{"id":108047,"date":"2026-09-20T20:40:51","date_gmt":"2026-09-20T12:40:51","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/108047.html"},"modified":"2026-09-20T20:40:51","modified_gmt":"2026-09-20T12:40:51","slug":"km-%e7%ae%97%e6%b3%95%e8%a7%a3%e6%9e%90%ef%bc%9a%e5%b8%a6%e6%9d%83%e4%ba%8c%e5%88%86%e5%9b%be%e6%9c%80%e4%bc%98%e5%8c%b9%e9%85%8d%e4%b8%8e%e9%a1%b6%e6%a0%87%e8%b0%83%e6%95%b4","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/108047.html","title":{"rendered":"KM \u7b97\u6cd5\u89e3\u6790\uff1a\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u4f18\u5339\u914d\u4e0e\u9876\u6807\u8c03\u6574"},"content":{"rendered":"

\u5f15\u8a00<\/h3>\n

\u5728\u4fe1\u5965\u65b0\u8d5b\u5b63\u7684\u56fe\u8bba\u5907\u8003\u4e2d，\u4e8c\u5206\u56fe\u5339\u914d\u662f\u4e00\u4e2a\u7ed5\u4e0d\u5f00\u7684\u9ad8\u9891\u8003\u70b9\u3002\u524d\u9762\u6211\u4eec\u804a\u8fc7\u300c\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u300d（\u5308\u7259\u5229\u7b97\u6cd5）\u6c42\u7684\u662f\u5339\u914d\u8fb9\u6570\u6700\u591a；\u800c\u771f\u5b9e\u7ade\u8d5b\u91cc\u66f4\u5e38\u89c1\u7684\u662f\u2014\u2014\u6bcf\u5bf9\u914d\u5bf9\u90fd\u6709\u4e00\u4e2a\u6743\u91cd，\u8981\u6c42\u9009\u51fa\u7684\u914d\u5bf9\u603b\u6743\u91cd\u6700\u5927\u3002\u6bd4\u5982\u79d1\u6280\u8282\u4e0a\u8ba9\u540c\u5b66\u548c\u5c55\u4f4d\u4e00\u4e00\u642d\u6863，\u8c01\u548c\u54ea\u4e2a\u9879\u76ee\u914d\u5408\u6700\u9ed8\u5951，\u5c31\u662f\u5178\u578b\u7684\u300c\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u4f18\u5339\u914d\u300d\u95ee\u9898\u3002<\/p>\n

\u89e3\u51b3\u5b83\u7684\u7b97\u6cd5\u53eb KM \u7b97\u6cd5（Kuhn\u2013Munkres，\u4e5f\u79f0\u5308\u7259\u5229\u7b97\u6cd5\u7684\u5e26\u6743\u7248\u672c），\u53ef\u4ee5\u5728 O(n\u00b3) \u65f6\u95f4\u5185\u6c42\u51fa\u6700\u5927\u6743\u5b8c\u7f8e\u5339\u914d\u3002\u672c\u6587\u7528\u4e00\u4e2a\u539f\u521b\u5b9e\u4f8b，\u5e26\u4f60\u5403\u900f\u9876\u6807\u3001\u76f8\u7b49\u5b50\u56fe\u3001\u4ea4\u9519\u6811\u4e0e\u9876\u6807\u8c03\u6574\u8fd9\u56db\u5757\u6838\u5fc3，\u5e76\u7ed9\u51fa C++ \/ Python \u53cc\u7248\u5b9e\u73b0\u3002<\/p>\n

\"\"<\/p>\n

\u9898\u76ee \/ \u9879\u76ee\u76ee\u6807<\/h3>\n

\u3010\u539f\u521b\u9898\u3011\u6821\u56ed\u79d1\u6280\u8282\u6700\u4f73\u642d\u6863\u914d\u5bf9<\/p>\n

