{"id":117672,"date":"2026-10-25T05:26:39","date_gmt":"2026-10-24T21:26:39","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/117672.html"},"modified":"2026-10-25T05:26:39","modified_gmt":"2026-10-24T21:26:39","slug":"c-%e7%ae%97%e6%b3%95%e4%ba%94","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/117672.html","title":{"rendered":"C++ \u7b97\u6cd5(\u4e94)"},"content":{"rendered":"

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

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🏠\u6211\u7684\u535a\u5ba2\u4e3b\u9875🏠<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u6570\u636e\u7ed3\u6784\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u7b97\u6cd5\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300aC++\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300aMySQL\u6570\u636e\u5e93\u300b\u0f12<\/font><\/p>\n

\u0f12\u4e13\u680f\u76ee\u5f55：\u300a\u524d\u7aef\u5f00\u53d1\u300b\u0f12<\/font><\/p>\n

\u0f12\u5176\u5b83\u6709\u8da3\u7684\u8ba1\u7b97\u673a\u77e5\u8bc6\u0f12<\/font><\/p>\n

\u0f3a\u4e16\u4e0a\u672c\u6ca1\u6709\u8def，\u8d70\u7684\u4eba\u591a\u4e86\u81ea\u7136\u5c31\u6709\u4e86\u0f3b<\/font><\/p>\n

\n

\u672c\u7bc7\u6587\u7ae0\u8bb2\u8ff0\u7684\u662f\u6709\u5173vector\u7684\u9898,\u5e0c\u671b\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9<\/p>\n

\u9898\u76ee\u94fe\u63a5： \u6768\u8f89\u4e09\u89d2 \u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u5b57i \u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570ii <\/p>\n

\n

\u6587\u7ae0\u76ee\u5f55<\/h4>\n
    \n
  • 1.\u6768\u8f89\u4e09\u89d2<\/li>\n
  • 2.\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u5b57i<\/li>\n
  • 3.\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570ii<\/li>\n
  • 4.\u62d3\u5c55\u6709\u5174\u8da3\u505a\u4e00\u4e0b<\/li>\n<\/ul>\n
    \n

    1.\u6768\u8f89\u4e09\u89d2<\/h2>\n

    \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u6768\u8f89\u4e09\u89d2\u662f\u4ece\u7b2c\u4e09\u884c\u5f00\u59cb\u5230\u6307\u5b9a\u884c\u9664\u53bb\u7b2c\u4e00\u4e2a\u5143\u7d20\u548c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5176\u5b83\u6570\u636e\u7684\u503c\u90fd\u4e3a\u8be5\u4f4d\u7f6e\u4e0a\u4e00\u4e2a\u5143\u7d20\u548c\u8be5\u4f4d\u7f6e\u4e0a\u4e00\u4e2a\u5143\u7d20\u7684\u524d\u4e00\u4e2a\u5143\u7d20\u4e4b\u548c,\u8fd9\u91cc\u6211\u4eec\u7528\u7684\u662fC++\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u4e2avector<vector>(\u5c31\u662f\u6570\u7ec4\u91cc\u7684\u5143\u7d20\u662f\u6574\u5f62\u6570\u7ec4)\u6211\u4eec\u6839\u636e\u6768\u8f89\u4e09\u89d2\u5148\u5c06\u6bcf\u4e00\u884c\u6240\u5177\u6709\u7684\u4e2a\u6570(\u5b9a\u4e49\u7684\u8be5\u5bf9\u8c61\u6bcf\u4e2a\u5143\u7d20\u90fd\u4e3a\u4e00\u4e2a\u6574\u5f62\u6570\u7ec4（\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u884c））)\u5b9a\u4e49\u4e3a1\u5728\u4e0d\u7528\u8003\u8651\u4e0b\u6807\u56e0\u4e3a\u5b83\u53ea\u8981\u6c42\u6bcf\u884c\u7b26\u5408\u5b83\u6240\u6709\u7684\u4e2a\u6570,\u7136\u540e\u4ece\u7b2c\u4e09\u884c\u5f00\u59cb(\u6570\u7ec4\u7684\u4e0b\u68072)）\u6bcf\u4e00\u884c\u9664\u4e86\u7b2c\u4e00\u4e2a\u5143\u7d20\u548c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5b83\u7684\u503c\u90fd\u4e3a\u8be5\u4e0b\u6807\u6b63\u5bf9\u4e0a\u4e00\u884c\u7684\u5143\u7d20\u548c\u8be5\u5143\u7d20\u524d\u9762\u7684\u5143\u7d20\u548c<\/p>\n

    class Solution {<\/span><\/p>\n

    public:<\/span><\/p>\n

    vector<<\/span>vector<<\/span>int<\/span>>><\/span> generate<\/span>(<\/span>int<\/span> numRows)<\/span> {<\/span><\/p>\n

    vector<<\/span>vector<<\/span>int<\/span>>><\/span> v;<\/span><\/p>\n

    \/\/ int num;<\/span><\/p>\n

    \/\/ cin >> num;\/\/\u6ca1\u770b\u9898\u76ee\u7ed9\u7684\u53c2\u6570\u5e94\u8be5\u7528numRows(\u5b83\u5df2\u7ecf\u7ed9\u4f60\u4e86\u4e0d\u7528\u7ba1)<\/span><\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> numRows;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    v.<\/span>push_back<\/span>(<\/span>vector<<\/span>int<\/span>><\/span>(<\/span>i,<\/span>1<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

