{"id":2557,"date":"2020-03-01T13:29:33","date_gmt":"2020-03-01T05:29:33","guid":{"rendered":"http:\/\/tihar-tech.cn\/?p=2557"},"modified":"2022-12-28T00:56:38","modified_gmt":"2022-12-27T16:56:38","slug":"merge-sort-%e5%bd%92%e5%b9%b6%e6%8e%92%e5%ba%8f%e8%af%a6%e8%a7%a3%e4%b8%8e%e4%bc%98%e5%8c%96","status":"publish","type":"post","link":"http:\/\/139.196.114.170\/?p=2557","title":{"rendered":"Merge Sort – \u5f52\u5e76\u6392\u5e8f\u8be6\u89e3\u4e0e\u4f18\u5316"},"content":{"rendered":"

\u5f52\u5e76\u6392\u5e8f<\/h2>\n

\u601d\u60f3<\/h3>\n

\u81ea\u9876\u5411\u4e0b\u5212\u5206<\/h4>\n

\u5e8f\u5217 [l, r] \u88ab\u9010\u6b65\u4e8c\u5206\u4e3a\u66f4\u5c0f\u7684\u5e8f\u5217 [l, m] \u3001[m+1, r]<\/p>\n

\u81ea\u5e95\u5411\u4e0a\u5f52\u5e76<\/h4>\n

\u5212\u5206\u7684\u6700\u5c0f\u6709\u5e8f\u5e8f\u5217\u4e3a\u5143\u7d20\u672c\u8eab\uff0c\u5b50\u5e8f\u5217\u4e4b\u95f4\u4e24\u4e24\u5f52\u5e76\uff0c\u5f52\u5e76\u6210\u4e3a\u65b0\u7684\u6709\u5e8f\u5e8f\u5217\u4e4b\u540e\u518d\u6b21\u4e24\u4e24\u5408\u5e76\uff0c\u76f4\u5230\u8c03\u548c\u6210\u4e3a\u5b8c\u6574\u7684\u6709\u5e8f\u5e8f\u5217<\/p>\n

\u5176\u4e2d\u7684\u5408\u5e76\u64cd\u4f5c\u4e3a \u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217<\/strong>\uff1a\u4ece\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\u9010\u4e00\u53d6\u503c\uff0c\u6309\u5927\u5c0f\u6b21\u5e8f\u4f9d\u6b21\u63d2\u5165\u65b0\u7684\u5e8f\u5217\uff0c\u53ef\u5408\u5e76\u4e3a\u4e00\u4e2a\u65b0\u7684\u6709\u5e8f\u5e8f\u5217\u3002\u65b0\u5e8f\u5217\u82e5\u53d6\u539f\u5e8f\u5217\u672c\u8eab\uff0c\u53ef\u80fd\u4f1a\u8986\u76d6\u5e8f\u5217\u539f\u503c\u5bfc\u81f4\u9519\u8bef\uff0c\u9700\u8981\u4e00\u4e2a \u8f85\u52a9\u5e8f\u5217aux<\/strong> \u6765\u4fdd\u5b58\u5408\u5e76\u7ed3\u679c<\/p>\n

\u6027\u80fd\u5206\u6790<\/h4>\n

\u65f6\u95f4\u590d\u6742\u5ea6 O(nlogn)
\n\u7a7a\u95f4\u590d\u6742\u5ea6 O(n)<\/p>\n

\u5b9e\u73b0\u4e0e\u4f18\u5316<\/h3>\n

\u9012\u5f52\u5b9e\u73b0\u6570\u7ec4\u6392\u5e8f<\/h4>\n

\u5b50\u9012\u5f52\u7ed3\u679c\u5b58\u5165aux\uff0c\u7236\u8c03\u7528\u65f6\u57fa\u4e8eaux\u7684\u526f\u672c\u8fdb\u884c\u5408\u5e76\uff0c\u5373\u5728\u5408\u5e76\u524d\u590d\u5236<\/p>\n

