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#include <bits/stdc++.h>
using namespace std;
#define LSOne(S) ((S) & -(S)) // the key operation
typedef long long ll; // for extra flexibility
typedef vector<ll> vll;
typedef vector<int> vi;
class FenwickTree { // index 0 is not used
private:
vll ft; // internal FT is an array
public:
FenwickTree(int m) { ft.assign(m+1, 0); } // create an empty FT
void build(const vll &f) {
int m = (int)f.size()-1; // note f[0] is always 0
ft.assign(m+1, 0);
for (int i = 1; i <= m; ++i) { // O(m)
ft[i] += f[i]; // add this value
if (i+LSOne(i) <= m) // i has parent
ft[i+LSOne(i)] += ft[i]; // add to that parent
}
}
FenwickTree(const vll &f) { build(f); } // create FT based on f
FenwickTree(int m, const vi &s) { // create FT based on s
vll f(m+1, 0);
for (int i = 0; i < (int)s.size(); ++i) // do the conversion first
++f[s[i]]; // in O(n)
build(f); // in O(m)
}
ll rsq(int j) { // returns RSQ(1, j)
ll sum = 0;
for (; j; j -= LSOne(j))
sum += ft[j];
return sum;
}
ll rsq(int i, int j) { return rsq(j) - rsq(i-1); } // inc/exclusion
// updates value of the i-th element by v (v can be +ve/inc or -ve/dec)
void update(int i, ll v) {
for (; i < (int)ft.size(); i += LSOne(i))
ft[i] += v;
}
int select(ll k) { // O(log m)
int p = 1;
while (p*2 < (int)ft.size()) p *= 2;
int i = 0;
while (p) {
if (k > ft[i+p]) {
k -= ft[i+p];
i += p;
}
p /= 2;
}
return i+1;
}
};
class RUPQ { // RUPQ variant
private:
FenwickTree ft; // internally use PURQ FT
public:
RUPQ(int m) : ft(FenwickTree(m)) {}
void range_update(int ui, int uj, ll v) {
ft.update(ui, v); // [ui, ui+1, .., m] +v
ft.update(uj+1, -v); // [uj+1, uj+2, .., m] -v
} // [ui, ui+1, .., uj] +v
ll point_query(int i) { return ft.rsq(i); } // rsq(i) is sufficient
};
class RURQ { // RURQ variant
private: // needs two helper FTs
RUPQ rupq; // one RUPQ and
FenwickTree purq; // one PURQ
public:
RURQ(int m) : rupq(RUPQ(m)), purq(FenwickTree(m)) {} // initialization
void range_update(int ui, int uj, ll v) {
rupq.range_update(ui, uj, v); // [ui, ui+1, .., uj] +v
purq.update(ui, v*(ui-1)); // -(ui-1)*v before ui
purq.update(uj+1, -v*uj); // +(uj-ui+1)*v after uj
}
ll rsq(int j) {
return rupq.point_query(j)*j - // optimistic calculation
purq.rsq(j); // cancelation factor
}
ll rsq(int i, int j) { return rsq(j) - rsq(i-1); } // standard
};
int main() {
vll f = {0,0,1,0,1,2,3,2,1,1,0}; // index 0 is always 0
FenwickTree ft(f);
printf("%lld\n", ft.rsq(1, 6)); // 7 => ft[6]+ft[4] = 5+2 = 7
printf("%d\n", ft.select(7)); // index 6, rsq(1, 6) == 7, which is >= 7
ft.update(5, 1); // update demo
printf("%lld\n", ft.rsq(1, 10)); // now 12
printf("=====\n");
RUPQ rupq(10);
RURQ rurq(10);
rupq.range_update(2, 9, 7); // indices in [2, 3, .., 9] updated by +7
rurq.range_update(2, 9, 7); // same as rupq above
rupq.range_update(6, 7, 3); // indices 6&7 are further updated by +3 (10)
rurq.range_update(6, 7, 3); // same as rupq above
// idx = 0 (unused) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10
// val = - | 0 | 7 | 7 | 7 | 7 |10 |10 | 7 | 7 | 0
for (int i = 1; i <= 10; i++)
printf("%d -> %lld\n", i, rupq.point_query(i));
printf("RSQ(1, 10) = %lld\n", rurq.rsq(1, 10)); // 62
printf("RSQ(6, 7) = %lld\n", rurq.rsq(6, 7)); // 20
return 0;
}