    }<\/span><\/p>\n

    for<\/span>(<\/span>int<\/span> j =<\/span> 2<\/span>;<\/span> j <<\/span> numRows;<\/span> j++<\/span>)<\/span><\/p>\n

    \/\/ for(int j = 2; j < v.size(); j++)\/\/\u8fd9\u91cc\u7684v.size()\u53ef\u4ee5\u6539\u7528numSize\u80fd\u7528\u53d8\u91cf\u5c31\u4e0d\u7528\u51fd\u6570<\/span><\/p>\n

    {<\/span><\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span>i <<\/span> v[<\/span>j]<\/span>.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> 1<\/span>;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    v[<\/span>j]<\/span>[<\/span>i]<\/span> =<\/span> v[<\/span>j –<\/span> 1<\/span>]<\/span>[<\/span>i –<\/span>1<\/span>]<\/span> +<\/span> v[<\/span>j –<\/span> 1<\/span>]<\/span>[<\/span>i]<\/span>;<\/span><\/p>\n

    \/\/ v[j][i] = v[j – 1][i] + v[j – 1][i + 1];\u8fd9\u4e2a\u9519\u4e86\u56e0\u8be5\u662f\u4e0a\u4e00\u884c\u5de6\u4e0a\u52a0\u4e0a\u4e0a\u4e00\u884c\u6b63\u4e0a<\/span><\/p>\n

    }<\/span><\/p>\n

    \/\/\u6700\u540e\u8bb0\u5f97\u8fd4\u56dev\u51fd\u6570\u8fd4\u56de\u7c7b\u578b\u662fvector<vector<int>><\/span><\/p>\n

    }<\/span><\/p>\n

    return<\/span> v;<\/span><\/p>\n

    }<\/span><\/p>\n

    }<\/span>;<\/span><\/p>\n

    vector<vector<int>> v; \u8fd9\u91cc\u6211\u4eec\u5148\u5b9a\u4e49\u4e00\u4e2a\u6bcf\u4e2a\u5143\u7d20\u90fd\u4e3a\u4e00\u4e2a\u6574\u5f62\u6570\u7ec4\u7684\u6570\u7ec4<\/p>\n

    \u7136\u540e\u6211\u4eec\u5c06\u6bcf\u4e2a\u5143\u7d20\u62e5\u6709\u7684\u5143\u7d20\u4e2a\u6570\u5b9a\u4e49\u597d（\u7b2c\u4e00\u4e2a\u5143\u7d20\u6307\u7684\u662f\u7b2c\u4e00\u884c\u7b2c\u4e8c\u4e2a\u5143\u7d20\u7b2c\u4e8c\u884c\u4ee5\u6b64\u7c7b\u63a8）<\/p>\n

    for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> numRows;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    v.<\/span>push_back<\/span>(<\/span>vector<<\/span>int<\/span>><\/span>(<\/span>i,<\/span> 1<\/span>)<\/span>)<\/span>;<\/span>
    \n }<\/span><\/p>\n

    \u8fd9\u91cc\u4ece\u4e00\u5f00\u59cbi \u4e3a1\u56e0\u4e3a\u6211\u4eec\u7684vector\u7c7b\u578b\u7684\u5bf9\u8c61\u8981push_back\u4e00\u4e2a\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u4e14\u5143\u7d20\u90fd\u4e3a1\u7684\u7528vector<int(i , 1)>\u8fd9\u91cc\u8bf4\u660e\u4e00\u70b9\u770b\u8d77\u6765\u4f20\u7684\u662f\u4e34\u65f6\u5bf9\u8c61\u4f46\u662f\u4e0d\u662f，vector<int(i , 1)>\u5728\u51fd\u6570\u91cc\u9762\u4f5c\u4e3a\u53c2\u6570\u5c31\u662f\u4e00\u4e2a\u666e\u901a\u5bf9\u8c61\u4e0d\u662f\u4e34\u65f6\u5bf9\u8c61\u751f\u547d\u5468\u671f\u957f<\/p>\n

    \u7136\u540e\u4e00\u4e2a\u4e2a\u63d2\u5165\u5faa\u73af\u653e\u5165\u5f62\u6210\u7b26\u5408\u6768\u8f89\u4e09\u89d2\u7684\u5f62\u72b6<\/p>\n

    for<\/span> (<\/span>int<\/span> j =<\/span> 2<\/span>;<\/span> j <<\/span> numRows;<\/span> j++<\/span>)<\/span><\/p>\n

    \/\/ for(int j = 2; j < v.size();<\/span>
    \n \/\/ j++)\/\/\u8fd9\u91cc\u7684v.size()\u53ef\u4ee5\u6539\u7528numSize\u80fd\u7528\u53d8\u91cf\u5c31\u4e0d\u7528\u51fd\u6570<\/span><\/p>\n