\u6709 n \u540d\u540c\u5b66（\u5de6\u90e8\u96c6\u5408 X）\u4e0e n \u4e2a\u5c55\u793a\u9879\u76ee（\u53f3\u90e8\u96c6\u5408 Y），\u5fc5\u987b\u4e3a\u6bcf\u4e2a\u540c\u5b66\u5206\u914d\u4e14\u53ea\u5206\u914d\u4e00\u4e2a\u9879\u76ee，\u6bcf\u4e2a\u9879\u76ee\u4e5f\u6070\u597d\u7531\u4e00\u4e2a\u540c\u5b66\u8d1f\u8d23\u3002\u5df2\u77e5\u540c\u5b66 i \u5bf9\u9879\u76ee j \u7684\u300c\u9002\u914d\u9ed8\u5951\u5ea6\u300d\u4e3a w[i][j]（\u53ef\u4e3a\u8d1f）\u3002\u8bf7\u8bbe\u8ba1\u4e00\u79cd\u4e00\u4e00\u914d\u5bf9\u65b9\u6848，\u4f7f\u6240\u6709\u914d\u5bf9\u7684\u9ed8\u5951\u5ea6\u4e4b\u548c\u6700\u5927\u3002<\/p>\n

\u4ee5 n = 4 \u4e3a\u4f8b，\u9ed8\u5951\u5ea6\u77e9\u9635\u5982\u4e0b（\u884c\u662f\u540c\u5b66，\u5217\u662f\u9879\u76ee）：<\/p>\n\n\u540c\u5b66 \\\\ \u9879\u76ee\u9879\u76ee0\u9879\u76ee1\u9879\u76ee2\u9879\u76ee3<\/tr>\n\n\n\n\n\n
\u540c\u5b660<\/td>\n3<\/td>\n5<\/td>\n4<\/td>\n2<\/td>\n<\/tr>\n
\u540c\u5b661<\/td>\n6<\/td>\n2<\/td>\n8<\/td>\n7<\/td>\n<\/tr>\n
\u540c\u5b662<\/td>\n4<\/td>\n3<\/td>\n5<\/td>\n1<\/td>\n<\/tr>\n
\u540c\u5b663<\/td>\n2<\/td>\n6<\/td>\n7<\/td>\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6700\u4f18\u914d\u5bf9\u4e3a：\u540c\u5b662\u2192\u9879\u76ee0(4)\u3001\u540c\u5b660\u2192\u9879\u76ee1(5)\u3001\u540c\u5b663\u2192\u9879\u76ee2(7)\u3001\u540c\u5b661\u2192\u9879\u76ee3(7)，\u603b\u9ed8\u5951\u5ea6 23\u3002\u4e0b\u9762\u89e3\u91ca\u7b97\u6cd5\u5982\u4f55\u81ea\u52a8\u7b97\u51fa\u8fd9\u4e2a\u7ed3\u679c\u3002<\/p>\n

