MATLAB实现堆排序

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已于 2024-10-22 10:45:17 修改

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分类专栏： Matlab 文章标签： Sort 堆排序 MATLAB

于 2019-12-06 10:07:08 首次发布

本文链接：https://blog.youkuaiyun.com/newcloudtech/article/details/103417364

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clear;clc;close all
x = [4,3,1,6,7,5,2,1,5,6,7,8];
node = floor(length(x)/2);
for i = node : -1 : 1
    x = heap(x, i, length(x));
end
for i = length(x) : -1 : 1
    x([1,i]) = x([i,1]);
    x = heap(x, 1, i-1);
end

function x = heap(x, node, sz)
left = node * 2;   % 左叶子节点
right = node * 2 + 1; % 右叶子节点
max_idx = node;
if left <= sz && x(left) > x(node)
    max_idx = left;
    x([left, node]) = x([node, left]);
end
if right <= sz && x(right) > x(node)
    max_idx = right;
    x([right, node]) = x([node, right]);
end
if max_idx ~= node
    x = heap(x, max_idx, sz);
end
end

感谢@Xunna老哥的指出，上面程序存在问题，等待左右孩子完成交换后，再进行搜索，会出现问题，如果左右孩子都进行了交换，那么左孩子的就被忽略，不会进行搜索过程，因此在每次完成交换后都应该马上进行子树的搜索，程序修改如下，欢迎批评指正。

clear;clc;close all
x = [4,3,1,6,7,5,2,1,5,6,7,8];
node = floor(length(x)/2);
for i = node : -1 : 1
    x = heap(x, i, length(x));
end
for i = length(x) : -1 : 1
    x([1,i]) = x([i,1]);
    x = heap(x, 1, i-1);
end
 
function x = heap(x, node, sz)
left = node * 2;   % 左叶子节点
right = node * 2 + 1; % 右叶子节点

if left <= sz && x(left) > x(node)
    max_idx = left;
    x([left, node]) = x([node, left]);
    x = heap(x, max_idx, sz);
end
if right <= sz && x(right) > x(node)
    max_idx = right;
    x([right, node]) = x([node, right]);
    x = heap(x, max_idx, sz);
end

end