Implicit Segment Tree Algorithm
The Implicit Segment Tree Algorithm is an advanced data structure that allows for efficient handling of dynamic range queries and updates on arrays. It is a variation of the standard segment tree, but with a critical difference: instead of explicitly storing every node in the tree, the implicit segment tree only stores nodes that have been accessed or modified. This lazy construction leads to a lower memory footprint and can be beneficial when dealing with large arrays or sparse data.
Implicit segment trees are built on-demand as queries and updates are made, which means that nodes are only created when they are needed. This is achieved through the use of a default value for uninitialized nodes, which is propagated through the tree as required. An implicit segment tree can support various types of range queries such as range minimum query, range sum query, and range maximum query, as well as range updates like adding a value to all elements in a given range or setting all elements in a range to a specific value. The time complexity for both queries and updates in an implicit segment tree is O(log n), where n is the size of the array.
/*************************************************************************************
Implicit segment tree with addition on the interval
and getting the value of some element.
Works on the intervals like [1..10^9].
O(logN) on query, O(NlogN) of memory.
Author: Bekzhan Kassenov.
Based on problem 3327 from informatics.mccme.ru
http://informatics.mccme.ru/moodle/mod/statements/view.php?chapterid=3327
*************************************************************************************/
#include <iostream>
#include <cstdio>
#include <cstdlib>
using namespace std;
typedef long long ll;
struct Node {
ll sum;
Node *l, *r;
Node() : sum(0), l(NULL), r(NULL) { }
};
void add(Node *v, int l, int r, int q_l, int q_r, ll val) {
if (l > r || q_r < l || q_l > r)
return;
if (q_l <= l && r <= q_r) {
v -> sum += val;
return;
}
int mid = (l + r) >> 1;
if (v -> l == NULL)
v -> l = new Node();
if (v -> r == NULL)
v -> r = new Node();
add(v -> l, l, mid, q_l, q_r, val);
add(v -> r, mid + 1, r, q_l, q_r, val);
}
ll get(Node *v, int l, int r, int pos) {
if (!v || l > r || pos < l || pos > r)
return 0;
if (l == r)
return v -> sum;
int mid = (l + r) >> 1;
return v -> sum + get(v -> l, l, mid, pos) + get(v -> r, mid + 1, r, pos);
}
int n, m, t, x, y, val;
char c;
int main() {
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
Node *root = new Node();
scanf("%d", &n);
for (int i = 0; i < n; i++) {
scanf("%d", &x);
add(root, 0, n - 1, i, i, x);
}
scanf("%d", &m);
for (int i = 0; i < m; i++) {
scanf("\n%c", &c);
if (c == 'a') {
scanf("%d%d%d", &x, &y, &val);
add(root, 0, n - 1, --x, --y, val);
} else {
scanf("%d", &x);
printf("%I64d ", get(root, 0, n - 1, --x));
}
}
return 0;
}
