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[LeetCode] 1345. Jump Game IV · Issue #1345 · grandyang/leetcode · GitHub

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1.75 1ZM1.5 2.75v9.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h6.5a.25.25 0 0 0 .25-.25v-9.5a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Z"></path><path d="M22.5 8.75a.25.25 0 0 0-.25-.25h-3.5a.75.75 0 0 1 0-1.5h3.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 22.25 20H21v1.543a1.457 1.457 0 0 1-2.487 1.03L15.939 20H10.75A1.75 1.75 0 0 1 9 18.25v-1.465a.75.75 0 0 1 1.5 0v1.465c0 .138.112.25.25.25h5.5a.75.75 0 0 1 .53.22l2.72 2.72v-2.19a.75.75 0 0 1 .75-.75h2a.25.25 0 0 0 .25-.25v-9.5Z"></path> </svg> <div> <div class="color-fg-default h4">Discussions</div> Collaborate outside of code </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" 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</li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Solutions <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0 pb-lg-3 mb-3 mb-lg-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-company-size-heading">By company size</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-company-size-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;enterprises&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;enterprises_link_solutions_navbar&quot;}" href="https://github.com/enterprise"> Enterprises </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;small_and_medium_teams&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;small_and_medium_teams_link_solutions_navbar&quot;}" href="https://github.com/team"> Small and medium teams </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;startups&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;startups_link_solutions_navbar&quot;}" href="https://github.com/enterprise/startups"> Startups </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;nonprofits&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;nonprofits_link_solutions_navbar&quot;}" href="/solutions/industry/nonprofits"> Nonprofits </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-use-case-heading">By use case</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-use-case-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;devsecops&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;devsecops_link_solutions_navbar&quot;}" href="/solutions/use-case/devsecops"> DevSecOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;devops&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;devops_link_solutions_navbar&quot;}" href="/solutions/use-case/devops"> DevOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;ci_cd&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;ci_cd_link_solutions_navbar&quot;}" href="/solutions/use-case/ci-cd"> CI/CD </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;view_all_use_cases&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;view_all_use_cases_link_solutions_navbar&quot;}" href="/solutions/use-case"> View all use cases </a></li> </ul> </div> </div> <div class="HeaderMenu-column px-lg-4"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-industry-heading">By industry</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-industry-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;healthcare&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;healthcare_link_solutions_navbar&quot;}" href="/solutions/industry/healthcare"> Healthcare </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;financial_services&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;financial_services_link_solutions_navbar&quot;}" href="/solutions/industry/financial-services"> Financial services </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;manufacturing&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;manufacturing_link_solutions_navbar&quot;}" href="/solutions/industry/manufacturing"> Manufacturing </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;government&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;government_link_solutions_navbar&quot;}" href="/solutions/industry/government"> Government </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;view_all_industries&quot;,&quot;context&quot;:&quot;solutions&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;view_all_industries_link_solutions_navbar&quot;}" href="/solutions/industry"> View all industries </a></li> </ul> </div> </div> <div class="HeaderMenu-trailing-link rounded-bottom-2 flex-shrink-0 mt-lg-4 px-lg-4 py-4 py-lg-3 f5 text-semibold"> <a href="/solutions"> View all solutions <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-right HeaderMenu-trailing-link-icon"> <path d="M6.22 3.22a.75.75 0 0 1 1.06 0l4.25 4.25a.75.75 0 0 1 0 1.06l-4.25 4.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L9.94 8 6.22 4.28a.75.75 0 0 1 0-1.06Z"></path> </svg> </a> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Resources <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="resources-topics-heading">Topics</span> <ul class="list-style-none f5" aria-labelledby="resources-topics-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;ai&quot;,&quot;context&quot;:&quot;resources&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;ai_link_resources_navbar&quot;}" href="/resources/articles/ai"> AI </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;devops&quot;,&quot;context&quot;:&quot;resources&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;devops_link_resources_navbar&quot;}" href="/resources/articles/devops"> DevOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;security&quot;,&quot;context&quot;:&quot;resources&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;security_link_resources_navbar&quot;}" href="/resources/articles/security"> Security </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" 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5.685a.25.25 0 0 0 .268 0l8.964-5.685a.75.75 0 0 1 .804 1.267l-8.965 5.685a1.749 1.749 0 0 1-1.874 0l-8.965-5.685a.75.75 0 0 1-.231-1.035Z"></path> </svg> <div> <div class="color-fg-default h4">Enterprise platform</div> AI-powered developer platform </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="enterprise-available-add-ons-heading">Available add-ons</span> <ul class="list-style-none f5" aria-labelledby="enterprise-available-add-ons-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;advanced_security&quot;,&quot;context&quot;:&quot;enterprise&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;advanced_security_link_enterprise_navbar&quot;}" href="https://github.com/enterprise/advanced-security"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-shield-check color-fg-subtle mr-3"> <path d="M16.53 