2023-01-04：有三个题库A、B、C，每个题库均有n道题目，且题目都是从1到n进行编号
每个题目都有一个难度值
题库A中第i个题目的难度为ai
题库B中第i个题目的难度为bi
题库C中第i个题目的难度为ci
小美准备组合出一套试题，试题共有三道题，
第一题来自题库A，第二题来自题库B，第三题来自题库C
试题要求题目难度递增，且梯度不能过大
具体地说，第二题的难度必须大于第一题的难度，但不能大于第一题难度的两倍
第三题的难度必须大于第二题的难度，但不能大于第二题难度的两倍
小美想知道在满足上述要求下，有多少种不同的题目组合
（三道题目中只要存在一道题目不同，则两个题目组合就视为不同
输入描述 第一行一个正整数n, 表示每个题库的题目数量
第二行为n个正整数a1, a2,… an，其中ai表示题库A中第i个题目的难度值
第三行为n个正整数b1, b2,… bn，其中bi表示题库B中第i个题目的难度值
第四行为n个正整数c1, c2,… cn，其中ci表示题库C中第i个题目的难度值
1 <= n <= 20000, 1 <= ai, bi, ci <= 10^9。
来自美团。
答案2023-01-04：
双指针不回退+前缀和数组。
时间复杂度O(N * logN)。因为要排序。
空间复杂度O(N)。
用rust和solidity写代码。
代码用rust编写。代码如下：
use rand::Rng;
use std::iter::repeat;
fn main() {
let mut a = vec![71, 29, 13, 74, 90, 8, 30, 25];
let mut b = vec![72, 1, 50, 98, 86, 86, 52, 57];
let mut c = vec![11, 24, 61, 70, 11, 90, 13, 30];
let ans = ways2(&mut a, &mut b, &mut c);
println!("ans = {}", ans);
let nn: i32 = 100;
let vv: i32 = 100;
let test_time: i32 = 5000;
println!("测试开始");
for i in 0..test_time {
let n = rand::thread_rng().gen_range(0, nn) + 1;
let mut a = random_array(n, vv);
let mut b = random_array(n, vv);
let mut c = random_array(n, vv);
let ans1 = ways1(&mut a, &mut b, &mut c);
let ans2 = ways2(&mut a, &mut b, &mut c);
if ans1 != ans2 {
println!("出错了!{}", i);
println!("ans1 = {}", ans1);
println!("ans2 = {}", ans2);
break;
}
}
println!("测试结束");
}
// 暴力方法
// 时间复杂度O(N^3)
// 为了验证
fn ways1(a: &mut Vec<i32>, b: &mut Vec<i32>, c: &mut Vec<i32>) -> i32 {
let n = a.len() as i32;
a.sort();
b.sort();
c.sort();
let mut ans = 0;
for i in 0..n {
let mut j = 0;
while j < n && b[j as usize] <= a[i as usize] * 2 {
if b[j as usize] > a[i as usize] {
let mut k = 0;
while k < n && c[k as usize] <= b[j as usize] * 2 {
if c[k as usize] > b[j as usize] {
ans += 1;
}
k += 1;
}
}
j += 1;
}
}
return ans;
}
// 正式方法
// 时间复杂度O(N * logN)
fn ways2(a: &mut Vec<i32>, b: &mut Vec<i32>, c: &mut Vec<i32>) -> i32 {
let n = a.len() as i32;
a.sort();
b.sort();
c.sort();
// B里面的记录
let mut help: Vec<i32> = repeat(0).take(n as usize).collect();
let mut i = 0;
let mut l = -1;
let mut r = 0;
while i < n {
while l + 1 < n && c[(l + 1) as usize] <= b[i as usize] {
l += 1;
}
while r < n && c[r as usize] <= b[i as usize] * 2 {
r += 1;
}
help[i as usize] = get_max(r - l - 1, 0);
i += 1;
}
for i in 1..n {
help[i as usize] += help[(i - 1) as usize];
}
let mut ans = 0;
let mut i = 0;
let mut l = -1;
let mut r = 0;
while i < n {
while l + 1 < n && b[(l + 1) as usize] <= a[i as usize] {
l += 1;
}
while r < n && b[r as usize] <= a[i as usize] * 2 {
r += 1;
}
if r - l - 1 > 0 {