\u6838\u5fc3\u8003\u70b9<\/h3>\n
  • \u53ef\u884c\u9876\u6807（Feasible Labeling）：\u7ed9\u6bcf\u4e2a\u8282\u70b9 i \u4e00\u4e2a\u9876\u6807 l(i)，\u8981\u6c42\u5bf9\u4efb\u610f\u8fb9 (u, v) \u6ee1\u8db3 l(u) + l(v) \u2265 w(u, v)\u3002\u521d\u59cb\u4ee4 lx[i] = max_j w[i][j]\u3001ly[i] = 0 \u5373\u662f\u4e00\u7ec4\u5408\u6cd5\u9876\u6807\u3002<\/li>\n
  • \u76f8\u7b49\u5b50\u56fe（Equality Subgraph）：\u53ea\u4fdd\u7559\u6ee1\u8db3 l(u) + l(v) == w(u, v) \u7684\u8fb9\u6784\u6210\u7684\u5b50\u56fe\u3002\u5b9a\u7406：\u82e5\u76f8\u7b49\u5b50\u56fe\u5b58\u5728\u5b8c\u7f8e\u5339\u914d，\u5219\u8be5\u5339\u914d\u5c31\u662f\u539f\u56fe\u7684\u6700\u5927\u6743\u5b8c\u7f8e\u5339\u914d（\u56e0\u4e3a\u4efb\u610f\u5b8c\u7f8e\u5339\u914d\u6743\u503c\u548c \u2264 \u6240\u6709\u9876\u6807\u4e4b\u548c）\u3002<\/li>\n
  • \u589e\u5e7f\u8def\u4e0e\u4ea4\u9519\u6811：\u5728\u76f8\u7b49\u5b50\u56fe\u91cc\u7528\u300c\u5308\u7259\u5229\u5f0f\u300dDFS \u627e\u589e\u5e7f\u8def；\u627e\u4e0d\u5230\u65f6，\u6240\u6709\u88ab\u8bbf\u95ee\u5230\u7684\u70b9\u6784\u6210\u4e00\u68f5\u4ea4\u9519\u6811\u3002<\/li>\n
  • \u9876\u6807\u8c03\u6574（\u677e\u5f1b）：\u627e\u4e0d\u5230\u589e\u5e7f\u8def\u65f6，\u8ba1\u7b97\u6700\u5c0f\u53ef\u6539\u8fdb\u91cf d = min(lx[x] + ly[y] – w[x][y])（x \u5728\u6811\u5185\u3001y \u5728\u6811\u5916），\u8ba9\u6811\u5185\u5de6\u90e8\u9876\u6807 -d\u3001\u6811\u5185\u53f3\u90e8\u9876\u6807 +d，\u4f7f\u81f3\u5c11\u4e00\u6761\u65b0\u8fb9\u8fdb\u5165\u76f8\u7b49\u5b50\u56fe，\u4e14\u4e0d\u7834\u574f\u5df2\u6709\u5339\u914d\u7684\u53ef\u884c\u6027\u3002<\/li>\n
  • slack \u6570\u7ec4：\u8bb0\u5f55\u6bcf\u4e2a\u53f3\u90e8\u70b9\u300c\u8fd8\u9700\u8981\u51cf\u5c11\u591a\u5c11\u300d\u624d\u80fd\u8fdb\u5165\u76f8\u7b49\u5b50\u56fe，\u907f\u514d\u6bcf\u6b21\u91cd\u65b0\u626b\u63cf，\u628a\u65f6\u95f4\u538b\u5230 O(n\u00b3)\u3002<\/li>\n
  • \u8865\u70b9\u6280\u5de7：\u82e5\u4e24\u8fb9\u70b9\u6570\u4e0d\u7b49，\u628a\u5c11\u7684\u4e00\u8fb9\u8865\u865a\u62df\u70b9\u3001\u865a\u8fb9\u6743\u8bbe 0，\u8f6c\u5316\u4e3a\u65b9\u9635\u6c42\u5b8c\u7f8e\u5339\u914d；\u6c42\u6700\u5c0f\u6743\u5339\u914d\u53ea\u9700\u628a\u6240\u6709\u6743\u53d6\u76f8\u53cd\u6570\u3002<\/li>\n

    \u89e3\u6cd5 \/ \u62c6\u89e3<\/h3>\n

    \u7b97\u6cd5\u4e3b\u6d41\u7a0b\u4e3a\u300c\u4e3a\u6bcf\u4e2a\u5de6\u90e8\u70b9\u4f9d\u6b21\u627e\u589e\u5e7f\u8def\u300d：\u521d\u59cb\u9876\u6807\u53ef\u884c \u2192 \u5728\u76f8\u7b49\u5b50\u56fe\u4e2d DFS \u627e\u589e\u5e7f \u2192 \u627e\u5230\u5c31\u5339\u914d\u3001\u5904\u7406\u4e0b\u4e00\u4e2a\u70b9；\u627e\u4e0d\u5230\u5c31\u8c03\u6574\u9876\u6807，\u76f4\u5230\u8be5\u70b9\u4e5f\u80fd\u5339\u914d\u3002\u6bcf\u4e2a\u5de6\u90e8\u70b9\u6700\u591a\u89e6\u53d1 O(n) \u6b21\u9876\u6807\u8c03\u6574，\u6bcf\u6b21\u8c03\u6574 O(n)，DFS \u672c\u8eab O(n)，\u6574\u4f53 O(n\u00b3)\u3002<\/p>\n