9.78a.75.75 0 0 0-1.06-1.06L11 13.19l-1.97-1.97a.75.75 0 0 0-1.06 1.06l2.5 2.5a.75.75 0 0 0 1.06 0l5-5Z"></path><path d="m12.54.637 8.25 2.675A1.75 1.75 0 0 1 22 4.976V10c0 6.19-3.771 10.704-9.401 12.83a1.704 1.704 0 0 1-1.198 0C5.77 20.705 2 16.19 2 10V4.976c0-.758.489-1.43 1.21-1.664L11.46.637a1.748 1.748 0 0 1 1.08 0Zm-.617 1.426-8.25 2.676a.249.249 0 0 0-.173.237V10c0 5.46 3.28 9.483 8.43 11.426a.199.199 0 0 0 .14 0C17.22 19.483 20.5 15.461 20.5 10V4.976a.25.25 0 0 0-.173-.237l-8.25-2.676a.253.253 0 0 0-.154 0Z"></path> </svg> <div> <div class="color-fg-default h4">Advanced Security</div> Enterprise-grade security features </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex 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1.517 1.258.364 2.233 1.721 2.605 2.656a.832.832 0 0 1 .053.22v2.869a.641.641 0 0 1-.078.256ZM12.172 11h-.344a4.323 4.323 0 0 1-.355.508C10.703 12.455 9.555 13 7.965 13c-1.725 0-2.989-.359-3.782-1.259a2.005 2.005 0 0 1-.085-.104L4 11.741v6.585c1.435.779 4.514 2.179 8 2.179 3.486 0 6.565-1.4 8-2.179v-6.585l-.098-.104s-.033.045-.085.104c-.793.9-2.057 1.259-3.782 1.259-1.59 0-2.738-.545-3.508-1.492a4.323 4.323 0 0 1-.355-.508h-.016.016Zm.641-2.935c.136 1.057.403 1.913.878 2.497.442.544 1.134.938 2.344.938 1.573 0 2.292-.337 2.657-.751.384-.435.558-1.15.558-2.361 0-1.14-.243-1.847-.705-2.319-.477-.488-1.319-.862-2.824-1.025-1.487-.161-2.192.138-2.533.529-.269.307-.437.808-.438 1.578v.021c0 .265.021.562.063.893Zm-1.626 0c.042-.331.063-.628.063-.894v-.02c-.001-.77-.169-1.271-.438-1.578-.341-.391-1.046-.69-2.533-.529-1.505.163-2.347.537-2.824 1.025-.462.472-.705 1.179-.705 2.319 0 1.211.175 1.926.558 2.361.365.414 1.084.751 2.657.751 1.21 0 1.902-.394 2.344-.938.475-.584.742-1.44.878-2.497Z"></path><path d="M14.5 14.25a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Zm-5 0a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Z"></path> </svg> <div> <div class="color-fg-default h4">Copilot for business</div> Enterprise-grade AI features </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{&quot;location&quot;:&quot;navbar&quot;,&quot;action&quot;:&quot;premium_support&quot;,&quot;context&quot;:&quot;enterprise&quot;,&quot;tag&quot;:&quot;link&quot;,&quot;label&quot;:&quot;premium_support_link_enterprise_navbar&quot;}" href="/premium-support"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-comment-discussion color-fg-subtle mr-3"> <path d="M1.75 1h12.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 14.25 14H8.061l-2.574 2.573A1.458 1.458 0 0 1 3 15.543V14H1.75A1.75 1.75 0 0 1 0 12.25v-9.5C0 1.784.784 1 1.75 1ZM1.5 2.75v9.5c0 .138.112.25.25.25h2a.75.75 0 0 1 .75.75v2.19l2.72-2.72a.749.749 0 0 1 .53-.22h6.5a.25.25 0 0 0 .25-.25v-9.5a.25.25 0 0 0-.25-.25H1.75a.25.25 0 0 0-.25.25Z"></path><path d="M22.5 8.75a.25.25 0 0 0-.25-.25h-3.5a.75.75 0 0 1 0-1.5h3.5c.966 0 1.75.784 1.75 1.75v9.5A1.75 1.75 0 0 1 22.25 20H21v1.543a1.457 1.457 0 0 1-2.487 1.03L15.939 20H10.75A1.75 1.75 0 0 1 9 18.25v-1.465a.75.75 0 0 1 1.5 0v1.465c0 .138.112.25.25.25h5.5a.75.75 0 0 1 .53.22l2.72 2.72v-2.19a.75.75 0 0 1 .75-.75h2a.25.25 0 0 0 .25-.25v-9.5Z"></path> </svg> <div> <div class="color-fg-default h4">Premium Support</div> Enterprise-grade 24/7 support </div> </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <a class="HeaderMenu-link no-underline 