    {<\/span><\/p>\n

    for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <<\/span> v[<\/span>j]<\/span>.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> 1<\/span>;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    v[<\/span>j]<\/span>[<\/span>i]<\/span> =<\/span> v[<\/span>j –<\/span> 1<\/span>]<\/span>[<\/span>i –<\/span> 1<\/span>]<\/span> +<\/span> v[<\/span>j –<\/span> 1<\/span>]<\/span>[<\/span>i]<\/span>;<\/span><\/p>\n

    \/\/ v[j][i] = v[j – 1][i] + v[j – 1][i +<\/span>
    \n \/\/ 1];\u8fd9\u4e2a\u9519\u4e86\u56e0\u8be5\u662f\u4e0a\u4e00\u884c\u5de6\u4e0a\u52a0\u4e0a\u4e0a\u4e00\u884c\u6b63\u4e0a<\/span>
    \n }<\/span><\/p>\n

    \/\/ \u6700\u540e\u8bb0\u5f97\u8fd4\u56dev\u51fd\u6570\u8fd4\u56de\u7c7b\u578b\u662fvector<vector<int>><\/span>
    \n }<\/span><\/p>\n

    \u63a5\u7740\u6211\u4eec\u4ece\u7b2c\u4e09\u884c\u5f00\u59cb(\u4e0b\u6807\u76842)\u5f00\u59cb\u5c06\u9664\u4e86\u7b2c\u4e00\u4e2a\u5143\u7d20\u548c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5176\u5b83\u5143\u7d20\u90fd\u4e3a\u5b83\u81ea\u8eab\u4e0b\u6807\u6b63\u4e0a\u65b9\u7684\u4e0b\u6807\u6240\u6307\u5411\u7684\u5143\u7d20\u4ee5\u53ca\u8be5\u5143\u7d20\u524d\u4e00\u4e2a\u4e0b\u6807\u6240\u6307\u5411\u7684\u5143\u7d20\u4e4b\u548c \u6211\u4eec\u5229\u7528\u4e24\u4e2afor\u5faa\u73af\u89e3\u51b3\u7b2c\u4e00\u4e2a j= < Rownums\u662f\u56e0\u4e3aRownums – 1\u5c31\u662f\u6700\u540e\u4e00\u884c \u7b2c\u4e8c\u4e2a\u5faa\u73af i = 1 \u5230 v[j].size() – 2 \u662f\u56e0\u4e3a\u7b2c\u4e00\u4e2a\u5143\u7d20\u548c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u4e0d\u7528\u6539(\u8be5\u884c\u4e0b\u6807\u4e3a0\u7684\u4f4d\u7f6e\u6307\u5411\u7684\u5143\u7d20\u4e3a1\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u4e0b\u6807\u4e3a v[j].size() – 1 \u6307\u5411\u7684\u5143\u7d20\u4e3a 1)<\/p>\n

    return v;<\/p>\n

    \u6700\u540e\u8fd4\u56de\u5b9a\u4e49\u7684\u5bf9\u8c61v\u5373\u4f7f\u6211\u4eec\u6240\u8bbe\u8ba1\u7684\u6768\u8f89\u4e09\u89d2<\/p>\n

    \n

    2.\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u5b57i<\/h2>\n

    \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u9898\u76ee\u8981\u6c42\u7ed9\u4f60\u4e00\u4e2a\u6574\u5f62\u6570\u7ec4(vector)\u6570\u7ec4\u91cc\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u53ea\u6709\u4e00\u4e2a\u5176\u5b83\u6570\u636e\u76f8\u540c\u7684\u6570\u636e\u90fd\u662f\u6210\u5bf9\u5b58\u5728\u7684<\/p>\n

    \u8fd9\u91cc\u6211\u4eec\u7528^\u6309\u4f4d\u5f02\u6216\u5b9a\u4e49\u4e00\u4e2a\u53d8\u91cf\u5f00\u59cb\u4e3a0\u5c06\u6574\u5f62\u6570\u7ec4\u7684\u6570\u636e\u4e00\u4e2a\u4e0e\u8fd9\u4e2a\u6570\u636e\u6309\u4f4d\u5f02\u6216\u5c31\u53ef\u4ee5\u5f97\u5230\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u5b57<\/p>\n

    \u539f\u56e0\u5f53\u6574\u5f62\u6570\u7ec4\u53ea\u6709\u4e00\u4e2a\u51fa\u73b0\u4e00\u6b21\u5176\u5b83\u90fd\u53ea\u51fa\u73b0\u4e24\u6b21\u7684\u65f6\u5019\u7528\u5c06\u5b83\u4eec\u4e92\u76f8\u6309\u4f4d\u5f02\u6216\u5f97\u5230\u7684\u6700\u7ec8\u7ed3\u679c\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u90a3\u4e2a\u6570\u636e<\/p>\n

    \u6309\u4f4dXX\u7684\u6211\u4eec\u4e00\u822c\u90fd\u7528\u5728\u670932\u4f4d\u7684\u6574\u578b\u4e0a<\/p>\n

