2023-09-05:请用go语言编写。一个图像有n个像素点,存储在一个长度为n的数组arr里, 每个像素点的取值范围[0,s]的整数, 请你给图像每个像素点值加上一个整数k(可以是负数), 像素值会

2023-09-05:请用go语言编写。一个图像有n个像素点,存储在一个长度为n的数组arr里,

每个像素点的取值范围[0,s]的整数,

请你给图像每个像素点值加上一个整数k(可以是负数),

像素值会自动截取到[0,s]范围,

当像素值<0,会更改为0,当新像素值>s,会更改为s,

这样就可以得到新的arr,想让所有像素点的平均值最接近中位值s/2, 向下取整。

请输出这个整数k, 如有多个整数k都满足, 输出小的那个。

1 <= n <= 10^6,

1 <= s <= 10^18。

来自华为OD。

来自左程云

答案2023-09-05:

根据代码和题目描述,可以将算法分为以下三种不同的方法:

方法一:暴力方法

  • 这种方法通过枚举k的值来计算每个像素值加上k后的平均值,然后选择平均值最接近中位值s/2的k。

  • 该方法采用两层循环:外层循环枚举k的取值,内层循环计算平均值。

  • 时间复杂度:O(n^2)

  • 空间复杂度:O(1)

方法二:优化暴力方法

  • 这种方法在暴力方法的基础上进行了一些优化,采用二分查找来减少计算的次数。

  • 首先,确定k的取值范围为[-s, s],然后进行二分查找来逼近平均值最接近中位值s/2的k。

  • 时间复杂度:O(n*log(s))

  • 空间复杂度:O(1)

方法三:正式方法(最优解)

  • 这种方法是一种最优解,通过先对数组arr进行排序,然后使用前缀和数组pre来存储累加和,以便在计算过程中快速计算区间和。

  • 确定k的取值范围,根据k的正负分别进行二分查找,得到最接近中位值s/2的k。

  • 时间复杂度:O(nlog(n) + log(s)log(n))

  • 空间复杂度:O(n)

go完整代码如下:

package main

import (
	"fmt"
	"math"
	"math/rand"
	"sort"
)

// 暴力方法
// 为了测试
func best1(arr []int, s int) int {
	half := s / 2
	average := -100000
	ans := -s
	for k := -s; k <= s; k++ {
		curAverage := average1(arr, k, s)
		if math.Abs(float64(half-curAverage)) < math.Abs(float64(half-average)) {
			average = curAverage
			ans = k
		}
	}
	return ans
}

// 暴力方法
// 为了测试
func average1(arr []int, k, s int) int {
	sum := 0
	for _, num := range arr {
		value := num + k
		if value < 0 {
			sum += 0
		} else if value > s {
			sum += s
		} else {
			sum += value
		}
	}
	return sum / len(arr)
}

// 优化了一下,但不是最优解
func best2(arr []int, s int) int {
	l := -s
	r := s
	m := 0
	half := s / 2
	average := -s
	ans := 0
	for l <= r {
		m = (l + r) / 2
		curAverage := average1(arr, m, s)
		if math.Abs(float64(half-curAverage)) < math.Abs(float64(half-average)) ||
			(math.Abs(float64(half-curAverage)) == math.Abs(float64(half-average)) && m < ans) {
			average = curAverage
			ans = m
		}
		if curAverage >= half {
			r = m - 1
		} else {
			l = m + 1
		}
	}
	return ans
}

// 正式方法
// 最优解
// O(N * logN) + O(logS *  logN)
func best3(arr []int, s int) int {
	sort.Ints(arr)
	sum := make([]int, len(arr))
	sum[0] = arr[0]
	for i := 1; i < len(arr); i++ {
		sum[i] = sum[i-1] + arr[i]
	}
	l := -s
	r := s
	m := 0
	half := s / 2
	average := -s
	ans := 0
	for l <= r {
		m = (l + r) / 2
		curAverage := average3(arr, sum, m, s)
		if math.Abs(float64(half-curAverage)) < math.Abs(float64(half-average)) ||
			(math.Abs(float64(half-curAverage)) == math.Abs(float64(half-average)) && m < ans) {
			average = curAverage
			ans = m
		}
		if curAverage >= half {
			r = m - 1
		} else {
			l = m + 1
		}
	}
	return ans
}

func average3(arr []int, pre []int, k, s int) int {
	n := len(arr)
	if k < 0 {
		l := bsZero(arr, k)
		sum := rangeSum(pre, l+1, n-1)
		return (sum + (k * (n - l - 1))) / n
	} else {
		r := bsS(arr, k, s)
		sum := rangeSum(pre, 0, r-1)
		return (sum + (k * r) + (s * (n - r))) / n
	}
}

func bsZero(arr []int, k int) int {
	ans := -1
	l := 0
	r := len(arr) - 1
	var m int
	for l <= r {
		m = (l + r) / 2
		if arr[m]+k <= 0 {
			ans = m
			l = m + 1
		} else {
			r = m - 1
		}
	}
	return ans
}

func bsS(arr []int, k, s int) int {
	ans := len(arr)
	l := 0
	r := len(arr) - 1
	var m int
	for l <= r {
		m = (l + r) / 2
		if arr[m]+k >= s {
			ans = m
			r = m - 1
		} else {
			l = m + 1
		}
	}
	return ans
}

func rangeSum(pre []int, l, r int) int {
	if l > r {
		return 0
	}
	if l == 0 {
		return pre[r]
	}
	return pre[r] - pre[l-1]
}