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data-target="react-app.embeddedData">{"payload":{"preloaded_records":{},"preloadedQueries":[{"queryId":"3dddeeb0bc5f88ccaca7204fa97a09b8","queryName":"IssueViewerViewQuery","variables":{"id":"repository","number":1345,"owner":"grandyang","repo":"leetcode"},"result":{"data":{"repository":{"isOwnerEnterpriseManaged":false,"issue":{"id":"MDU6SXNzdWU0NTAzOTY3MTI=","updatedAt":"2023-09-14T06:56:34Z","title":"[LeetCode] 1345. Jump Game IV","number":1345,"repository":{"nameWithOwner":"grandyang/leetcode","id":"MDEwOlJlcG9zaXRvcnkxODk0NDQ0MjM=","name":"leetcode","owner":{"__typename":"User","login":"grandyang","id":"MDQ6VXNlcjg1NTMwMTA=","url":"https://github.com/grandyang"},"isArchived":false,"isPrivate":false,"databaseId":189444423,"slashCommandsEnabled":false,"viewerCanInteract":false,"viewerInteractionLimitReasonHTML":"","planFeatures":{"maximumAssignees":10},"visibility":"PUBLIC","pinnedIssues":{"totalCount":0},"viewerCanPinIssues":false,"issueTypes":null},"titleHTML":"[LeetCode] 1345. Jump Game IV","url":"https://github.com/grandyang/leetcode/issues/1345","viewerCanUpdateNext":false,"issueType":null,"state":"OPEN","stateReason":null,"duplicateOf":null,"linkedPullRequests":{"nodes":[]},"subIssuesSummary":{"total":0,"completed":0},"__isLabelable":"Issue","labels":{"edges":[],"pageInfo":{"endCursor":null,"hasNextPage":false}},"__isNode":"Issue","assignees":{"nodes":[]},"milestone":null,"databaseId":450396712,"viewerDidAuthor":false,"locked":false,"author":{"__typename":"User","__isActor":"User","login":"grandyang","id":"MDQ6VXNlcjg1NTMwMTA=","profileUrl":"https://github.com/grandyang","avatarUrl":"https://avatars.githubusercontent.com/u/8553010?u=e77fff8485af7a0dd7160048240bf9272e4be8cf\u0026v=4"},"__isComment":"Issue","body":" \n\n\nGiven an array of integers `arr`, you are initially positioned at the first index of the array.\n\nIn one step you can jump from index `i` to index:\n\n * `i + 1` where: `i + 1 \u003c arr.length`.\n * `i - 1` where: `i - 1 \u003e= 0`.\n * `j` where: `arr[i] == arr[j]` and `i != j`.\n\n\n\nReturn _the minimum number of steps_ to reach the **last index** of the array.\n\nNotice that you can not jump outside of the array at any time.\n\n**Example 1:**\n\n**Input:** arr = [100,-23,-23,404,100,23,23,23,3,404] \n**Output:** 3 \n**Explanation:** You need three jumps from index 0 --\u003e 4 --\u003e 3 --\u003e 9\\. Note that index 9 is the last index of the array.\n\n**Example 2:**\n\n**Input:** arr = [7] \n**Output:** 0 \n**Explanation:** Start index is the last index. You do not need to jump.\n\n**Example 3:**\n\n**Input:** arr = [7,6,9,6,9,6,9,7] \n**Output:** 1 \n**Explanation:** You can jump directly from index 0 to index 7 which is last index of the array.\n\n**Constraints:**\n\n * `1 \u003c= arr.length \u003c= 5 * 104`\n * `-108 \u003c= arr[i] \u003c= 108`\n\n \n\n\n这道题是跳跃游戏 Jump Game 系列的第四道题,这个系列目前至少已经有八道题了,每道题都有些许不同,基本都是跳跃的方式不同,这道题说是每次可以跳到左右相邻的两个位置,以及所有和当前位置上的数字相同的位置。这道题独特的地方就是这个可以跳到和当前位置上数字相同的任意位置,相当于开了一个虫洞,可以连接任意两个点,这也是本题的难点所在。这里求的是到达数组末尾位置的最少跳跃步数,如果把每个位置都当作一个结点,能到达的下一个位置当作与之相连的结点,则左右两个位置,以及相同数字的位置都是相邻的结点,这样看的话数组就变成了一个无向图,则最小步数就是起始结点和目标结点间的最短距离了。\n\n想通了这种转换,就可以通过图的遍历来求最短距离了,这里使用广度优先遍历 BFS 是比较合适的。由于需要遍历每个结点的所有相邻结点,就需要快速知道相同数字的位置都有哪些,这里使用一个 HashMap 来建立每个数字跟所有出现该数字位置的集合之间的映射,只需要遍历一遍原数组,就可以建立好这个 HashMap。之后就是 BFS 的实现了,使用队列 queue 来辅助遍历,队列里放数组坐标,初始化把位置0放进去。