最大总和增加子序列
最大总和增加子序列是给定整数列表的子序列，该整数列表的总和为最大，并且在该子序列中，所有元素均按升序排序。
假设有一个数组来存储最大和增加子序列，使得L[i]是最大和增加子序列，并以array[i]结尾。
输入输出
Input:
Sequence of integers. {3, 2, 6, 4, 5, 1}
Output:
Increasing subsequence whose sum is maximum. {3, 4, 5}.算法
maxSumSubSeq(array, n)
输入：数字序列，元素数。
输出：递增子序列的最大和。
Begin
define array of arrays named subSeqLen of size n.
add arr[0] into the subSeqLen
for i in range (1 to n-1), do
for j in range (0 to i-1), do
if arr[i] > arr[j] and sum of subSeqLen [i] < sum of subSeqLen [j], then
subSeqLen[i] := subSeqLen[j]
done
done
add arr[i] into subSeqLen[i]
res := subSeqLen[0]
for all values of subSeqLen, do
if sum of subSeqLen[i] > sum of subSeqLen[res], then
res := subSeqLen[i]
done
print the values of res.
End示例
#include <iostream>
#include <vector>
using namespace std;
int findAllSum(vector<int> arr) { //find sum of all vector elements
int sum = 0;
for(int i = 0; i<arr.size(); i++) {
sum += arr[i];
}
return sum;
}
void maxSumSubSeq(int arr[], int n) {
vector <vector<int> > subSeqLen(n); //max sum increasing subsequence ending with arr[i]
subSeqLen[0].push_back(arr[0]);
for (int i = 1; i < n; i++) { //from index 1 to all
for (int j = 0; j < i; j++) { //for all j, j<i
if ((arr[i] > arr[j]) && (findAllSum(subSeqLen[i]) < findAllSum(subSeqLen[j])))
subSeqLen[i] = subSeqLen[j];
}
subSeqLen[i].push_back(arr[i]); //sub Sequence ends with arr[i]
}
vector<int> res = subSeqLen[0];
for(int i = 0; i<subSeqLen.size(); i++) {
if (findAllSum(subSeqLen[i]) > findAllSum(res))
res = subSeqLen[i];
}
for(int i = 0; i<res.size(); i++)
cout << res[i] << " ";
cout << endl;
}
int main() {
int arr[] = { 3, 2, 6, 4, 5, 1 };
int n = 6;
cout << "The Maximum Sum Subsequence is: ";
maxSumSubSeq(arr, n);
}输出结果
The Maximum Sum Subsequence is: 3 4 5