    C++ \u5b9e\u73b0<\/h4>\n

    #include <bits\/stdc++.h>
    \nusing namespace std;<\/p>\n

    const int N = 310;
    \nconst int INF = 1e9;
    \nint n;
    \nint w[N][N];
    \nint lx[N], ly[N];
    \nint match[N]; \/\/ match[y] = x（\u53f3\u90e8\u70b9 y \u5339\u914d\u5230\u7684\u5de6\u90e8\u70b9）
    \nbool visx[N], visy[N];
    \nint slack[N];<\/p>\n

    \/\/ \u4e3a\u5de6\u90e8\u70b9 x \u5728\u76f8\u7b49\u5b50\u56fe\u4e2d\u5bfb\u627e\u589e\u5e7f\u8def
    \nbool dfs(int x) {
    \n visx[x] = true;
    \n for (int y = 0; y < n; y++) {
    \n if (visy[y]) continue; \/\/ \u53f3\u90e8\u70b9\u5df2\u5728\u4ea4\u9519\u6811\u4e2d，\u8df3\u8fc7
    \n int gap = lx[x] + ly[y] – w[x][y]; \/\/ \u4e0e\u76f8\u7b49\u5b50\u56fe\u7684\u8ddd\u79bb
    \n if (gap == 0) { \/\/ \u76f8\u7b49\u8fb9：\u53ef\u8d70
    \n visy[y] = true;
    \n if (match[y] == -1 || dfs(match[y])) {
    \n match[y] = x;
    \n return true;
    \n }
    \n } else { \/\/ \u8bb0\u5f55\u677e\u5f1b\u91cf
    \n slack[y] = min(slack[y], gap);
    \n }
    \n }
    \n return false;
    \n}<\/p>\n

    int km() {
    \n memset(match, -1, sizeof(match));
    \n for (int i = 0; i < n; i++) {
    \n lx[i] = *max_element(w[i], w[i] + n); \/\/ \u5de6\u90e8\u9876\u6807\u53d6\u884c\u6700\u5927\u503c
    \n ly[i] = 0; \/\/ \u53f3\u90e8\u9876\u6807\u521d\u59cb\u4e3a 0
    \n }
    \n for (int cx = 0; cx < n; cx++) { \/\/ \u4f9d\u6b21\u4e3a\u6bcf\u4e2a\u5de6\u90e8\u70b9\u627e\u5339\u914d
    \n fill(slack, slack + n, INF);
    \n while (true) {
    \n memset(visx, 0, sizeof(visx));
    \n memset(visy, 0, sizeof(visy));
    \n if (dfs(cx)) break; \/\/ \u627e\u5230\u589e\u5e7f\u8def，\u5339\u914d\u6210\u529f
    \n int d = INF; \/\/ \u6700\u5c0f\u53ef\u6539\u8fdb\u91cf
    \n for (int y = 0; y < n; y++)
    \n if (!visy[y]) d = min(d, slack[y]);
    \n \/\/ \u8c03\u6574\u9876\u6807：\u4ea4\u9519\u6811\u5185\u5de6\u90e8 -d，\u53f3\u90e8 +d
    \n for (int x = 0; x < n; x++)
    \n if (visx[x]) lx[x] -= d;
    \n for (int y = 0; y < n; y++) {
    \n if (visy[y]) ly[y] += d;
    \n else slack[y] -= d;
    \n }
    \n }
    \n }
    \n int sum = 0;
    \n for (int y = 0; y < n; y++)
    \n if (match[y] != -1) sum += w[match[y]][y];
    \n return sum;
    \n}<\/p>\n

    int main() {
    \n n = 4;
    \n int ex[4][4] = {
    \n {3,5,4,2},
    \n {6,2,8,7},
    \n {4,3,5,1},
    \n {2,6,7,4}
    \n };
    \n for (int i = 0; i < n; i++)
    \n for (int j = 0; j < n; j++)
    \n w[i][j] = ex[i][j];
    \n cout << km() << endl; \/\/ \u8f93\u51fa 23
    \n return 0;
    \n}<\/p>\n