    \u6309\u4f4d\u5f02\u6216： \u5047\u5982\u6709\u4e24\u4e2a\u6574\u6570 \u5c06\u7b2c\u4e00\u4e2a\u6574\u657032\u4f4d\u4e2d(\u4ece\u53f3\u5f80\u5de6\u4e0b\u68070\u5230\u4e0b\u680731)\u6bcf\u4e00\u4f4d\u4e8e\u7b2c\u4e8c\u4e2a\u6574\u6570\u5b83\u4eec\u6240\u5bf9\u5e94\u7684\u4e0b\u6807\u8fdb\u884c\u5339\u914d\u76f8\u540c\u7684\u4e3a0\u4e0d\u540c\u4e3a1\u6240\u4ee5\u5982\u679c\u4e24\u4e2a\u6574\u6570\u76f8\u7b49\u6240\u4ee5\u5b83\u4eec\u768432\u4f4d\u4e0a\u7684 \u6570\u5b57\u76f8\u7b49\u6240\u4ee5\u8fd4\u56de\u7684\u662f32\u4e3a\u4e0a\u90fd\u4e3a0\u7684\u6574\u6570(\u8fd9\u4e2a\u6574\u6570\u4e3a0) ，0\u6309\u4f4d\u5f02\u6216\u4efb\u4f55\u6570\u90fd\u4e3a\u6211\u4eec\u7528\u6309\u4f4d\u5f02\u62160\u7684\u90a3\u4e2a\u6570<\/p>\n

    \u6240\u4ee5\u6211\u4eec\u5c06\u4e00\u4e2a\u6574\u5f62\u6570\u7ec4（\u8be5\u6570\u7ec4\u53ea\u6709\u4e00\u4e2a\u51fa\u73b0\u4e00\u6b21\u5176\u5b83\u6570\u636e\u90fd\u51fa\u73b0\u4e3a\u5076\u6570）\u6309\u4f4d\u5f02\u6216\u5f97\u5230\u7684\u5c31\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u90a3\u4e2a\u6570\u5b57<\/p>\n

    class Solution {<\/span><\/p>\n

    public:<\/span><\/p>\n

    int<\/span> singleNumber<\/span>(<\/span>vector<<\/span>int<\/span>><\/span>&<\/span> nums)<\/span> {<\/span><\/p>\n

    int<\/span> result =<\/span> 0<\/span>;<\/span><\/p>\n

    \/\/\u5229\u7528\u8303\u56f4for\u904d\u5386\u4ee5\u53ca\u5f02\u6216\u6c42\u51fa\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570（\u4e14\u53ea\u6709\u4e00\u4e2a\u6570\u51fa\u73b0\u4e00\u6b21）\u524d\u63d0\u662f\u5176\u5b83\u6570\u636e\u7684\u4e2a\u6570\u90fd\u662f\u5076\u6570<\/span><\/p>\n

    for<\/span>(<\/span>auto<\/span> e:<\/span> nums)<\/span><\/p>\n

    {<\/span><\/p>\n

    result ^=<\/span> e;<\/span><\/p>\n

    }<\/span><\/p>\n

    return<\/span> result;<\/span>\/\/0\u5f02\u6216\u4efb\u4f55\u6570\u90fd\u662f\u90a3\u4e2a\u6570（\u4e0e0\u5f02\u6216\u7684\u6570）<\/span><\/p>\n

    }<\/span><\/p>\n

    }<\/span>;<\/span><\/p>\n

    int result = 0; \u9996\u5148\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2aint\u7c7b\u578b\u7684result\u4e3a0\u56e0\u4e3a0\u6309\u4f4d\u5f02\u6216\u4efb\u4f55\u6574\u6570\u90fd\u4e3a\u8be5\u6570<\/p>\n

    \u7136\u540e\u5229\u7528\u8303\u56f4for\u904d\u5386nums\u5bf9\u8c61(\u6574\u5f62\u6570\u7ec4)\u5c06\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u90fd\u4e8eresult\u6309\u4f4d\u5f02\u6216\u6700\u540e\u8fd4\u56de\u7684\u5c31\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e<\/p>\n

    \n

    3.\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570ii<\/h2>\n

    \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \u8fd9\u91cc\u8981\u6c42\u662f\u6709\u4e00\u4e2a\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u5176\u5b83\u7684\u6570\u636e\u90fd\u51fa\u73b0\u4e09\u6b21 \u4e0a\u4e00\u4e2a\u9898\u662f\u5176\u5b83\u7684\u6570\u636e\u90fd\u51fa\u73b0\u4e8c\u6b21\u8fd9\u91cc\u4e0d\u80fd\u7528\u6309\u4f4d\u5f02\u6216\u56e0\u4e3a\u6309\u4f4d\u5f02\u6216\u53ea\u80fd\u62b5\u6d88\u51fa\u73b0\u6b21\u6570\u4e3a\u5076\u6570\u7684 \u6211\u4eec\u8fd9\u91cc\u6709\u4e00\u4e2a\u901a\u6cd5\u6709\u4e00\u4e2a\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u5176\u5b83\u7684\u6570\u636e\u90fd\u51fa\u73b0k\u6b21(\u5176\u5b83\u53ea\u51fa\u73b0\u4e24\u6b21\u4e5f\u53ef\u4ee5\u7528\u53ea\u662f\u7528for\u5faa\u73af\u6309\u4f4d\u5f02\u6216\u4ee3\u7801\u5c11)<\/p>\n