\nclass Solution {\n    public int[] sortArray(int[] nums) {\n        int[] aux = new int[nums.length];\n        mergeSort(nums, 0, nums.length - 1, aux);\n        return aux;\n    }\n\n    public void mergeSort(int[] nums, int i, int j, int[] aux) {\n        \/\/ \u9012\u5f52\u8fb9\u754c\uff1a\u4e0d\u5408\u6cd5\u8fd4\u56de\n        if (i > j) return;\n\n        \/\/ \u9012\u5f52\u8fb9\u754c\uff1a\u6700\u5c0f\u5b50\u5e8f\u5217\u662f\u5143\u7d20\u672c\u8eab\uff0c\u5408\u5e76\u5165\u65b0\u5e8f\u5217aux\n        if (i == j) {\n            aux[i] = nums[i];\n            return;\n        }\n\n        \/\/ \u81ea\u9876\u5411\u4e0b\u5212\u5206\u5b50\u5e8f\u5217\uff0c\u9012\u5f52\u8fd4\u56de\u65f6\u4e24\u90e8\u5206\u7684aux\u5df2\u7ecf\u5206\u522b\u6709\u5e8f\n        int m = i + ((j - i) >> 1);\n        mergeSort(nums, i, m, aux);\n        mergeSort(nums, m + 1, j, aux);\n\n        \/\/ \u540e\u7eed\u5f52\u5e76\u57fa\u4e8e\u5206\u522b\u6709\u5e8f\u7684\u5b50\u5e8f\u5217\uff0c\u539f\u5730\u5f52\u5e76\u4f1a\u8986\u76d6\u539f\u503c\uff0c\u5c06\u90e8\u5206\u6709\u5e8f\u7ed3\u679c\u590d\u5236\u56denums\n        for (int k = i; k <= j; k++) {\n            nums[k] = aux[k];\n        }\n\n        \/\/ \u57fa\u4e8enums\u4e2d\u7684\u4e24\u6709\u5e8f\u5e8f\u5217[l, m] \u3001[m+1, r]\u5408\u5e76\u5230aux\u4e2d\uff0c\u5408\u5e76\u65f6\u8003\u8651\u6307\u9488\u5230\u5934\u60c5\u51b5\n        int s = i, f = m + 1, id = i;\n        while (s <= m || f <= j) {\n            if (s > m) aux[id++] = nums[f++];\n            else if (f > j) aux[id++] = nums[s++];\n            else if (nums[s] <= nums[f]) aux[id++] = nums[s++];\n            else aux[id++] = nums[f++];\n        }\n    }\n}\n<\/pre>\n
\u4f18\u5316\u9012\u5f52\u6570\u7ec4\u6392\u5e8f<\/h4>\n
\u4f18\u5316\u70b91\uff1a\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u5408\u5e76<\/strong>\uff0c\u4e24\u6709\u5e8f\u5e8f\u5217\u672c\u8eab\u5df2\u7ecf\u7ec4\u6210\u65b0\u7684\u6709\u5e8f\u5e8f\u5217\u65f6\uff0c\u7701\u53bb\u5408\u5e76
\n\u4f18\u5316\u70b92\uff1a\u5408\u5e76\u9012\u5f52\u8fb9\u754c\u51cf\u5c11\u590d\u5236<\/strong>\uff0c\u5355\u4e2a\u5143\u7d20\u81ea\u6210\u5e8f\u4e0d\u518d\u5904\u7406\uff0c\u610f\u5473\u7740\u4fdd\u5b58\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\u7684\u662fnums\uff0c\u9700\u8981\u59cb\u7ec8\u5c06\u5408\u5e76\u7ed3\u679c\u5b58\u5165nums\u3002\u5408\u5e76\u64cd\u4f5c\u57fa\u4e8enums\u8f93\u51fa\u5230\u8f85\u52a9\u6570\u7ec4aux\u540e\u9700\u8981\u590d\u5236\u56de\u5230nums<\/p>\n
\nclass Solution {\n    public int[] sortArray(int[] nums) {\n        int[] aux = new int[nums.length];\n        mergeSort(nums, 0, nums.length - 1, aux);\n        return nums;\n    }\n\n    public void mergeSort(int[] nums, int i, int j, int[] aux) {\n        \/\/ \u9012\u5f52\u8fb9\u754c\uff0ci > j\u4e0d\u5408\u6cd5\uff0ci = j\u65f6nums[i]\u81ea\u6210\u5e8f\n        if(i >= j) return;\n\n        \/\/ \u5b50\u9012\u5f52\u5212\u5206\u548c\u5f52\u5e76\uff0c\u6267\u884c\u5b8c\u540e\u5de6\u53f3\u90e8\u5206\u5404\u81ea\u6709\u5e8f\n        int m = i + ((j - i) >> 1);\n        mergeSort(nums, i, m, aux);\n        mergeSort(nums, m + 