    Python \u5b9e\u73b0<\/h4>\n

    def km_max(w, n):
    \n INF = float('inf')
    \n lx = [max(row) for row in w] # \u5de6\u90e8\u9876\u6807：\u6bcf\u884c\u6700\u5927\u503c
    \n ly = [0] * n # \u53f3\u90e8\u9876\u6807
    \n match = [-1] * n # match[y] = x<\/p>\n

    for cx in range(n): # \u4f9d\u6b21\u4e3a\u6bcf\u4e2a\u5de6\u90e8\u70b9\u627e\u589e\u5e7f\u8def
    \n slack = [INF] * n
    \n while True:
    \n visx = [False] * n
    \n visy = [False] * n<\/p>\n

    def dfs(x):
    \n visx[x] = True
    \n for y in range(n):
    \n if visy[y]:
    \n continue
    \n gap = lx[x] + ly[y] – w[x][y]
    \n if gap == 0: # \u76f8\u7b49\u8fb9
    \n visy[y] = True
    \n if match[y] == -1 or dfs(match[y]):
    \n match[y] = x
    \n return True
    \n else:
    \n slack[y] = min(slack[y], gap)
    \n return False<\/p>\n

    if dfs(cx):
    \n break
    \n d = min(slack[y] for y in range(n) if not visy[y])
    \n for x in range(n):
    \n if visx[x]:
    \n lx[x] -= d
    \n for y in range(n):
    \n if visy[y]:
    \n ly[y] += d
    \n else:
    \n slack[y] -= d<\/p>\n

    return sum(w[match[y]][y] for y in range(n))<\/p>\n

    # \u793a\u4f8b
    \nw = [
    \n [3, 5, 4, 2],
    \n [6, 2, 8, 7],
    \n [4, 3, 5, 1],
    \n [2, 6, 7, 4],
    \n]
    \nprint(km_max(w, 4)) # \u8f93\u51fa 23<\/p>\n

    \u8dd1\u4e0a\u9762\u7684\u4f8b\u5b50，\u4e24\u79cd\u8bed\u8a00\u90fd\u8f93\u51fa 23，\u4e0e\u624b\u7b97\u7684\u6700\u4f18\u65b9\u6848\u4e00\u81f4：\u540c\u5b662\u2192\u9879\u76ee0\u3001\u540c\u5b660\u2192\u9879\u76ee1\u3001\u540c\u5b663\u2192\u9879\u76ee2\u3001\u540c\u5b661\u2192\u9879\u76ee3\u3002<\/p>\n

    \u65f6\u95f4 \/ \u7a7a\u95f4\u590d\u6742\u5ea6<\/h3>\n
      \n
    • \u65f6\u95f4\u590d\u6742\u5ea6：O(n\u00b3)\u3002\u5916\u5c42\u4e3a n \u4e2a\u5de6\u90e8\u70b9，\u6bcf\u4e2a\u70b9\u6700\u591a O(n) \u6b21\u9876\u6807\u8c03\u6574，\u6bcf\u6b21\u8c03\u6574\u4e0e DFS \u5747\u4e3a O(n)\u3002<\/li>\n
    • \u7a7a\u95f4\u590d\u6742\u5ea6：O(n\u00b2)，\u4e3b\u8981\u6765\u81ea\u6743\u91cd\u77e9\u9635 w[n][n] \u4e0e\u82e5\u5e72\u957f\u5ea6\u4e3a n \u7684\u8f85\u52a9\u6570\u7ec4（\u9876\u6807\u3001\u6807\u8bb0\u3001slack）\u3002<\/li>\n<\/ul>\n