BFS 遍历需要避免重复,即需要知道哪些结点已经访问过了,博主最开始想的是用一个布尔型的 visited 数组来记录每个位置是否访问过,但是这种方法最终超时了 Time Limit Exceed,这里需要利用之前建立的 HashMap 来优化一下 BFS。使用一个 while 循环开始 BFS 遍历,因为要求最短距离,这里用一个 for 循环进行层序遍历,一次要处理完每一层的结点。\n\n在 for 循环中,取出队首结点,然后判断是否是末尾位置,是的话就返回结果 res。否则就要将其所有相邻的结点加入队列,先来找左右相邻的结点,左结点存在的条件是当前坐标位置大于0,同时没有被访问过,如何确定没有被访问过呢,就看该位置上的数字是否在 HashMap 中存在(因为最开始时建立了数组中所有数字的映射),存在的话就将左位置排入队列。同理,对右结点进行相同的操作。接下来就是处理相同数字位置了,根据之前建立 HashMap 找到所有相同数字的位置,并进行遍历,将不是当前位置的所有位置排入队列。最后在 HashMap 中将当前数字移除,因为当前数字已经访问完了,这样 HashMap 帮助我们进行去重复操作了。for 循环结束后,结果 res 自增1即可,参见代码如下:\n\n \n\n \n \n class Solution {\n public:\n int minJumps(vector\u003cint\u003e\u0026 arr) {\n int res = 0, n = arr.size();\n unordered_map\u003cint, vector\u003cint\u003e\u003e m;\n queue\u003cint\u003e q{{0}};\n for (int i = 0; i \u003c n; ++i) {\n m[arr[i]].push_back(i);\n }\n while (!q.empty()) {\n for (int i = q.size(); i \u003e 0; --i) {\n int t = q.front(); q.pop();\n if (t == n - 1) return res;\n if (t \u003e 0 \u0026\u0026 m.count(arr[t - 1])) {\n q.push(t - 1);\n }\n if (t \u003c n - 1 \u0026\u0026 m.count(arr[t + 1])) {\n q.push(t + 1);\n }\n if (m.count(arr[t])) {\n for (int idx : m[arr[t]]) {\n if (idx != t) {\n q.push(idx);\n }\n }\n }\n m.erase(arr[t]);\n }\n ++res;\n }\n return res;\n }\n };\n \n\n \n\n\nGithub 同步地址:\n\n\u003chttps://github.com/grandyang/leetcode/issues/1345\u003e\n\n \n\n\n类似题目:\n\n[Jump Game](http://www.cnblogs.com/grandyang/p/4371526.html)\n\n[Jump Game II](http://www.cnblogs.com/grandyang/p/4373533.html)\n\n[Jump Game III](https://www.cnblogs.com/grandyang/p/16367963.html)\n\n[Jump Game V](https://www.cnblogs.com/grandyang/p/17317999.html)\n\nJump Game VI\n\nJump Game VII\n\nJump Game VIII\n\n \n\n\n参考资料:\n\n\u003chttps://leetcode.com/problems/jump-game-iv/\u003e\n\n\u003chttps://leetcode.com/problems/jump-game-iv/solutions/502699/java-c-bfs-solution-clean-code-o-n/\u003e\n\n\u003chttps://leetcode.com/problems/jump-game-iv/solutions/1690813/best-explanation-ever-possible-for-this-question/\u003e\n\n \n\n\n[LeetCode All in One 题目讲解汇总(持续更新中...)](https://www.cnblogs.com/grandyang/p/4606334.html)\n\n \n\n\n[ (欢迎加入博主的知识星球,博主将及时答疑解惑,并分享刷题经验与总结,快快加入吧~) ](https://t.zsxq.com/02qRNVBYv)\n\n \n[![知识星球](https://blog-static.cnblogs.com/files/grandyang/zsxq.gif)](https://t.zsxq.com/02qRNVBYv) **喜欢请点赞,疼爱请打赏❤️~.~** \n\n\n \n**微信打赏** \n\n\n \n![](https://blog-static.cnblogs.com/files/grandyang/wepay.gif) | \n\n \n**Venmo 打赏** \n\n\n \n![](https://blog-static.cnblogs.com/files/grandyang/venmo.gif) \n---|---\n","bodyHTML":"\u003cp dir=\"auto\"\u003eGiven an array of integers \u003ccode class=\"notranslate\"\u003earr\u003c/code\u003e, you are initially positioned at the first index of the array.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn one step you can jump from index \u003ccode class=\"notranslate\"\u003ei\u003c/code\u003e to index:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode class=\"notranslate\"\u003ei + 1\u003c/code\u003e where: \u003ccode class=\"notranslate\"\u003ei + 1 \u0026lt; arr.length\u003c/code\u003e.\u003c/li\u003e\n\u003cli\u003e\u003ccode class=\"notranslate\"\u003ei - 1\u003c/code\u003e where: \u003ccode class=\"notranslate\"\u003ei - 1 \u0026gt;= 0\u003c/code\u003e.