segment_tree_update.cpp

void update(int node, int b, int e, int i, int newval) {
  // index is out of range
  if (b > i || e < i) return;
  
  // we're at leaf node
  if (b == i && e == i) {
    tree[node] = newval;
    a[i] = newval;
    return;
  }
  
  int left = 2*node;
  int right = 2*node + 1;
  int mid = (b + e)/2;
  
  update(left, b, mid, i, newval);
  update(right, mid + 1, e, i, newval);
  tree[node] = tree[left] + tree[right];
}