      \u6613\u9519\u70b9<\/h3>\n
    • \u9876\u6807\u521d\u59cb\u5316\u9519\u8bef：\u5fc5\u987b lx[i] = max_j w[i][j]，\u800c\u4e0d\u662f\u7b80\u5355\u53d6 0 \u6216\u968f\u610f\u8d4b\u503c，\u5426\u5219\u521d\u59cb\u9876\u6807\u53ef\u80fd\u4e0d\u53ef\u884c（\u5b58\u5728 lx+ly < w \u7684\u8fb9）\u3002<\/li>\n
    • \u76f8\u7b49\u8fb9\u5224\u65ad\u7528 == \u800c\u975e \u2264：\u53ea\u8d70 lx+ly == w \u7684\u300c\u76f8\u7b49\u8fb9\u300d，\u8d70 \u2265 \u7684\u8fb9\u4f1a\u7834\u574f\u76f8\u7b49\u5b50\u56fe\u5b9a\u7406，\u5bfc\u81f4\u7ed3\u679c\u4e0d\u662f\u6700\u5927\u6743\u3002<\/li>\n
    • \u9876\u6807\u8c03\u6574\u53ea\u52a8\u4ea4\u9519\u6811\u5185\u7684\u70b9：lx[x] -= d \u4ec5\u5bf9 visx[x] \u4e3a\u771f\u8005\u3001ly[y] += d \u4ec5\u5bf9 visy[y] \u4e3a\u771f\u8005；\u6811\u5916\u70b9\u52a8\u4e0d\u5f97，\u5426\u5219\u4f1a\u7834\u574f\u5df2\u6709\u7684\u53ef\u884c\u9876\u6807\u6027\u8d28\u3002<\/li>\n
    • d \u5fc5\u987b\u53d6\u6700\u5c0f：d = min(slack[y])（y \u5728\u6811\u5916）\u3002\u53d6\u5927\u4f1a\u8df3\u8fc7\u672c\u5e94\u8fdb\u5165\u7684\u8fb9；\u53d6\u5c0f\u867d\u4ecd\u6b63\u786e\u4f46\u6548\u7387\u4f4e\u3002<\/li>\n
    • slack \u7684\u4f20\u9012\u66f4\u65b0：\u6bcf\u6b21\u9876\u6807 -d \u540e，\u6811\u5916\u70b9\u7684 slack \u8981 -d（\u56e0\u4e3a gap \u540c\u51cf d）\u3002\u82e5\u6bcf\u6b21\u91cd\u65b0\u5168\u91cf\u8ba1\u7b97\u867d\u6b63\u786e\u4f46\u9000\u5316\u4e3a O(n\u2074)，\u5931\u53bb\u4f18\u5316\u610f\u4e49\u3002<\/li>\n
    • \u975e\u65b9\u9635\u8981\u8865\u70b9：\u5de6\u53f3\u70b9\u6570\u4e0d\u7b49\u65f6\u5148\u628a\u5c11\u7684\u4e00\u4fa7\u8865\u865a\u62df\u70b9\u3001\u865a\u8fb9\u6743\u8bbe 0，\u5426\u5219\u300c\u5b8c\u7f8e\u5339\u914d\u300d\u524d\u63d0\u4e0d\u6210\u7acb，\u7b97\u6cd5\u4f1a\u6f0f\u89e3\u3002<\/li>\n

      \u8fdb\u9636<\/h3>\n
        \n
      • \u6700\u5c0f\u6743\u5339\u914d：\u628a\u6240\u6709\u8fb9\u6743\u53d6\u76f8\u53cd\u6570\u8dd1\u6700\u5927\u6743 KM，\u7ed3\u679c\u518d\u53d6\u53cd\u5373\u53ef\u3002<\/li>\n
      • \u975e\u65b9\u9635 \/ \u6700\u5927\u6743\u5339\u914d（\u4e0d\u4e00\u5b9a\u5b8c\u5907）：\u628a\u7f3a\u5931\u7684\u8fb9\u6743\u8865 0 \u540e\u6c42\u5b8c\u7f8e\u5339\u914d；\u82e5\u53ea\u6c42\u300c\u8fb9\u6570\u6700\u591a\u4e14\u6743\u6700\u5927\u300d，\u53ef\u8865\u8db3\u591f\u5c0f\u7684\u8d1f\u6743\u865a\u62df\u8fb9\u3002<\/li>\n
      • \u4e0e\u8d39\u7528\u6d41\u7684\u5173\u7cfb：\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u5927\u6743\u5339\u914d\u7b49\u4ef7\u4e8e\u4e8c\u5206\u56fe\u6700\u5c0f\u8d39\u7528\u6700\u5927\u6d41（\u8fb9\u6743\u53d6\u8d1f），KM \u662f\u4e13\u95e8\u9488\u5bf9\u300c\u5b8c\u7f8e\u5339\u914d\u300d\u8fd9\u4e00\u7279\u6b8a\u7ed3\u6784\u7684 O(n\u00b3) \u9ad8\u6548\u7b97\u6cd5；\u89c4\u6a21\u5f88\u5927\u6216\u5e26\u5bb9\u91cf\u9650\u5236\u65f6\u6539\u7528\u8d39\u7528\u6d41\u66f4\u901a\u7528\u3002<\/li>\n
      • \u5308\u7259\u5229\u7b97\u6cd5\u662f KM \u7684\u7279\u4f8b：\u628a\u6240\u6709\u8fb9\u6743\u90fd\u89c6\u4e3a 1，KM \u9000\u5316\u4e3a\u666e\u901a\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u3002<\/li>\n
      • \u7ecf\u5178\u6a21\u677f\u9898：\u6d1b\u8c37 P6577\u3010\u6a21\u677f\u3011\u4e8c\u5206\u56fe\u6700\u5927\u6743\u5b8c\u7f8e\u5339\u914d，\u53ef\u62ff\u6765\u7ec3\u624b\u9a8c\u8bc1\u81ea\u5df1\u7684\u677f\u5b50\u3002<\/li>\n<\/ul>\n

