matlab构造逆序对为m的数列

Question

matlab构造逆序对为m的元素个数为n的数列，请解解难
matlab构造逆序对为m的元素个数为n的数列，请解解难

Answer 1

先生成一个长度为n的随机数列

nums = randperm(n);

然后，可以编写一个归并排序的函数，用于将随机数列排序并计算逆序对的数量

function [count, sorted_nums] = merge_sort_with_count(nums)
    n = length(nums);
    if n <= 1
        count = 0;
        sorted_nums = nums;
        return;
    end
    mid = floor(n/2);
    [count1, nums1] = merge_sort_with_count(nums(1:mid));
    [count2, nums2] = merge_sort_with_count(nums(mid+1:n));
    [count, sorted_nums] = merge_with_count(nums1, nums2);
    count = count + count1 + count2;
end

function [count, merged_nums] = merge_with_count(nums1, nums2)
    i = 1;
    j = 1;
    count = 0;
    n1 = length(nums1);
    n2 = length(nums2);
    merged_nums = zeros(1, n1+n2);
    k = 1;
    while i <= n1 && j <= n2
        if nums1(i) <= nums2(j)
            merged_nums(k) = nums1(i);
            i = i + 1;
        else
            merged_nums(k) = nums2(j);
            j = j + 1;
            count = count + (n1 - i + 1);
        end
        k = k + 1;
    end
    if i <= n1
        merged_nums(k:end) = nums1(i:end);
    end
    if j <= n2
        merged_nums(k:end) = nums2(j:end);
    end
end

最后，可以在主程序中调用 merge_sort_with_count 函数生成一个逆序对为 m 的长度为 n 的数列

m = 10; % 目标逆序对数量
n = 20