从一组整数中找到最长增加子序列的长度。
Input: A set of integers. {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15}
Output: The length of longest increasing subsequence. Here it is 6.
The subsequence is 0, 2, 6, 9, 13, 15.算法
longestSubSeq（子数组，n）
输入：子数组和子数组的大小。
输出：最长的子序列长度增加。
Begin
define array length of size n
initially set 0 to all entries of length
for i := 1 to n-1, do
for j := 0 to i-1, do
if subarray[j] < subarray[i] and length[j] > length[i], then
length[i] := length[j]
done
increase length[i] by 1
done
lis := 0
for i := 0 to n-1, do
lis := maximum of lis and length[i]
done
return lis
End范例程式码
#include <iostream>
using namespace std;
int longestSubSeq(int subArr[], int n) {
int length[n] = { 0 }; //set all length to 0
length[0] = 1; //subsequence ending with subArr[0] is 1
for (int i = 1; i < n; i++) { //ignore first character, second to all
for (int j = 0; j < i; j++) { //subsequence ends with subArr[j]
if (subArr[j] < subArr[i] && length[j] > length[i])
length[i] = length[j];
}
length[i]++; //add arr[i]
}
int lis = 0;
for (int i = 0; i<n; i++) // find longest increasing subsequence
lis = max(lis, length[i]);
return lis;
}
int main() {
int arr[] = { 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 };
int n = 16;
cout << "Length of Longest Increasing Subsequence is: " << longestSubSeq(arr, n);
return 0;
}输出结果
Length of Longest Increasing Subsequence is: 6