1, j, aux);\n\n        \/\/ \u5de6\u53f3\u90e8\u5206\u5728\u672c\u8f6e\u5408\u5e76\u524d\u5df2\u6709\u5e8f\uff0c\u526a\u679d\n        if(nums[m] < nums[m+1]) return;\n\n        \/\/ \u57fa\u4e8e\u6709\u5e8f\u7684nums\u8fdb\u884c\u5f52\u5e76\n        int s = i, f = m + 1, id = i;\n        while(s <= m || f <= j) {\n            if(s > m) aux[id++] = nums[f++];\n            else if(f > j) aux[id++] = nums[s++];\n            else if(nums[s] > nums[f]) aux[id++] = nums[f++];\n            else aux[id++] = nums[s++];\n        }\n\n        \/\/ \u6062\u590dnums\u7684\u6709\u5e8f\u6027\uff0c\u4f9b\u4e0b\u8f6eaux\u5408\u5e76\u4f7f\u7528\n        for(int k = i; k <= j; k++) {\n            nums[k] = aux[k];\n        }\n    }\n}\n<\/pre>\n
\u9012\u5f52\u5b9e\u73b0\u94fe\u8868\u6392\u5e8f<\/h4>\n
\u81ea\u9876\u5411\u4e0b\u5212\u5206\u65f6\u9700\u8981\u627e\u5230\u94fe\u8868\u4e2d\u70b9\u5e76\u5207\u5206\u4e3a\u4e24\u4e2a\u94fe\u8868\uff0c\u6e05\u7a7a\u7b2c\u4e00\u4e2a\u8868\u5c3enext\u57df
\n\u5728\u5408\u5e76\u9636\u6bb5\u53ef\u4f7f\u7528 \u865a\u62df\u5934\u8282\u70b9<\/strong> \uff0c\u907f\u514d\u590d\u6742\u7684\u8fb9\u754c\u6761\u4ef6\u5224\u65ad
\n\u5408\u5e76\u65f6\u4e24\u4e2a\u94fe\u8868\u5df2\u7ecf\u6709\u5e8f\uff0c\u5176\u4e2d\u4e00\u4e2a\u94fe\u8868\u5230\u8fbe\u5c3d\u5934\uff0c\u76f4\u63a5\u5c06\u53e6\u4e00\u6761\u94fe\u8868\u63a5\u5230\u8868\u5c3e\u5373\u53ef<\/p>\n
\nclass RecursiveMergeSort {\n    public ListNode sortList(ListNode head) {\n        return mergeSort(head);\n    }\n\n    public ListNode mergeSort(ListNode head) {\n        \/\/ \u9012\u5f52\u8fb9\u754c\uff0c\u7a7a\u8282\u70b9\u6216\u5355\u4e2a\u8282\u70b9\u81ea\u6709\u5e8f\n        if (head == null || head.next == null) {\n            return head;\n        }\n\n        \/\/ \u5f97\u5230\u94fe\u8868\u4e2d\u70b9\u540e\u5207\u5f00\u4e24\u4e2a\u94fe\u8868\n        ListNode fast = head, mid = head, clr = null;\n        while (fast != null && fast.next != null) {\n            fast = fast.next.next;\n            clr = mid;\n            mid = mid.next;\n        }\n        clr.next = null;\n\n        \/\/ \u81ea\u9876\u5411\u4e0b\u5212\u5206\u5f97\u5230\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\n        head = mergeSort(head);\n        mid = mergeSort(mid);\n\n        \/\/ \u81ea\u5e95\u5411\u4e0a\u5f52\u5e76\n        ListNode dum = new ListNode(Integer.MIN_VALUE, null);\n        ListNode cur = dum;\n        while (head != null && mid != null) {\n            if (head.val < mid.val) {\n                cur.next = head;\n                head = head.next;\n            } else {\n                cur.next = mid;\n                mid = mid.next;\n            }\n            cur = cur.next;\n        }\n\n        \/\/ \u5904\u7406\u4e00\u4e2a\u6307\u9488\u5230\u5934\u7684\u60c5\u51b5\uff0c\u6b64\u65f6\u4e24\u94fe\u8868\u5747\u6709\u5e8f\n        if (head == null) cur.next = mid;\n        if (mid == null) cur.next = head;\n\n        \/\/ \u8fd4\u56de\u5408\u5e76\u540e\u94fe\u8868\u7684\u65b0\u5934\u8282\u70b9\n        return dum.next;\n    }\n}\n<\/pre>\n
\u8fed\u4ee3<\/h3>\n
