Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Maximum Sum Increasing Subsequence using Binary Indexed Tree in C++
In this problem, we are given an array arr[] of N elements. Our task is to create a program to find the maximum Sum Increasing Subsequence using Binary Indexed Tree in C++.
Let’s take an example to understand the problem,
Input
arr[] = {4, 1, 9, 2, 3, 7}Output
13
Explanation
Maximum increasing subsequence is 1, 2, 3, 7. Sum = 13
Solution Approach
To solve the problem, we will use the Binary Indexed Tree in which we will insert values and map them to binary indexed tree. Then find the maximum value.
Example
Program to illustrate the working of our solution,
#include <bits/stdc++.h>
using namespace std;
int calcMaxSum(int BITree[], int index){
int maxSum = 0;
while (index > 0){
maxSum = max(maxSum, BITree[index]);
index -= index & (-index);
}
return maxSum;
}
void updateBIT(int BITree[], int newIndex, int index, int val){
while (index <= newIndex){
BITree[index] = max(val, BITree[index]);
index += index & (-index);
}
}
int maxSumIS(int arr[], int n){
int index = 0, maxSum;
map<int, int> arrMap;
for (int i = 0; i < n; i++){
arrMap[arr[i]] = 0;
}
for (map<int, int>::iterator it = arrMap.begin(); it != arrMap.end(); it++){
index++;
arrMap[it->first] = index;
}
int* BITree = new int[index + 1];
for (int i = 0; i <= index; i++){
BITree[i] = 0;
}
for (int i = 0; i < n; i++){
maxSum = calcMaxSum(BITree, arrMap[arr[i]] - 1);
updateBIT(BITree, index, arrMap[arr[i]], maxSum + arr[i]);
}
return calcMaxSum(BITree, index);
}
int main() {
int arr[] = {4, 6, 1, 9, 2, 3, 5, 8};
int n = sizeof(arr) / sizeof(arr[0]);
cout<<"The Maximum sum increasing subsequence using Binary Indexed Tree is "<<maxSumIS(arr, n);
return 0;
}Output
The Maximum sum increasing subsquence using Binary Indexed Tree is 19
Updated on: 15-Oct-2020
63 Views
Advertisements