\u003c/li\u003e\n\u003cli\u003e\u003ccode class=\"notranslate\"\u003ej\u003c/code\u003e where: \u003ccode class=\"notranslate\"\u003earr[i] == arr[j]\u003c/code\u003e and \u003ccode class=\"notranslate\"\u003ei != j\u003c/code\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eReturn \u003cem\u003ethe minimum number of steps\u003c/em\u003e to reach the \u003cstrong\u003elast index\u003c/strong\u003e of the array.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eNotice that you can not jump outside of the array at any time.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eExample 1:\u003c/strong\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eInput:\u003c/strong\u003e arr = [100,-23,-23,404,100,23,23,23,3,404]\u003cbr\u003e\n\u003cstrong\u003eOutput:\u003c/strong\u003e 3\u003cbr\u003e\n\u003cstrong\u003eExplanation:\u003c/strong\u003e You need three jumps from index 0 --\u0026gt; 4 --\u0026gt; 3 --\u0026gt; 9. Note that index 9 is the last index of the array.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eExample 2:\u003c/strong\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eInput:\u003c/strong\u003e arr = [7]\u003cbr\u003e\n\u003cstrong\u003eOutput:\u003c/strong\u003e 0\u003cbr\u003e\n\u003cstrong\u003eExplanation:\u003c/strong\u003e Start index is the last index. You do not need to jump.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eExample 3:\u003c/strong\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eInput:\u003c/strong\u003e arr = [7,6,9,6,9,6,9,7]\u003cbr\u003e\n\u003cstrong\u003eOutput:\u003c/strong\u003e 1\u003cbr\u003e\n\u003cstrong\u003eExplanation:\u003c/strong\u003e You can jump directly from index 0 to index 7 which is last index of the array.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eConstraints:\u003c/strong\u003e\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode class=\"notranslate\"\u003e1 \u0026lt;= arr.length \u0026lt;= 5 * 104\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode class=\"notranslate\"\u003e-108 \u0026lt;= arr[i] \u0026lt;= 108\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003e这道题是跳跃游戏 Jump Game 系列的第四道题,这个系列目前至少已经有八道题了,每道题都有些许不同,基本都是跳跃的方式不同,这道题说是每次可以跳到左右相邻的两个位置,以及所有和当前位置上的数字相同的位置。这道题独特的地方就是这个可以跳到和当前位置上数字相同的任意位置,相当于开了一个虫洞,可以连接任意两个点,这也是本题的难点所在。这里求的是到达数组末尾位置的最少跳跃步数,如果把每个位置都当作一个结点,能到达的下一个位置当作与之相连的结点,则左右两个位置,以及相同数字的位置都是相邻的结点,这样看的话数组就变成了一个无向图,则最小步数就是起始结点和目标结点间的最短距离了。\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e想通了这种转换,就可以通过图的遍历来求最短距离了,这里使用广度优先遍历 BFS 是比较合适的。由于需要遍历每个结点的所有相邻结点,就需要快速知道相同数字的位置都有哪些,这里使用一个 HashMap 来建立每个数字跟所有出现该数字位置的集合之间的映射,只需要遍历一遍原数组,就可以建立好这个 HashMap。之后就是 BFS 的实现了,使用队列 queue 来辅助遍历,队列里放数组坐标,初始化把位置0放进去。BFS 遍历需要避免重复,即需要知道哪些结点已经访问过了,博主最开始想的是用一个布尔型的 visited 数组来记录每个位置是否访问过,但是这种方法最终超时了 Time Limit Exceed,这里需要利用之前建立的 HashMap 来优化一下 BFS。使用一个 while 循环开始 BFS 遍历,因为要求最短距离,这里用一个 for 循环进行层序遍历,一次要处理完每一层的结点。\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e在 for 循环中,取出队首结点,然后判断是否是末尾位置,是的话就返回结果 res。否则就要将其所有相邻的结点加入队列,先来找左右相邻的结点,左结点存在的条件是当前坐标位置大于0,同时没有被访问过,如何确定没有被访问过呢,就看该位置上的数字是否在 HashMap 中存在(因为最开始时建立了数组中所有数字的映射),存在的话就将左位置排入队列。同理,对右结点进行相同的操作。接下来就是处理相同数字位置了,根据之前建立 HashMap 找到所有相同数字的位置,并进行遍历,将不是当前位置的所有位置排入队列。最后在 HashMap 中将当前数字移除,因为当前数字已经访问完了,这样 HashMap 帮助我们进行去重复操作了。