        \u5c0f\u7ed3\u4e0e\u4e92\u52a8<\/h3>\n

        KM \u7b97\u6cd5\u7684\u7075\u9b42\u5728\u4e8e\u300c\u7528\u9876\u6807\u628a\u96be\u89e3\u7684\u6700\u5927\u6743\u5339\u914d，\u7f29\u5230\u76f8\u7b49\u5b50\u56fe\u91cc\u7528\u719f\u6089\u7684\u589e\u5e7f\u8def\u53bb\u89e3\u300d\u3002\u8bb0\u4f4f\u4e09\u6b65\u66f2：\u9876\u6807\u521d\u59cb\u5316 \u2192 \u76f8\u7b49\u5b50\u56fe\u627e\u589e\u5e7f \u2192 \u627e\u4e0d\u5230\u5c31\u8c03\u9876\u6807，\u518d\u914d\u5408 slack \u628a\u590d\u6742\u5ea6\u538b\u5230 O(n\u00b3)，\u8fd9\u9053\u9898\u5c31\u7a33\u4e86\u3002<\/p>\n

        👉 \u4f60\u7b2c\u4e00\u6b21\u5b66 KM \u65f6，\u6700\u5bb9\u6613\u5361\u5728\u54ea\u4e00\u6b65？\u662f\u9876\u6807\u8c03\u6574\u7684\u65b9\u5411，\u8fd8\u662f\u76f8\u7b49\u5b50\u56fe\u7684\u5b9a\u7406\u8bc1\u660e？\u6b22\u8fce\u5728\u8bc4\u8bba\u533a\u804a\u804a，\u4e5f\u6b22\u8fce\u628a\u8fd9\u7bc7\u5206\u4eab\u7ed9\u6b63\u5728\u5907\u8d5b\u7684\u540c\u5b66～<\/p>\n

        \"\"<\/p>\n

        \n

        📚 \u514d\u8d39\u5c11\u513f\u7f16\u7a0b\u8d44\u6599（\u5938\u514b\u7f51\u76d8\u9886\u53d6）<\/h3>\n

        \u4ee5\u4e0b\u8d44\u6599\u6765\u81ea\u5938\u514b\u7f51\u76d8\u5206\u4eab，\u70b9\u51fb\u94fe\u63a5\u53ef\u76f4\u63a5\u4fdd\u5b58；\u82e5\u9700\u5728 App \u5185\u6253\u5f00，\u4e5f\u53ef\u590d\u5236\u4e0b\u65b9\u660e\u6587\u94fe\u63a5：<\/p>\n

