在这里我们不多介绍原理，直接看代码就好了。
C语言版本
#include<stdio.h>
#include<string.h>
const int maxn=305;
const int INF=(1<<30)-1;
int g[maxn][maxn];
int lx[maxn],ly[maxn];
int match[maxn];
bool visx[maxn],visy[maxn];
int slack[maxn];
int n;
bool dfs(int cur)
{int y,t;visx[cur]=true;for(y=1;y<=n;y++){if(visy[y])continue;t=lx[cur]+ly[y]-g[cur][y];if(t==0){visy[y]=true;if(match[y]==-1||dfs(match[y])){match[y]=cur;return true;}}else if(slack[y]>t)slack[y]=t;}return false;
}
int KM()
{int i,j,x;memset(match,-1,sizeof(match));memset(ly,0,sizeof(ly));for(i=1;i<=n;i++){lx[i]=-INF;for(j=1;j<=n;j++)if(g[i][j]>lx[i])lx[i]=g[i][j];}//对ly[i]置0,对lx[i]取每行的最大值for(x=1;x<=n;x++){for(i=1;i<=n;i++)slack[i]=INF;while(true){memset(visx,false,sizeof(visx));memset(visy,false,sizeof(visy));if(dfs(x))break;int d=INF;for(i=1;i<=n;i++){if(!visy[i]&&d>slack[i])d=slack[i];}for(i=1;i<=n;i++){if(visx[i])lx[i]-=d;}for(i=1;i<=n;i++){if(visy[i])ly[i]+=d;elseslack[i]-=d;}}}int result=0;for(i=1;i<=n;i++)if(match[i]>-1)result+=g[match[i]][i];return result;
}
int main()
{int cost,i,j;while(scanf("%d",&n)!=EOF){for(i=1;i<=n;i++){for(j=1;j<=n;j++){scanf("%d",&cost);g[i][j]=cost;}}printf("%d\n",KM());}return 0;
}Matlab版本
% 带权二部图匹配（KM算法）
clc
clear
close allglobal N
global adj_matrix
global label_left
global label_right
global match_right
global visit_left
global visit_right
% 左右各有N个点
% KM算法要求左右两边的节点数相等，可以通过添加虚拟节点的方法实现
N = 5;
adj_matrix = [3 4 6 4 9;6 4 5 3 8;7 5 3 4 2;6 3 2 2 5;8 4 5 4 7];
% N = 9;
% adj_matrix = round(rand(N)*100);
% adj_matrix(adj_matrix<70) = 0;
% 初始化顶标
label_left = max(adj_matrix, [], 2);
label_right = zeros(N, 1);
% 初始化匹配结果
match_right = ones(N, 1) * nan;
% 初始化辅助变量
visit_left = ones(N, 1) * false;
visit_right = ones(N, 1) * false;
res = KM();% KM主函数
function res = KM()
global N
global adj_matrix
global label_left
global label_right
global match_right
global visit_left
global visit_rightgraph_num = 1;
display_graph(graph_num, '原始二部图');
% 对左边的点依次进行处理
for i = 1: Nwhile 1% 重置辅助变量visit_left = ones(N, 1) * false;visit_right = ones(N, 1) * false;% 能找到可行匹配if find_path(i)break;end% 不能找到可行匹配，修改顶标% (1)将所有在增广路中的X方点的label全部减去一个常数d% (2)将所有在增广路中的Y方点的label全部加上一个常数dd = Inf;for j = 1: Nif visit_left(j)for k = 1: Nif ~visit_right(k)% 左边的点中已经访问过的点，即已经匹配过的点可能需要重新匹配以得到更大的总权值，% 所以修改顶标，往子图中添加一条边，重新寻找增广路看能不能增广% 取与左边的点相邻的未匹配边中跟当前存在子图中的以该点为端点的边相差最小的两条边% 这样才能保持总权值最大d = min(d, label_left(j) + label_right(k) - adj_matrix(j, k));endendendendfor k = 1: Nif visit_left(k)label_left(k) = label_left(k) - d;endif visit_right(k)label_right(k) = label_right(k) + d;endendendgraph_num = graph_num + 1;display_graph(graph_num, ['第' num2str(i) '步']);
endgraph_num = graph_num + 1;
display_graph(graph_num, '最终结果');res = 0;
