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,

 Live Demo

#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