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codeforces Round #261(div2) D解题报告

2024-07-28 18:13:04   226人阅读

D. Pashmak and Parmida‘s problem
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Parmida is a clever girl and she wants to participate in Olympiads this year. Of course she wants her partner to be clever too (although he‘s not)! Parmida has prepared the following test problem for Pashmak.

There is a sequence a that consists of n integers a1,?a2,?...,?an. Let‘s denote f(l,?r,?x) the number of indices k such that: l?≤?k?≤?r and ak?=?x. His task is to calculate the number of pairs of indicies i,?j (1?≤?i?<?j?≤?n) such that f(1,?i,?ai)?>?f(j,?n,?aj).

Help Pashmak with the test.

Input

The first line of the input contains an integer n (1?≤?n?≤?106). The second line contains n space-separated integers a1,?a2,?...,?an (1?≤?ai?≤?109).

Output

Print a single integer — the answer to the problem.

Sample test(s)
input
7
1 2 1 1 2 2 1
output
8
input
3
1 1 1
output
1
input
5
1 2 3 4 5
output
0

题目大意：

给出数组A，定义f(l,r,x)为A[]的下标l到r之间，等于x的元素数。i和j符合f(1,i,a[i])>f(j,n,a[j])，求有多少对这样的(i,j).

解法：

我们可以通过预处理，在O(n)之内，算出f(1, i, a[i]) 定义数组为l[i]， 算出f(j, n, a[j]) 定义数组为r[i]。

题目就转化为：求出 l[i] > r[j]  (i < j)。

本质上，就是一个求逆序对的做法，用树状数组。

代码：

#include <cstdio>
#include <map>
#include <iostream>
#define LL long long
#define N_max 3*1234567

using namespace std;

map <int, int> l, r;
int n;
int bit[N_max], a[N_max];
LL ans;


void init() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)  scanf("%d", &a[i]);
}

void add(int i, int x) {
	while (i <= n) {
		bit[i] += x;
		i += i&-i;
	}
}

LL sum(int i) {
	LL s = 0;

	while (i > 0) {
		s += bit[i];
		i -= i&-i;
	}

	return s;
}

void solve() {
	l.clear();
	r.clear();

	for (int i = n; i >= 1; i--) {
		l[a[i]]++;
		add(l[a[i]], 1);
	}

	for (int i = 1; i <= n; i++) {
		r[a[i]]++;

		add(l[a[i]], -1);
		l[a[i]]--;
		
		ans += sum(r[a[i]]-1);
	}

	cout << ans << endl;
}

int main() {
	init();
	solve();
}

codeforces Round #261(div2) D解题报告


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