2022-07-03: there are 0 and 1 in the array. Be sure to flip an interval. Flip: 0 becomes 1, 1 becomes 0. What is the maximum number of 1 after turning? From little red book. 3.13 written examination.

2022-07-03： In the array are 0 and 1, Be sure to flip an interval , Flip ：0 change 1,1 change 0.
Can you turn it over to make 1 What is the maximum number of ？
From little red book .3.13 written examination .

answer 2022-07-03：

Some interval ,0 Number -1 Number = Maximum .
0 become 1,1 become -1, Find the maximum cumulative sum of subarrays .

The code to use rust To write . The code is as follows ：

use rand::Rng;
fn main() {
    
    let nn: i32 = 100;
    let test_time: i32 = 20000;
    println!(" Beginning of the test ");
    for i in 0..test_time {
    
        let n = rand::thread_rng().gen_range(0, nn) + 1;
        let mut arr = random_array(n);
        let mut arr2 = arr.clone();
        let ans1 = max_one_numbers1(&mut arr);
        let ans2 = max_one_numbers2(&mut arr2);
        if ans1 != ans2 {
    
            println!(" Something went wrong !{}", i);
            println!("ans1 = {}", ans1);
            println!("ans2 = {}", ans2);
            break;
        }
    }
    println!(" End of test ");
}

fn max_one_numbers1(arr: &mut Vec<i32>) -> i32 {
    
    let mut ans = 0;
    for l in 0..arr.len() as i32 {
    
        for r in l..arr.len() as i32 {
    
            reverse(arr, l, r);
            ans = get_max(ans, one_numbers(arr));
            reverse(arr, l, r);
        }
    }
    return ans;
}

fn reverse(arr: &mut Vec<i32>, l: i32, r: i32) {
    
    for i in l..=r {
    
        arr[i as usize] ^= 1;
    }
}

fn one_numbers(arr: &mut Vec<i32>) -> i32 {
    
    let mut ans = 0;
    for num in arr.iter() {
    
        ans += *num;
    }
    return ans;
}

fn get_max<T: Clone + Copy + std::cmp::PartialOrd>(a: T, b: T) -> T {
    
    if a > b {
    
        a
    } else {
    
        b
    }
}

fn max_one_numbers2(arr: &mut Vec<i32>) -> i32 {
    
    let mut ans = 0;
    for num in arr.iter() {
    
        ans += *num;
    }
    for i in 0..arr.len() as i32 {
    
        arr[i as usize] = if arr[i as usize] == 0 {
     1 } else {
     -1 };
    }
    let mut max = -2147483648;
    let mut cur = 0;
    for i in 0..arr.len() as i32 {
    
        cur += arr[i as usize];
        max = get_max(max, cur);
        cur = if cur < 0 {
     0 } else {
     cur };
    }
    return ans + max;
}

//  In order to test 
fn random_array(n: i32) -> Vec<i32> {
    
    let mut arr: Vec<i32> = vec![];
    for _i in 0..n {
    
        arr.push(rand::thread_rng().gen_range(0, 2));
    }
    return arr;
}

The results are as follows ：

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