    \u8fd9\u91cc\u8bb2\u4e00\u4e0b\u6309\u4f4d\u4e0e\u548c\u6309\u4f4d\u6216<\/p>\n

    \u6211\u4eec\u8fd9\u91cc\u8ba8\u8bba\u768432\u4f4d\u6307\u7684\u662f2\u8fdb\u5236\u768432\u4f4d &(\u6309\u4f4d\u4e0e) \u540c\u4e3a1\u624d\u4e3a1\u5426\u5219\u4e3a0 |(\u6309\u4f4d\u6216) \u67091\u5c31\u4e3a1\u5426\u5219\u4e3a0<\/p>\n

    \u89e3\u91ca\u4e00\u4e0b int num; num >> i(i\u4e3a\u6574\u578b)\u662f\u4ec0\u4e48\u610f\u601d \u6211\u4eec\u77e5\u9053num\u4e3a\u6574\u5f62 \u5c06\u5b83 >> i\u7684\u610f\u601d\u662f\u5c06num\u768432\u4f4d\u6574\u4f53\u5f80\u540e\u79fb\u52a8i\u4e2a\u4f4d\u7f6e32\u524d\u9762\u7684\u7684\u4f4d\u7f6e\u88650 num << i\u7684\u610f\u601d\u662f\u5c06num\u768432\u4f4d\u6574\u4f53\u5f80\u524d\u79fb\u52a8i\u4e2a\u4f4d\u7f6e32\u540e\u9762\u7684\u7684\u4f4d\u7f6e\u88650<\/p>\n

    \/\/\u8fd9\u79cd\u9898\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u4e3a\u4e00\u4e2a\u5176\u5b83\u6570\u636e\u90fd\u4e3a\u4e3ak\u4e2a\u7684\u90fd\u53ef\u4ee5\u7528\u6309\u4f4d\u7edf\u8ba1<\/span><\/p>\n

    \/\/\u4e4b\u524d\u90a3\u4e2a\u5176\u5b83\u4e3a2\u4e2a\u7684\u53ef\u4ee5\u7528\u6309\u4f4d\u5f02\u6216\u7b80\u5316\u4ee3\u7801<\/span><\/p>\n

    class Solution {<\/span><\/p>\n

    public:<\/span><\/p>\n

    int<\/span> singleNumber<\/span>(<\/span>vector<<\/span>int<\/span>><\/span>&<\/span> nums)<\/span> {<\/span><\/p>\n

    int<\/span> result =<\/span> 0<\/span>;<\/span>\/\/\u7559\u7740\u653e\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e<\/span><\/p>\n

    \/\/\u6574\u6570\u670932\u4f4d（\u7b2c32\u4f4d\u662f\u6b63\u8d1f\u503c\u5929\u7136\u7b26\u5408\u6b63\u8d1f\u503c\u6574\u6570）\u6211\u4eec\u5c0632\u4f4d\u904d\u5386\u5c06\u67d0\u4f4d\u4e0a\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u503c\u4fdd\u7559（\u5c06k\u4e2a\u7684% k\u53bb\u9664）\u8fd4\u56de\u5c31\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u5b57(32\u4f4d\u4ece\u53f3\u5230\u5de6\u4e0b\u6807\u662f\u4ece0\u5f00\u59cb\u6240\u4ee5\u6700\u540e\u4e00\u4e2a\u4e0b\u6807\u4e3a31)<\/span><\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> 32<\/span>;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    int<\/span> count =<\/span> 0<\/span>;<\/span>\/\/\u7edf\u8ba1\u6570\u7ec4\u4e2d\u6240\u6709\u6570\u636e\u91cc\u7684\u7b2ci\u4f4d\u7684\u548c\u6700\u540e\u5c06\u5176% k\u82e5\u662f\u6709\u6570\u636e(1)\u8bf4\u660e\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u5728\u8be5\u4f4d\u67091\u653e\u5165result\u91cc\u904d\u538632\u4f4d\u5c0632\u4f4d\u91cc\u5b58\u7740\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u7684\u4f4d\u4e0a\u76841\u5168\u653e\u5165result\u4e2d\u6240\u5f97\u7684\u5c31\u662f\u8be5\u6570\u7ec4\u4e2d\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e（\u5229\u7528\u6309\u4f4d\u4e0e\u548c\u6309\u4f4d\u6216\u4ee5\u53ca>> << \u5c06\u4f4d\u6570\u79fb\u52a8\u5373\u53ef\u5b9e\u73b0）<\/span><\/p>\n