ans += sum(&mut help, l + 1, r - 1);
}
i += 1;
}
return ans;
}
fn sum(help: &mut Vec<i32>, l: i32, r: i32) -> i32 {
return if l == 0 {
help[r as usize]
} else {
help[r as usize] - help[(l - 1) as usize]
};
}
fn get_max<T: Clone + Copy + std::cmp::PartialOrd>(a: T, b: T) -> T {
if a > b {
a
} else {
b
}
}
// 为了测试
fn random_array(n: i32, v: i32) -> Vec<i32> {
let mut arr: Vec<i32> = vec![];
for _i in 0..n {
arr.push(rand::thread_rng().gen_range(0, v));
}
return arr;
}
代码用solidity编写。代码如下：
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.17;
contract Hello{
function main() public pure returns (int32){
int32[] memory a = new int32[](8);
a[0] = 71;
a[1] = 29;
a[2] = 13;
a[3] = 74;
a[4] = 90;
a[5] = 8;
a[6] = 30;
a[7] = 25;
int32[] memory b = new int32[](8);
b[0] = 72;
b[1] = 1;
b[2] = 50;
b[3] = 98;
b[4] = 86;
b[5] = 86;
b[6] = 52;
b[7] = 57;
int32[] memory c = new int32[](8);
c[0] = 11;
c[1] = 24;
c[2] = 61;
c[3] = 70;
c[4] = 11;
c[5] = 90;
c[6] = 13;
c[7] = 30;
int32 ans = ways2(a,b,c);
return ans;
}
// 正式方法
// 时间复杂度O(N * logN)
function ways2(int32[] memory a, int32[] memory b, int32[] memory c) public pure returns (int32){
int32 n = int32(int(a.length));
sort(a);
sort(b);
sort(c);
// B里面的记录
int32[] memory help = new int32[](uint(uint32(n)));
int32 l = -1;
int32 r = 0;
for (int32 i = 0; i < n; i++) {
while (l + 1 < n && c[uint(uint32(l + 1))] <= b[uint(uint32(i))]) {
l++;
}
while (r < n && c[uint(uint32(r))] <= b[uint(uint32(i))] * 2) {
r++;
}
help[uint(uint32(i))] = getMax(r - l - 1, 0);
}
for (int32 i = 1; i < n; i++) {
help[uint(uint32(i))] += help[uint(uint32(i - 1))];
}
int32 ans = 0;
l = -1;
r = 0;
for (int32 i = 0; i < n; i++) {
while (l + 1 < n && b[uint(uint32(l + 1))] <= a[uint(uint32(i))]) {
l++;
}
while (r < n && b[uint(uint32(r))] <= a[uint(uint32(i))] * 2) {
r++;
}
if (r - l - 1 > 0) {
ans += sum(help, l + 1, r - 1);
}
}
return ans;
}
function sum(int32[] memory help, int32 l, int32 r) public pure returns (int32){
return l == 0 ? help[uint(uint32(r))] : help[uint(uint32(r))] - help[uint(uint32(l - 1))];
}
function getMax(int32 a,int32 b) public pure returns (int32){
if(a>b){
return a;
}else{
return b;
}
}
function sort(int32[] memory arr)public pure{
int32 temp = 0;
for(int32 i = 1; i <= int32(int(arr.length)) - 1; i++) {
for(int32 j = i; j > 0; j--) {
if(arr[uint(uint32(j - 1))] > arr[uint(uint32(j))]) {
temp = arr[uint(uint32(j))];
arr[uint(uint32(j))] = arr[uint(uint32(j - 1))];
arr[uint(uint32(j - 1))] = temp;
}else {
//不满足条件结束循环即可
break;
}
}
}
}
}
