How to compute weighted probability for nitialization of centers using kmeans++? How kmeans++ is differ from kmeans?

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AS 2020-8-24

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https://ww2.mathworks.cn/matlabcentral/answers/583685-how-to-compute-weighted-probability-for-nitialization-of-centers-using-kmeans-how-kmeans-is-dif

load dara1.dat;
nc=4;
niters=100;
[r,col]=size(data1);
p=randperm(r);
p=p(1:nc);
c=data1(p,:);
id=eye(nc);
for n=1:niters
    old_c=c;
    d2=dist2(data1,c);
    %d2=d2';
    [minval,indx]=min(d2,[],2);
    post=id(indx,:);
    num_points=sum(post,1);
    for jj=1:nc
        if num_points(jj) > 0
            c(jj,:)=sum(data1(find(post(:,jj)),:),1)/num_points(jj);
        end
    end
    e=sum(minval);
    if n>1
        if max(max(abs(c-old_c))) <0.00001 &&  abs(old_e-e) <0.00001
            options(8)=e;
            return;
        end
    end
   old_e=e
en

This is simple kmeans algorithm for clustering. But I want to applied kmeans++ algorithm instead of simple kmeans, where I have to initialize the centers by suing a weighted probability distribution where a point x is chosen with probability proportional to d2. I am not understanding that how to initialize the center using kmeans++ algorithm: please help me on this.