    \/\/\u7528\u8303\u56f4for\u904d\u5386\u6570\u7ec4\u5c06\u8be5\u4f4d\u4e0a\u7684\u6570\u636e\u52a0\u8d77\u6765<\/span><\/p>\n

    for<\/span>(<\/span>auto<\/span> num :<\/span> nums)<\/span><\/p>\n

    {<\/span><\/p>\n

    count +=<\/span> (<\/span>num >><\/span> i)<\/span> &<\/span> 1<\/span>;<\/span>\/\/\u6309\u4f4d\u4e0e(&)\u4e24\u4e2a\u6570\u636e\u67d0\u4f4d\u4e0a\u90fd\u4e3a1\u624d\u4e3a1\u5426\u5219\u5168\u4e3a0\u5229\u7528\u8fd9\u4e2a\u53ea\u7559\u4e0b\u8be5\u4f4d\u7684\u6570\u636e（\u53ef\u80fd\u4e3a0\u4e5f\u53ef\u80fd\u4e3a1）\u5176\u4f59\u4f4d\u4e0a\u90fd\u4e3a0（num >> i \u7684\u610f\u601d\u662f\u5c06\u6570\u636e\u768432\u4f4d\u6574\u4f53\u5411\u53f3\u79fb\u52a8i\u4f4d\u5229\u7528\u8fd9\u4e2a\u6211\u4eec\u53ef\u4ee5\u904d\u5386\u6240\u6709\u6570\u636e\u4e2d\u8be5\u4f4d\u7684\u503c(\u8fd9\u4e2a\u662f\u4f4d\u79fb\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\u5927\u4e8e\u6309\u4f4d\u4e0e\u548c\u6309\u4f4d\u6216)）<\/span><\/p>\n

    \/\/\u5224\u65ad\u8be5\u4f4d\u4e0a\u662f\u5426\u53ef\u4ee5\u4f59k(\u6570\u636e\u76f8\u540c\u7684\u4e2a\u6570)\u4e0d\u4e3a0\u8bf4\u660e\u8be5\u4f4d\u4e0a\u6709\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u5728\u8be5\u4f4d\u4e0a\u7684\u6570\u636e\u5c06\u5b83\u79fb\u5230result<\/span><\/p>\n

    \/\/\u5224\u65adcount\u662f\u5426\u53ef\u4ee5 % 3\u540e\u6709\u4f59\u6570\u5728count\u52a0\u5b8c\u5728\u5224\u65ad<\/span><\/p>\n

    }<\/span><\/p>\n

    if<\/span>(<\/span>count %<\/span> 3<\/span> !=<\/span> 0<\/span>)<\/span><\/p>\n

    result |=<\/span> 1<\/span> <<<\/span> i;<\/span>\/\/(x << i\u610f\u601d\u662f\u5c06\u67d0\u6570\u636e\u5411\u5de6\u79fb\u52a8i\u4f4d\u8fd9\u91cc\u76ee\u7684\u662f\u5c06\u67d0\u4f4d\u4e0a\u7684\u53ea\u6709\u4e00\u4e2a\u6570\u7684\u6570\u636e\u5728\u6539\u4f4d\u4e0a\u76841\u653e\u5728result\u4e0a（\u8fd9\u4e24\u4e2a\u4f4d\u79fb\u8fd0\u7b97\u7b26\u5b9e\u9645\u4e0a\u662f\u5c06\u8be5\u6570\u636e\u6539\u53d8）)（\u6309\u4f4d\u6216\u610f\u601d\u662f\u67091\u5c31\u4e3a1\u6ca1\u5c31\u4e3a0\u5c06\u4f4d\u79fb\u540e\u76841\u6240\u5f62\u6210\u7684\u6570\u636e（\u8be5\u6570\u636e\u5c31\u5728I\u4f4d\u67091\u5176\u4f59\u90fd\u4e3a0）\u6309\u4f4d\u4e0eresult\u91cc\u56e0\u4e3a\u4e4b\u524d\u7684\u6570\u636e\u4f4d\u6570\u4e0a\u6709\u4e00\u4e5f\u67090\u6709\u4e00\u7684\u8fd8\u662f1\u4e3a0\u7684\u4f4d\u4e0e\u53f3\u8fb9\u6570\u636e\u540c\u4f4d\u4e0a\u7684\u6570\u4e5f\u4e3a0（i\u79fb\u52a8\u7684\u90a3\u4f4d\u67091\u90a3\u4e00\u5b9a\u662f1））<\/span><\/p>\n