for 循环结束后,结果 res 自增1即可,参见代码如下:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"class Solution {\npublic:\n int minJumps(vector\u0026lt;int\u0026gt;\u0026amp; arr) {\n int res = 0, n = arr.size();\n unordered_map\u0026lt;int, vector\u0026lt;int\u0026gt;\u0026gt; m;\n queue\u0026lt;int\u0026gt; q{{0}};\n for (int i = 0; i \u0026lt; n; ++i) {\n m[arr[i]].push_back(i);\n }\n while (!q.empty()) {\n for (int i = q.size(); i \u0026gt; 0; --i) {\n int t = q.front(); q.pop();\n if (t == n - 1) return res;\n if (t \u0026gt; 0 \u0026amp;\u0026amp; m.count(arr[t - 1])) {\n q.push(t - 1);\n }\n if (t \u0026lt; n - 1 \u0026amp;\u0026amp; m.count(arr[t + 1])) {\n q.push(t + 1);\n }\n if (m.count(arr[t])) {\n for (int idx : m[arr[t]]) {\n if (idx != t) {\n q.push(idx);\n }\n }\n }\n m.erase(arr[t]);\n }\n ++res;\n }\n return res;\n }\n};\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode class=\"notranslate\"\u003eclass Solution {\npublic:\n int minJumps(vector\u0026lt;int\u0026gt;\u0026amp; arr) {\n int res = 0, n = arr.size();\n unordered_map\u0026lt;int, vector\u0026lt;int\u0026gt;\u0026gt; m;\n queue\u0026lt;int\u0026gt; q{{0}};\n for (int i = 0; i \u0026lt; n; ++i) {\n m[arr[i]].push_back(i);\n }\n while (!q.empty()) {\n for (int i = q.size(); i \u0026gt; 0; --i) {\n int t = q.front(); q.pop();\n if (t == n - 1) return res;\n if (t \u0026gt; 0 \u0026amp;\u0026amp; m.count(arr[t - 1])) {\n q.push(t - 1);\n }\n if (t \u0026lt; n - 1 \u0026amp;\u0026amp; m.count(arr[t + 1])) {\n q.push(t + 1);\n }\n if (m.count(arr[t])) {\n for (int idx : m[arr[t]]) {\n if (idx != t) {\n q.push(idx);\n }\n }\n }\n m.erase(arr[t]);\n }\n ++res;\n }\n return res;\n }\n};\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eGithub 同步地址:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca class=\"issue-link js-issue-link\" data-error-text=\"Failed to load title\" data-id=\"450396712\" data-permission-text=\"Title is private\" data-url=\"https://github.com/grandyang/leetcode/issues/1345\" data-hovercard-type=\"issue\" data-hovercard-url=\"/grandyang/leetcode/issues/1345/hovercard\" href=\"https://github.com/grandyang/leetcode/issues/1345\"\u003e#1345\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e类似题目:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://www.cnblogs.com/grandyang/p/4371526.html\" rel=\"nofollow\"\u003eJump Game\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://www.cnblogs.com/grandyang/p/4373533.html\" rel=\"nofollow\"\u003eJump Game II\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://www.cnblogs.com/grandyang/p/16367963.html\" rel=\"nofollow\"\u003eJump Game III\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://www.cnblogs.com/grandyang/p/17317999.html\" rel=\"nofollow\"\u003eJump Game V\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eJump Game VI\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eJump Game VII\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eJump Game VIII\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e参考资料:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://leetcode.com/problems/jump-game-iv/\" rel=\"nofollow\"\u003ehttps://leetcode.com/problems/jump-game-iv/\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://leetcode.com/problems/jump-game-iv/solutions/502699/java-c-bfs-solution-clean-code-o-n/\" rel=\"nofollow\"\u003ehttps://leetcode.com/problems/jump-game-iv/solutions/502699/java-c-bfs-solution-clean-code-o-n/\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://leetcode.com/problems/jump-game-iv/solutions/1690813/best-explanation-ever-possible-for-this-question/\" rel=\"nofollow\"\u003ehttps://leetcode.com/problems/jump-game-iv/solutions/1690813/best-explanation-ever-possible-for-this-question/\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://www.cnblogs.com/grandyang/p/4606334.html\" rel=\"nofollow\"\u003eLeetCode All in One 题目讲解汇总(持续更新中...)