\u5076\u6570\u5bf9\u53ef\u4ee5\u4e24\u4e24\u5408\u5e76\uff0c\u56db\u56db\u5408\u5e76\uff0c\u516b\u516b\u5408\u5e76<\/p>\n
\u5076\u6570\u5bf9\u5408\u5e76\u8fc7\u7a0b\u793a\u4f8b\n01 23 45 67\n0123 4567\n01234567\n<\/code><\/pre>\n
\u5947\u6570\u5bf9\u5143\u7d20\u7684\u5408\u5e76\u5904\u7406\u8fc7\u7a0b\u9700\u8981\u7279\u6b8a\u5904\u7406<\/p>\n
\u5947\u6570\u5bf9\u5408\u5e76\u8fc7\u7a0b\u793a\u4f8b\n01 23 45 6\n0123 456\n0123456\n\n\u5947\u6570\u5bf9\u5408\u5e76\u8fc7\u7a0b\u793a\u4f8b\n01 23 4\n0123 4\n01234\n\n\u5947\u6570\u5bf9\u5408\u5e76\u8fc7\u7a0b\u793a\u4f8b\n01 23 45\n0123 45\n012345\n<\/code><\/pre>\n
\nclass MergeSortIteration {\n    public int[] sortArray(int[] nums) {\n        int[] aux = new int[nums.length];\n\n        \/\/ sz\u6269\u5230\u4f55\u65f6\u505c\u6b62\uff1f\u7531\u4e8e\u5947\u6570\u7684\u7279\u6b8a\u6027\u4e0d\u80fd\u4f7fsz\u5728N\/2\u65f6\u505c\u6b62\uff0c\u5e94\u6269\u5230\u548c\u6570\u7ec4\u540c\u957f\u5ea6\u65f6\uff0c\u540c\u957f\u5ea6\u4e3a\u6700\u540e\u4e00\u8f6e\u5df2\u6210\u5e8f\u65e0\u9700\u5f52\u5e76\n        for (int sz = 1; sz < nums.length; sz <<= 1) {\n\n            \/\/ lo\u79fb\u5230\u4f55\u65f6\u505c\u6b62\uff1f\u6700\u540e\u90e8\u5206\u5c0f\u4e8esz\u65f6lo + sz < nums.length\n            for (int lo = 0; lo + sz < nums.length; lo += (sz << 1)) {\n                int s = lo, st = lo + sz;\n\n                \/\/ \u4e0d\u8db3sz\u7684\u540e\u534a\u90e8\u5206\u672b\u5c3e\u8bbe\u5b9a\u4e3anum.length\n                int f = lo + sz, ft = Math.min(lo + (sz << 1), nums.length);\n                int id = lo;\n\n                \/\/ \u5408\u5e76 [s, st) [f, ft)\n                while (s < st && f < ft) {\n                    if (nums[s] < nums[f]) aux[id++] = nums[s++];\n                    else aux[id++] = nums[f++];\n                }\n\n                \/\/ \u4ee5nums\u4e3a\u57fa\u7840\u5f52\u5e76\u5230aux\u4e2d\n                if (s >= st) while (f < ft) aux[id++] = nums[f++];\n                if (f >= ft) while (s < st) aux[id++] = nums[s++];\n\n                \/\/ \u590d\u5236\u56denums\n                for (int k = lo; k < ft; k++)\n                    nums[k] = aux[k];\n            }\n        }\n        return nums;\n    }\n}\n<\/pre>\n
\u53c2\u8003\u8d44\u6599<\/h3>\n
Sedgewick R, Wayne K. Algorithms, Fourth Edition[M]. 4. \u4eba\u6c11\u90ae\u7535\u51fa\u7248\u793e, 2012.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5f52\u5e76\u6392\u5e8f \u601d\u60f3 \u81ea\u9876\u5411\u4e0b\u5212\u5206 \u5e8f\u5217 [l, r] \u88ab\u9010\u6b65\u4e8c\u5206\u4e3a\u66f4\u5c0f\u7684\u5e8f\u5217 [l, m] \u3001[m+1, r] \u81ea … <\/p>\n
\u7ee7\u7eed\u9605\u8bfb\u201cMerge Sort – \u5f52\u5e76\u6392\u5e8f\u8be6\u89e3\u4e0e\u4f18\u5316\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2557"}],"collection":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2557"}],"version-history":[{"count":6,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2557\/revisions"}],"predecessor-version":[{"id":2572,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2557\/revisions\/2572"}],"wp:attachment":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2557"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}