二维峰值算法找不到峰值

Question

I just started an MIT course on algorithm, and we were taught the 2D Peak Finding algo. I tried dry running and implementing it yet the algo seems to be failing for this input.

{5, 0, 3, 2}
{1, 1, 2, 4}
{1, 2, 4, 4}

This is the Algorithm:

• Pick middle column j = m/2
• Find global maximum on column j at (i,j)
• Compare(i,j−1),(i,j),(i,j+1)
• Pick left columns of(i,j−1)>(i,j)
• Similarly for right
• (i,j) is a 2D-peak if neither condition holds ← WHY?
• Solve the new problem with half the number of columns.
• When you have a single column, find global maximum and you‘re done.

Update, Here is the code which I tried and doesn't seem to be working:

#include <bits/stdc++.h> 
using namespace std; 

const int MAX = 100; 

int findMax(int arr[][MAX], int rows, int mid, int& max) 
{ 
    int max_index = 0; 
    for (int i = 0; i < rows; i++) { 
        if (max < arr[i][mid]) { 
            max = arr[i][mid]; 
            max_index = i; 
        } 
    } 
    return max_index; 
} 

int findPeakRec(int arr[][MAX], int rows, int columns, int mid) 
{ 
    int max = 0; 
    int max_index = findMax(arr, rows, mid, max); 
    if (mid == 0 || mid == columns - 1) 
        return max; 
    if (max >= arr[max_index][mid - 1] && max >= arr[max_index][mid + 1]) 
        return max; 
    if (max < arr[max_index][mid - 1]) 
        return findPeakRec(arr, rows, columns, mid - ceil((double)mid / 2)); 
    return findPeakRec(arr, rows, columns, mid + ceil((double)mid / 2)); 
} 

int findPeak(int arr[][MAX], int rows, int columns) 
{ 
    return findPeakRec(arr, rows, columns, columns / 2); 
} 

int main() 
{ 
    int arr[][MAX] = { { 5, 0, 3, 2 }, 
                       { 1, 1, 2, 4 }, 
                       { 1, 2, 4, 4 }, 
                       { 3, 2, 0, 1 } }; 
    int rows = 4, columns = 4; 
    cout << findPeak(arr, rows, columns); 
    return 0; 
} 

this is how I implemented the algorithm.

Answer 1

The algorithm is correct (Just a spelling mistake in the fourth bullet point: "of" should read "if").

You missed a correct definition of "peak". The algorithm for peak finding intends to find a local maximum, not necessarily the global maximum. For a global maximum the algorithm is trivial, you just look for the maximum value with a row by row scan.

But peak finding can be more efficient as not all values need to be inspected.