    }<\/span><\/p>\n

    return<\/span> result;<\/span><\/p>\n

    }<\/span><\/p>\n

    }<\/span>;<\/span><\/p>\n

    \u6211\u4eec\u5148\u5b9a\u4e49\u4e00\u4e2aresult\u4e3a0，32\u4f4d\u90fd\u4e3a0 \u6211\u4eec\u9898\u76ee\u662f\u8981\u6c42\u6709\u6570\u636e\u76f8\u540c\u4e2a\u6570\u4e3a3\u4e2a\u8fd9\u4e9b\u76f8\u540c\u7684\u6570\u636e32\u4f4d\u5bf9\u5e94\u7684\u6bcf\u4e00\u4f4d\u76f8\u52a0（\u8fd9\u91cc\u6211\u4eec\u4e0d\u7528\u7ba1\u67d0\u4f4d\u4e3a0\u7684）1\u5728 \u4f59(%)3\u5f97\u5230\u7684\u5c31\u662f0 \u5982\u679c\u6709\u4e00\u4e2a\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u4e5f\u53c2\u657032\u4f4d\u6240\u5bf9\u5e94\u7684\u4f4d\u4e0a\u7684\u52a0(\u8fd9\u91cc\u6211\u95e8\u53ea\u7ba1\u4f4d\u4e3a1\u76840\u7684\u4e0d\u7528\u7ba1)\u90a3\u4e48\u8be5\u4f4d\u4f59\u6570\u5c31\u4e3a1\u4e0d\u4e3a0\u8bf4\u660e\u8be5\u4f4d\u4e0a\u6709\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u76841\u6211\u4eec\u53ea\u8981\u628a32\u4f4d\u4e2d\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u572832\u4f4d\u4e0a\u76841\u5168\u627e\u51fa\u6765\u5c31\u53ef\u4ee5\u5f97\u5230\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e(\u4e8c\u8fdb\u5236\u4f4d\u4e0a\u53ea\u67091\u548c0)<\/p>\n

    int result = 0;\/\/\u7559\u7740\u653e\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e<\/p>\n

    \u9996\u5148\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2aresult\u5c06\u6240\u6709\u6570\u636e\u768432\u4e3a\u904d\u5386\u4e00\u904d\u5c0632\u4f4d\u4e0a\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e\u4e0a\u768432\u4e3a\u4f4d\u4e0a\u4e3a1\u7684\u653e\u5230\u5bf9\u5e94\u7684\u4f4d\u4e0aresult\u5f97\u5230\u7684\u5c31\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e<\/p>\n

    for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> 32<\/span>;<\/span> i++<\/span>)<\/span><\/p>\n

    {<\/span><\/p>\n

    int<\/span> count =<\/span> 0<\/span>;<\/span>\/\/\u7edf\u8ba1\u6570\u7ec4\u4e2d\u6240\u6709\u6570\u636e\u91cc\u7684\u7b2ci\u4f4d\u7684\u548c\u6700\u540e\u5c06\u5176% k\u82e5\u662f\u6709\u6570\u636e(1)\u8bf4\u660e\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u5728\u8be5\u4f4d\u67091\u653e\u5165result\u91cc\u904d\u538632\u4f4d\u5c0632\u4f4d\u91cc\u5b58\u7740\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u7684\u4f4d\u4e0a\u76841\u5168\u653e\u5165result\u4e2d\u6240\u5f97\u7684\u5c31\u662f\u8be5\u6570\u7ec4\u4e2d\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e（\u5229\u7528\u6309\u4f4d\u4e0e\u548c\u6309\u4f4d\u6216\u4ee5\u53ca>> << \u5c06\u4f4d\u6570\u79fb\u52a8\u5373\u53ef\u5b9e\u73b0）<\/span><\/p>\n

    \/\/\u7528\u8303\u56f4for\u904d\u5386\u6570\u7ec4\u5c06\u8be5\u4f4d\u4e0a\u7684\u6570\u636e\u52a0\u8d77\u6765<\/span><\/p>\n

    for<\/span>(<\/span>auto<\/span> num :<\/span> nums)<\/span><\/p>\n

    {<\/span><\/p>\n

    count +=<\/span> (<\/span>num >><\/span> i)<\/span> &<\/span> 1<\/span>;<\/span>\/\/\u6309\u4f4d\u4e0e(&)\u4e24\u4e2a\u6570\u636e\u67d0\u4f4d\u4e0a\u90fd\u4e3a1\u624d\u4e3a1\u5426\u5219\u5168\u4e3a0\u5229\u7528\u8fd9\u4e2a\u53ea\u7559\u4e0b\u8be5\u4f4d\u7684\u6570\u636e（\u53ef\u80fd\u4e3a0\u4e5f\u53ef\u80fd\u4e3a1）\u5176\u4f59\u4f4d\u4e0a\u90fd\u4e3a0（num >> i \u7684\u610f\u601d\u662f\u5c06\u6570\u636e\u768432\u4f4d\u6574\u4f53\u5411\u53f3\u79fb\u52a8i\u4f4d\u5229\u7528\u8fd9\u4e2a\u6211\u4eec\u53ef\u4ee5\u904d\u5386\u6240\u6709\u6570\u636e\u4e2d\u8be5\u4f4d\u7684\u503c(\u8fd9\u4e2a\u662f\u4f4d\u79fb\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\u5927\u4e8e\u6309\u4f4d\u4e0e\u548c\u6309\u4f4d\u6216)）<\/span><\/p>\n

