{"id":281,"date":"2022-01-17T13:27:44","date_gmt":"2022-01-17T05:27:44","guid":{"rendered":"https:\/\/www.wennroy.com\/?p=281"},"modified":"2022-01-17T13:31:19","modified_gmt":"2022-01-17T05:31:19","slug":"373-find-k-pairs-with-smallest-sums","status":"publish","type":"post","link":"https:\/\/wennroy.com\/index.php\/2022\/01\/17\/373-find-k-pairs-with-smallest-sums\/","title":{"rendered":"373. \u67e5\u627e\u548c\u6700\u5c0f\u7684 K \u5bf9\u6570\u5b57"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u7ed9\u5b9a\u4e24\u4e2a\u4ee5 \u5347\u5e8f\u6392\u5217 \u7684\u6574\u6570\u6570\u7ec4 <code>nums1<\/code> \u548c <code>nums2<\/code>&nbsp;,&nbsp;\u4ee5\u53ca\u4e00\u4e2a\u6574\u6570 <code>k<\/code>&nbsp;\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9a\u4e49\u4e00\u5bf9\u503c&nbsp;<code>(u,v)<\/code>\uff0c\u5176\u4e2d\u7b2c\u4e00\u4e2a\u5143\u7d20\u6765\u81ea&nbsp;<code>nums1<\/code>\uff0c\u7b2c\u4e8c\u4e2a\u5143\u7d20\u6765\u81ea <code>nums2<\/code>&nbsp;\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bf7\u627e\u5230\u548c\u6700\u5c0f\u7684 <code>k<\/code>&nbsp;\u4e2a\u6570\u5bf9&nbsp;<code>(u1,v1), (u2,v2) \u2026 (uk,vk)<\/code>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b98\u65b9\u89e3\u6cd5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u65b9\u6cd5\u4e00\uff1a\u4f18\u5148\u961f\u5217<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c<a rel=\"noreferrer noopener\" href=\"https:\/\/leetcode-cn.com\/problems\/kth-smallest-element-in-a-sorted-matrix\/\" target=\"_blank\">719. \u627e\u51fa\u7b2c k \u5c0f\u7684\u8ddd\u79bb\u5bf9<\/a>\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5df2\u77e5\u542b\u6709 <code>n<\/code> \u4e2a\u6570\u5bf9\u7684\u65f6\u5019\uff0c\u90a3\u4e48\u7b2c <code>n+1<\/code> \u4e2a\u6570\u5bf9\u5fc5\u5b9a\u4ece\u4ee5\u4e0b\u7ec4\u5408\u4e2d\u4ea7\u751f\uff0c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><code>(a1+1,b1), (a1,b1+1), (a2+1,b2), (a2,b2+1), ... , (an,bn+1)<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d <code>a1<\/code>,<code>a2<\/code> \u4ee3\u8868\u7684\u662f\u5728\u5347\u5e8f <code>nums1<\/code>, <code>nums2<\/code> \u7684\u4f4d\u5e8f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b97\u6cd5\u5b9e\u73b0\u65b9\u9762\u4f7f\u7528<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">class Solution:\n    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:\n        m, n = len(nums1), len(nums2)\n        ans = []\n        pq = [(nums1[i] + nums2[0], i, 0) for i in range(min(k, m))]\n        while pq and len(ans) &lt; k:\n            _, i, j = heappop(pq)\n            ans.append([nums1[i], nums2[j]])\n            if j + 1 &lt; n:\n                heappush(pq, (nums1[i] + nums2[j + 1], i, j + 1))\n        return ans<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u65b9\u6cd5\u4e8c\uff1a\u4e8c\u5206\u67e5\u627e<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c<a rel=\"noreferrer