      • \u5168\u56fd\u9752\u5c11\u5e74\u4fe1\u606f\u7d20\u517b\u5927\u8d5b\u590d\u8d5b\u96c6\u8bad\u9898\u76eePython&C++.docx https:\/\/pan.quark.cn\/s\/93995d3cb150<\/li>\n
      • 2024\u4fe1\u606f\u7d20\u517b-\u667a\u80fd\u7b97\u6cd5\u5e94\u7528\u6311\u6218\u8d5b-\u590d\u8d5b\u521d\u4e2d\u7ec4\u9898\u76ee7\u67087\u65e5.pdf https:\/\/pan.quark.cn\/s\/da97b5dbf75d<\/li>\n
      • Python\u80cc\u8bb0\u624b\u518c.pdf https:\/\/pan.quark.cn\/s\/7568ae9ca92b<\/li>\n
      • Python\u8bfe\u7a0b https:\/\/pan.quark.cn\/s\/a94bf02d00c6<\/li>\n
      • 2024\u4fe1\u606f\u7d20\u517b\u5927\u8d5b\u56fe\u5f62\u5316\u590d\u8d5b\u96c6\u8bad\u9898\u7b54\u68483-9 https:\/\/pan.quark.cn\/s\/6ccab7ec3cbc<\/li>\n
      • 2025\u5e7403\u6708\u4efd\u7535\u5b50\u5b66\u4f1a\u8003\u7ea7\u771f\u9898 https:\/\/pan.quark.cn\/s\/4403c4228912<\/li>\n
      • 2025\u5168\u56fd\u9752\u5c11\u5e74\u4fe1\u606f\u7d20\u517b\u5927\u8d5b\u8d5b\u9879\u8bf4\u660e https:\/\/pan.quark.cn\/s\/d9d0df4a9f29<\/li>\n
      • \u9752\u5c11\u513f\u4fe1\u606f\u7d20\u517b\u5927\u8d5b\u7f16\u7a0b\u8d44\u6599 https:\/\/pan.quark.cn\/s\/4ab6bd83be8a<\/li>\n

        \u8d44\u6599\u6301\u7eed\u66f4\u65b0，\u5173\u6ce8\u83b7\u53d6\u6700\u65b0\u5206\u4eab\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u5f15\u8a00
        \n\u5728\u4fe1\u5965\u65b0\u8d5b\u5b63\u7684\u56fe\u8bba\u5907\u8003\u4e2d，\u4e8c\u5206\u56fe\u5339\u914d\u662f\u4e00\u4e2a\u7ed5\u4e0d\u5f00\u7684\u9ad8\u9891\u8003\u70b9\u3002\u524d\u9762\u6211\u4eec\u804a\u8fc7\u300c\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u300d（\u5308\u7259\u5229\u7b97\u6cd5）\u6c42\u7684\u662f\u5339\u914d\u8fb9\u6570\u6700\u591a；\u800c\u771f\u5b9e\u7ade\u8d5b\u91cc\u66f4\u5e38\u89c1\u7684\u662f\u2014\u2014\u6bcf\u5bf9\u914d\u5bf9\u90fd\u6709\u4e00\u4e2a\u6743\u91cd，\u8981\u6c42\u9009\u51fa\u7684\u914d\u5bf9\u603b\u6743\u91cd\u6700\u5927\u3002\u6bd4\u5982\u79d1\u6280\u8282\u4e0a\u8ba9\u540c\u5b66\u548c\u5c55\u4f4d\u4e00\u4e00\u642d\u6863，\u8c01\u548c\u54ea\u4e2a\u9879\u76ee\u914d\u5408\u6700\u9ed8\u5951，\u5c31\u662f\u5178\u578b\u7684\u300c\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u4f18\u5339\u914d\u300d\u95ee\u9898\u3002
        \n\u89e3\u51b3\u5b83\u7684\u7b97\u6cd5\u53eb KM \u7b97\u6cd5（Kuhn\u2013Munkres&#xff<\/p>\n","protected":false},"author":2,"featured_media":108045,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[12304,55,81,4651,427],"topic":[],"class_list":["post-108047","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-bfs","tag-c","tag-python","tag-4651","tag-427"],"yoast_head":"\nKM \u7b97\u6cd5\u89e3\u6790\uff1a\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u4f18\u5339\u914d\u4e0e\u9876\u6807\u8c03\u6574 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/108047.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KM \u7b97\u6cd5\u89e3\u6790\uff1a\u5e26\u6743\u4e8c\u5206\u56fe\u6700\u4f18\u5339\u914d\u4e0e\u9876\u6807\u8c03\u6574 - 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