    \/\/\u5224\u65ad\u8be5\u4f4d\u4e0a\u662f\u5426\u53ef\u4ee5\u4f59k(\u6570\u636e\u76f8\u540c\u7684\u4e2a\u6570)\u4e0d\u4e3a0\u8bf4\u660e\u8be5\u4f4d\u4e0a\u6709\u53ea\u6709\u4e00\u4e2a\u7684\u6570\u636e\u5728\u8be5\u4f4d\u4e0a\u7684\u6570\u636e\u5c06\u5b83\u79fb\u5230result<\/span><\/p>\n

    \/\/\u5224\u65adcount\u662f\u5426\u53ef\u4ee5 % 3\u540e\u6709\u4f59\u6570\u5728count\u52a0\u5b8c\u5728\u5224\u65ad<\/span><\/p>\n

    }<\/span><\/p>\n

    if<\/span>(<\/span>count %<\/span> 3<\/span> !=<\/span> 0<\/span>)<\/span><\/p>\n

    result |=<\/span> 1<\/span> <<<\/span> i;<\/span>\/\/(x << i\u610f\u601d\u662f\u5c06\u67d0\u6570\u636e\u5411\u5de6\u79fb\u52a8i\u4f4d\u8fd9\u91cc\u76ee\u7684\u662f\u5c06\u67d0\u4f4d\u4e0a\u7684\u53ea\u6709\u4e00\u4e2a\u6570\u7684\u6570\u636e\u5728\u6539\u4f4d\u4e0a\u76841\u653e\u5728result\u4e0a（\u8fd9\u4e24\u4e2a\u4f4d\u79fb\u8fd0\u7b97\u7b26\u5b9e\u9645\u4e0a\u662f\u5c06\u8be5\u6570\u636e\u6539\u53d8）)（\u6309\u4f4d\u6216\u610f\u601d\u662f\u67091\u5c31\u4e3a1\u6ca1\u5c31\u4e3a0\u5c06\u4f4d\u79fb\u540e\u76841\u6240\u5f62\u6210\u7684\u6570\u636e（\u8be5\u6570\u636e\u5c31\u5728I\u4f4d\u67091\u5176\u4f59\u90fd\u4e3a0）\u6309\u4f4d\u4e0eresult\u91cc\u56e0\u4e3a\u4e4b\u524d\u7684\u6570\u636e\u4f4d\u6570\u4e0a\u6709\u4e00\u4e5f\u67090\u6709\u4e00\u7684\u8fd8\u662f1\u4e3a0\u7684\u4f4d\u4e0e\u53f3\u8fb9\u6570\u636e\u540c\u4f4d\u4e0a\u7684\u6570\u4e5f\u4e3a0（i\u79fb\u52a8\u7684\u90a3\u4f4d\u67091\u90a3\u4e00\u5b9a\u662f1））<\/span><\/p>\n

    }<\/span><\/p>\n

    return<\/span> result;<\/span><\/p>\n

    \u6211\u4eec\u904d\u538632\u4f4d(\u6709\u4e0b\u6807\u4ece0\u523031)\u6211\u4eec\u5148\u4ece\u6240\u6709\u6570\u636e\u4e0b\u6807\u4e3a0\u6240\u6307\u5411\u7684\u4f4d\u6570\u5f00\u59cb\u5c06\u6570\u636e\u5168\u90e8\u76f8\u52a0 count += (num >> i) & 1;\u8fd9\u4e2a\u6211\u524d\u9762\u4ecb\u7ecd\u8fc7 \u7136\u540e\u5224\u65ad\u8fd9\u4f4d\u4e0a%3(\u8fd9\u91cc\u53ef\u4ee5\u662f3\u6216\u8005\u5176\u5b83\u53ea\u8981\u662f\u6574\u5f62\u6570\u7ec4\u53ea\u6709\u4e00\u4e2a\u53ea\u51fa\u73b0\u4e00\u6b21\u5176\u5b83\u53ea\u51fa\u73b0k\u6b21\u65f6\u5c31\u53ef\u4ee5\u7528\u6b64\u65b9\u6cd5)\u540e\u662f\u5426\u4e3a0\u4e0d\u4e3a0\u7684\u8bdd\u5c31\u5c06\u8be5\u4f4d\u4e0a\u76841\u79fb\u5230result\u4e0a<\/p>\n

    \u904d\u5386\u5b8c32\u4f4d\u65f6\u6211\u4eec\u8fd4\u56de\u7684result\u5c31\u662f\u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570\u636e<\/p>\n

    \n

    4.\u62d3\u5c55\u6709\u5174\u8da3\u505a\u4e00\u4e0b<\/h2>\n

    \u53ea\u51fa\u73b0\u4e00\u6b21\u7684\u6570iii \u6570\u7ec4\u4e2d\u51fa\u73b0\u6b21\u6570\u8d85\u8fc7\u4e00\u534a\u7684\u6570\u5b57<\/p>\n

    \n

    \u6587\u7ae0\u5230\u6b64\u5c31\u544a\u4e00\u6bb5\u843d，\u5e0c\u671b\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9，\u611f\u8c22\u89c2\u770b!<\/p>\n","protected":false},"excerpt":{"rendered":"

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    \n\u0f12\u5176\u5b83\u6709\u8da3\u7684\u8ba1\u7b97\u673a\u77e5\u8bc6\u0f12
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