for j = 1: Nif match_right(j) >=0 && match_right(j) < Nres = res + adj_matrix(match_right(j), j);end
end
end% 寻找增广路，深度优先
function result = find_path(i)
global N
global adj_matrix
global label_left
global label_right
global match_right
global visit_left
global visit_right
visit_left(i) = true;
for j = 1: length(adj_matrix(i, :))match_weight = adj_matrix(i, j);if visit_right(j)% 已被匹配（解决递归中的冲突）continue;endgap = label_left(i) + label_right(j) - match_weight;% 当 gap == 0 时 x_i 和 y_j 之间存在一条边，且该边是当前 x_i 可以匹配的权值最大的边if gap == 0% 找到可行匹配visit_right(j) = true;% j未被匹配，或虽然j已被匹配，但是j的已匹配对象有其他可选备胎% 此处同匈牙利算法if isnan(match_right(j)) || find_path(match_right(j))match_right(j) = i;result = true;return;endend
end
result = false;
return;
endfunction display_graph(graph_num, title_name)
global N
global adj_matrix
global label_left
global label_right
global match_right
global visit_left
global visit_right
figure(graph_num);
set(gcf, 'Position', [100, 100, 1000, 500]);
subplot(1,2,1);
cla
set( gca, 'XTick', [], 'YTick', [] );
set( gca, 'TickLength', [0 0]);
box on
hold on
xlim([-1, 2]);
ylim([-N, 1]);
temp = N - 1;
% 绘制匹配边
for j = 1: length(match_right)if ~isnan(match_right(j))plot([0, 1], [(match_right(j) - 1) * -temp/(N-1), (j - 1) * -temp/(N-1)], 'r', 'LineWidth', 2); end
end
% 绘制点
scatter(zeros(1, N), 0:-temp/(N-1):-temp, 20, [217/255 83/255 25/255], 'filled');
scatter(ones(1, N), 0:-temp/(N-1):-temp, 20, [0 114/255 189/255], 'filled');
for j = 1: Ntext(-0.2, (j - 1) * -temp/(N-1), ['x_' num2str(j)]);
end
for j = 1: Ntext(1.1, (j - 1) * -temp/(N-1), ['y_' num2str(j)]);
end
for j = 1: Ntext(-0.5, (j - 1) * -temp/(N-1), num2str(label_left(j)), 'Color', [217/255 83/255 25/255], 'FontSize', 15);
end
for j = 1: Ntext(1.4, (j - 1) * -temp/(N-1), num2str(label_right(j)), 'Color', [0 114/255 189/255], 'FontSize', 15);
endtitle(title_name);% 边权重
subplot(1,2,2);
cla
set( gca, 'XTick', [], 'YTick', [] );
set( gca, 'TickLength', [0 0]);
box on
hold on
xlim([-1, N]);
ylim([-N, 1]);
for j = 0 : N-1plot([j, j], [-N, 1], 'k') ;
end
for j = -N+1 : 0plot([-1, N], [j, j], 'k') ;
end
for j = 1: Ndisplay_text(j, 0, ['x_' num2str(j)], 0);
end
for j = 1: Ndisplay_text(0, j, ['y_' num2str(j)], 0);
end
for i = 1: Nfor j = 1: Nif match_right(j) == idisplay_text(i, j, num2str(adj_matrix(i,j)), 1);elsedisplay_text(i, j, num2str(adj_matrix(i,j)), 0);endend
end
% saveas(gcf, [num2str(graph_num) '.png']);
end% 在x行y列显示t文本
function display_text(x, y, t, bold)
if boldtext(y - 0.5, -x + 0.5, t, 'FontSize', 15, 'FontWeight', 'bold', 'Color', 'r');
elsetext(y - 0.5, -x + 0.5, t, 'FontSize', 15, 'FontWeight', 'normal', 'Color', 'k');
end
end有需要再matlab中改代码的联系我。私信支持付费。！
蜂窝用户匹配问题！等等！
 - RH294)