// 为了测试
func randomArray(n, s int) []int {
	arr := make([]int, n)
	for i := 0; i < n; i++ {
		arr[i] = randInt(0, s)
	}
	return arr
}

func randInt(min, max int) int {
	return min + rand.Intn(max-min+1)
}

func main() {
	N := 50
	S := 500
	testTimes := 10000
	fmt.Println("测试开始")
	for i := 0; i < testTimes; i++ {
		n := randInt(1, N)
		s := randInt(1, S)
		arr := randomArray(n, s)
		ans1 := best1(arr, s)
		ans2 := best2(arr, s)
		ans3 := best3(arr, s)
		if ans1 != ans2 || ans1 != ans3 {
			fmt.Println("出错了!")
		}
	}
	fmt.Println("测试结束")
}

在这里插入图片描述

c++完整代码如下:

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int average1(vector<int>& arr, int k, int s);
int average3(vector<int>& arr, vector<int>& pre, int k, int s);
int bsZero(vector<int>& arr, int k);
int bsS(vector<int>& arr, int k, int s);
int rangeSum(vector<int>& pre, int l, int r);
int best1(vector<int>& arr, int s);
int best2(vector<int>& arr, int s);
int best3(vector<int>& arr, int s);
vector<int> randomArray(int n, int s);
void test();

int average1(vector<int>& arr, int k, int s) {
    int sum = 0;
    for (int num : arr) {
        int value = num + k;
        if (value < 0) {
            sum += 0;
        }
        else if (value > s) {
            sum += s;
        }
        else {
            sum += value;
        }
    }
    return sum / arr.size();
}

int average3(vector<int>& arr, vector<int>& pre, int k, int s) {
    int n = arr.size();
    if (k < 0) {
        int l = bsZero(arr, k);
        int sum = rangeSum(pre, l + 1, n - 1);
        return (sum + (k * (n - l - 1))) / n;
    }
    else {
        int r = bsS(arr, k, s);
        int sum = rangeSum(pre, 0, r - 1);
        return (sum + (k * r) + (s * (n - r))) / n;
    }
}

int bsZero(vector<int>& arr, int k) {
    int ans = -1;
    int l = 0;
    int r = arr.size() - 1;
    int m;
    while (l <= r) {
        m = (l + r) / 2;
        if (arr[m] + k <= 0) {
            ans = m;
            l = m + 1;
        }
        else {
            r = m - 1;
        }
    }
    return ans;
}

int bsS(vector<int>& arr, int k, int s) {
    int ans = arr.size();
    int l = 0;
    int r = arr.size() - 1;
    int m;
    while (l <= r) {
        m = (l + r) / 2;
        if (arr[m] + k >= s) {
            ans = m;
            r = m - 1;
        }
        else {
            l = m + 1;
        }
    }
    return ans;
}

int rangeSum(vector<int>& pre, int l, int r) {
    if (l > r) {
        return 0;
    }
    return l == 0 ? pre[r] : (pre[r] - pre[l - 1]);
}

int best1(vector<int>& arr, int s) {
    int half = s / 2;
    int average = -100000;
    int ans = -s;
    for (int k = -s; k <= s; k++) {
        int curAverage = average1(arr, k, s);
        if (abs(half - curAverage) < abs(half - average)) {
            average = curAverage;
            ans = k;
        }
    }
    return ans;
}

int best2(vector<int>& arr, int s) {
    int l = -s;
    int r = s;
    int m = 0;
    int half = s / 2;
    int average = -s;
    int ans = 0;
    while (l <= r) {
        m = (l + r) / 2;
        int curAverage = average1(arr, m, s);
        if ((abs(half - curAverage) < abs(half - average))
            || ((abs(half - curAverage) == abs(half - average)) && m < ans)) {
            average = curAverage;
            ans = m;
        }
        if (curAverage >= half) {
            r = m - 1;
        }
        else {
            l = m + 1;
        }
    }
    return ans;
}

int best3(vector<int>& arr, int s) {
    sort(arr.begin(), arr.end());
    vector<int> sum(arr.size());
    sum[0] = arr[0];
    for (int i = 1; i < arr.size(); i++) {
        sum[i] = sum[i - 1] + arr[i];
    }
    int l = -s;
    int r = s;
    int m = 0;
    int half = s / 2;
    int average = -s;
    int ans = 0;
    while (l <= r) {
        m = (l + r) / 2;
        int curAverage = average3(arr, sum, m, s);
        if ((abs(half - curAverage) < abs(half - average))
            || ((abs(half - curAverage) == abs(half - average)) && m < ans)) {
            average = curAverage;
            ans = m;
        }
        if (curAverage >= half) {
            r = m - 1;
        }
        else {
            l = m + 1;
        }
    }
    return ans;
}

vector<int> randomArray(int n, int s) {
    vector<int> arr(n);
    for (int i = 0; i < n; i++) {
        arr[i] = rand() % (s + 1);
    }
    return arr;
}

void test() {
    int N = 50;
    int S = 500;
    int testTimes = 10000;
    cout << "测试开始" << endl;
    for (int i = 0; i < testTimes; i++) {
        int n = rand() % N + 1;
        int s = rand() % S + 1;
        vector<int> arr = randomArray(n, s);
        int ans1 = best1(arr, s);
        int ans2 = best2(arr, s);
        int ans3 = best3(arr, s);
        if (ans1 != ans2 || ans1 != ans3) {
            cout << "出错了!" << endl;
        }
    }
    cout << "测试结束" << endl;
}

int main() {
    test();
    return 0;
}

在这里插入图片描述

posted @ 2023-09-05 10:06  福大大架构师每日一题  阅读(18)  评论(0编辑  收藏  举报