noopener\" href=\"https:\/\/leetcode-cn.com\/problems\/kth-smallest-element-in-a-sorted-matrix\/\" target=\"_blank\">378. \u6709\u5e8f\u77e9\u9635\u4e2d\u7b2c K \u5c0f\u7684\u5143\u7d20<\/a>\u300d<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">class Solution:\n    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:\n        m, n = len(nums1), len(nums2)\n\n        # \u4e8c\u5206\u67e5\u627e\u7b2c k \u5c0f\u7684\u6570\u5bf9\u548c\n        left, right = nums1[0] + nums2[0], nums1[m - 1] + nums2[n - 1] + 1\n        while left &lt; right:\n            mid = (left + right) \/\/ 2\n            cnt = 0\n            i, j = 0, n - 1\n            while i &lt; m and j >= 0:\n                if nums1[i] + nums2[j] > mid:\n                    j -= 1\n                else:\n                    cnt += j + 1\n                    i += 1\n            if cnt &lt; k:\n                left = mid + 1\n            else:\n                right = mid\n        pairSum = left\n\n        ans = []\n        # \u627e\u6570\u5bf9\u548c\u5c0f\u4e8e pairSum \u7684\u6570\u5bf9\n        i = n - 1\n        for num1 in nums1:\n            while i >= 0 and num1 + nums2[i] >= pairSum:\n                i -= 1\n            for j in range(i + 1):\n                ans.append([num1, nums2[j]])\n                if len(ans) == k:\n                    return ans\n\n        # \u627e\u6570\u5bf9\u548c\u7b49\u4e8e pairSum \u7684\u6570\u5bf9\n        i = n - 1\n        for num1 in nums1:\n            while i >= 0 and num1 + nums2[i] > pairSum:\n                i -= 1\n            j = i\n            while j >= 0 and num1 + nums2[j] == pairSum:\n                ans.append([num1, nums2[j]])\n                if len(ans) == k:\n                    return ans\n                j -= 1\n        return ans<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6765\u6e90\uff1a\u529b\u6263\uff08LeetCode\uff09<br>\u94fe\u63a5\uff1a<a href=\"https:\/\/leetcode-cn.com\/problems\/find-k-pairs-with-smallest-sums\">https:\/\/leetcode-cn.com\/problems\/find-k-pairs-with-smallest-sums<\/a><br>\u8457\u4f5c\u6743\u5f52\u9886\u6263\u7f51\u7edc\u6240\u6709\u3002\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u8054\u7cfb\u5b98\u65b9\u6388\u6743\uff0c\u975e\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Python\u5c0f\u77e5\u8bc6<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5806<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9e\u9645\u4e0a\uff0cPython\u6ca1\u6709\u72ec\u7acb\u7684\u5806\u7c7b\u578b\uff0c\u800c\u53ea\u6709\u4e00\u4e2a\u5305\u542b\u4e00\u4e9b\u5806\u64cd\u4f5c\u51fd\u6570\u7684\u6a21\u5757\u3002\u8fd9\u4e2a\u6a21\u5757\u540d\u4e3a<code>heapq<\/code>\uff08\u5176\u4e2d\u7684q\u8868\u793a\u961f\u5217\uff09\uff0c\u5b83\u5305\u542b6\u4e2a\u51fd\u6570\uff0c\u5176\u4e2d\u524d4\u4e2a\u4e0e\u5806\u64cd\u4f5c\u76f4\u63a5\u76f8\u5173\u3002\u5fc5\u987b\u4f7f\u7528\u5217\u8868\u6765\u8868\u793a\u5806\u5bf9\u8c61\u672c\u8eab\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f18\u5148\u961f\u5217\uff1a<code>import