📌 Problem Description

Write a program to input an integer array and find the maximum and minimum values within it.

• Requirements:

• Support dynamic input for array length

• Output the maximum and minimum values

• Advanced: Minimize the number of comparisons as much as possible

Example:

Input array: 3 9 2 5 7  Output: Maximum=9, Minimum=2   

Difficulty:⭐️⭐️ (Basic problem, but optimizing the number of comparisons is challenging)

💡 Basic Implementation (Linear Scan Method)

#include <stdio.h>
void find_min_max(int arr[], int n, int *min, int *max) {    if (n == 0) return; // Handle empty array    *min = *max = arr[0]; // Initialize
    for (int i = 1; i < n; i++) {        if (arr[i] < *min) *min = arr[i];        if (arr[i] > *max) *max = arr[i];    }}
int main() {    int n;    printf("Input array length:");    scanf("%d", &n);    int arr[n];
    printf("Input %d elements:", n);    for (int i = 0; i < n; i++) scanf("%d", &arr[i]);
    int min, max;    find_min_max(arr, n, &min, &max);    printf("Minimum=%d, Maximum=%d", min, max);    return 0;}

Output Example:

Input array: 3 9 2 5 7 → Minimum=2, Maximum=9  

Key Points:

• Time Complexity O(n): Traverse the array once

• Number of Comparisons 2(n-1): Each element is compared twice (to find minimum and maximum)

<span>⚡</span><span> Advanced Optimization (Pairwise Comparison Method)</span>

<span>Reduce the number of comparisons by </span><strong><span>processing elements in pairs</span></strong><span> (Number of comparisons ≈ 1.5n):</span>

void find_min_max_opt(int arr[], int n, int *min, int *max) {    if (n == 0) return;    int i;    // Initialize (handle odd/even length)
    if (n % 2 == 1) *min = *max = arr[0], i = 1;    else {        *min = (arr[0] < arr[1]) ? arr[0] : arr[1];        *max = (arr[0] > arr[1]) ? arr[0] : arr[1];        i = 2;    }
    // Pairwise comparison    for (; i < n; i += 2) {        int local_min, local_max;        if (arr[i] < arr[i+1]) {            local_min = arr[i];            local_max = arr[i+1];        } else {            local_min = arr[i+1];            local_max = arr[i];        }        if (local_min < *min) *min = local_min;        if (local_max > *max) *max = local_max;    }}

Optimization Principle:

1. Each time, take two elements and compare their sizes (1 comparison)

2. Compare the smaller one with the current minimum and the larger one with the current maximum (2 comparisons)

3. Total number of comparisons = 3*(n/2) ≈ 1.5n

⚡ Extended Features

1. Return the indices of the maximum/minimum values

void find_min_max_index(int arr[], int n, int *min_idx, int *max_idx) {    *min_idx = *max_idx = 0;    for (int i = 1; i < n; i++) {        if (arr[i] < arr[*min_idx]) *min_idx = i;        if (arr[i] > arr[*max_idx]) *max_idx = i;    }}

2. Find the second largest number simultaneously

int find_second_max(int arr[], int n) {    int max = arr[0], second_max = arr[0];    for (int i = 1; i < n; i++) {        if (arr[i] > max) {            second_max = max;            max = arr[i];        } else if (arr[i] > second_max) {            second_max = arr[i];        }    }    return second_max;}

🤔 Common Error Analysis

Issue	Cause	Solution
Uninitialized<span>min</span>/<span>max</span>	Did not handle the case when the array length is 0	Add empty array check
Array with all identical elements	Did not consider the case where all elements are equal	Initial values are sufficient to handle this
Input data contains non-numeric values	Did not validate<span>scanf</span> return value	Add input validation loop

🎯 Today’s Challenge

Try to implement the following features (choose one):

1. Count comparisons: Compare the actual number of comparisons between the linear scan method and the pairwise comparison method

2. Handle floating-point arrays: Support<span>double</span> type

🚀 Next Preview No. 13: Removing Duplicates from Array Elements: How to Efficiently Remove Duplicates?

📢 Interaction Time

1. What issues have you encountered when finding extreme values? Feel free to leave a comment!

2. Vote: Which method do you think is more efficient?

• 👍 Linear Scan Method (Simple and Intuitive)

• ❤️ Pairwise Comparison Method (Performance Optimized)

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Article Author:Vv Computer Graduate Examination World (Focusing on Computer Graduate Examination Tutoring8 years)

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