heapq<\/code> \u5806\u7684\u4f7f\u7528\u65b9\u5f0f\uff1a<code>heapq.heappop()<\/code> \u662f\u538b\u51fa\u6700\u5c0f\u7684\u5143\u7d20\uff0c<code>heapq.heappush()<\/code>\u662f\u538b\u8fdb\u5806\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5143\u7d20\u7684\u6392\u5217\u987a\u5e8f\u5e76\u4e0d\u50cf\u770b\u8d77\u6765\u90a3\u4e48\u968f\u610f\u3002\u5b83\u4eec\u867d\u7136\u4e0d\u662f\u4e25\u683c\u6392\u5e8f\u7684\uff0c\u4f46\u5fc5\u987b\u4fdd\u8bc1\u4e00\u70b9\uff1a\u4f4d\u7f6ei\u5904\u7684\u5143\u7d20\u603b\u662f\u5927\u4e8e\u4f4d\u7f6ei \/\/ 2\u5904\u7684\u5143\u7d20\uff08\u53cd\u8fc7\u6765\u8bf4\u5c31\u662f\u5c0f\u4e8e\u4f4d\u7f6e2 * i\u548c2 * i + 1\u5904\u7684\u5143\u7d20\uff09\u3002\u8fd9\u662f\u5e95\u5c42\u5806\u7b97\u6cd5\u7684\u57fa\u7840\uff0c\u79f0\u4e3a\u5806\u7279\u5f81\uff08heap property\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fd\u6570heappop\u5f39\u51fa\u6700\u5c0f\u7684\u5143\u7d20\uff08\u603b\u662f\u4f4d\u4e8e\u7d22\u5f150\u5904\uff09\uff0c\u5e76\u786e\u4fdd\u5269\u4f59\u5143\u7d20\u4e2d\u6700\u5c0f\u7684\u90a3\u4e2a\u4f4d\u4e8e\u7d22\u5f150\u5904\uff08\u4fdd\u6301\u5806\u7279\u5f81\uff09\u3002\u867d\u7136\u5f39\u51fa\u5217\u8868\u4e2d\u7b2c\u4e00\u4e2a\u5143\u7d20\u7684\u6548\u7387\u901a\u5e38\u4e0d\u662f\u5f88\u9ad8\uff0c\u4f46\u8fd9\u4e0d\u662f\u95ee\u9898\uff0c\u56e0\u4e3aheappop\u4f1a\u5728\u5e55\u540e\u505a\u4e9b\u5de7\u5999\u7684\u79fb\u4f4d\u64cd\u4f5c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f18\u5148\u961f\u5217\u8ba9\u4f60\u80fd\u591f\u4ee5\u4efb\u610f\u987a\u5e8f\u6dfb\u52a0\u5bf9\u8c61\uff0c\u5e76\u968f\u65f6\uff08\u53ef\u80fd\u662f\u5728\u4e24\u6b21\u6dfb\u52a0\u5bf9\u8c61\u4e4b\u95f4\uff09\u627e\u51fa\uff08\u5e76\u5220\u9664\uff09\u6700\u5c0f\u7684\u5143\u7d20\u3002\u76f8\u6bd4\u4e8e\u5217\u8868\u65b9\u6cd5min\uff0c\u8fd9\u6837\u505a\u7684\u6548\u7387\u8981\u9ad8\u5f97\u591a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u89c1 <a href=\"https:\/\/blog.csdn.net\/jamfiy\/article\/details\/88185512\">python\u9ad8\u7ea7\uff08\u5806heapq\u6a21\u5757\uff09<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7ed9\u5b9a\u4e24\u4e2a\u4ee5 \u5347\u5e8f\u6392\u5217 \u7684\u6574\u6570\u6570\u7ec4 nums1 \u548c  &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","footnotes":""},"categories":[6,30,29],"tags":[25,32,31],"class_list":["post-281","post","type-post","status-publish","format-standard","hentry","category-leetcode","category-binary_search","category-priority_queue","tag-leetcode","tag-32","tag-31"],"_links":{"self":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/comments?post=281"}],"version-history":[{"count":2,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions"}],"predecessor-version":[{"id":283,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions\/283"}],"wp:attachment":[{"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/categories?post=281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wennroy.com\/index.php\/wp-json\/wp\/v2\/tags?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}