\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://t.zsxq.com/02qRNVBYv\" rel=\"nofollow\"\u003e (欢迎加入博主的知识星球,博主将及时答疑解惑,并分享刷题经验与总结,快快加入吧~) \u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://t.zsxq.com/02qRNVBYv\" rel=\"nofollow\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/b00c4615cf899b62d5a4ddfccbab04b34f8835714f9b2fae28a61d8a70e98d62/68747470733a2f2f626c6f672d7374617469632e636e626c6f67732e636f6d2f66696c65732f6772616e6479616e672f7a7378712e676966\" alt=\"知识星球\" data-animated-image=\"\" data-canonical-src=\"https://blog-static.cnblogs.com/files/grandyang/zsxq.gif\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e \u003cstrong\u003e喜欢请点赞,疼爱请打赏❤️~.~\u003c/strong\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003e微信打赏\u003c/strong\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://camo.githubusercontent.com/e6acd0ed55e6818484ea98c8143919527646ec720d8cf86ca13c4e02606880e4/68747470733a2f2f626c6f672d7374617469632e636e626c6f67732e636f6d2f66696c65732f6772616e6479616e672f77657061792e676966\"\u003e\u003cimg src=\"https://camo.githubusercontent.com/e6acd0ed55e6818484ea98c8143919527646ec720d8cf86ca13c4e02606880e4/68747470733a2f2f626c6f672d7374617469632e636e626c6f67732e636f6d2f66696c65732f6772616e6479616e672f77657061792e676966\" alt=\"\" data-animated-image=\"\" data-canonical-src=\"https://blog-static.cnblogs.com/files/grandyang/wepay.gif\" style=\"max-width: 100%;\"\u003e\u003c/a\u003e |\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003cstrong\u003eVenmo 打赏\u003c/strong\u003e\u003c/p\u003e\n\u003cp 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src="https://avatars.githubusercontent.com/u/8553010?u=e77fff8485af7a0dd7160048240bf9272e4be8cf&amp;v=4&amp;size=48" data-testid="github-avatar"/></a></div><div class="Box-sc-g0xbh4-0 koxHLL ActivityHeader-module__narrowViewportWrapper--Hjl75"><div class="Box-sc-g0xbh4-0 dqmClk"><a class="Box-sc-g0xbh4-0 cRhwji prc-Link-Link-85e08" href="https://github.com/grandyang" data-hovercard-url="/users/grandyang/hovercard" data-testid="issue-body-header-author">grandyang</a></div><div class="Box-sc-g0xbh4-0 bJQcYY ActivityHeader-module__footer--FVHp7"><span>opened </span><a class="Box-sc-g0xbh4-0 bjFvWy prc-Link-Link-85e08" href="https://github.com/grandyang/leetcode/issues/1345#issue-450396712" data-testid="issue-body-header-link"><relative-time sx="[object Object]" class="sc-aXZVg gcWyXp">on <!-- -->May 30, 2019</relative-time></a></div></div><div class="Box-sc-g0xbh4-0 kgTqOk ActivityHeader-module__narrowViewportWrapper--Hjl75"><div class="Box-sc-g0xbh4-0 izrTon ActivityHeader-module__edits--LwHTE"></div><div class="Box-sc-g0xbh4-0 kpoUe"><div class="Box-sc-g0xbh4-0 ezcJRX"></div><div class="Box-sc-g0xbh4-0 dnyPuu"><button data-component="IconButton" type="button" aria-haspopup="true" aria-expanded="false" tabindex="0" class="prc-Button-ButtonBase-c50BI prc-Button-IconButton-szpyj" data-loading="false" data-no-visuals="true" data-size="small" data-variant="invisible" aria-describedby=":R15bd5db:-loading-announcement" aria-labelledby=":Rv5bd5db:" id=":R15bd5db:"><svg aria-hidden="true" focusable="false" class="octicon octicon-kebab-horizontal" viewBox="0 0 16 16" width="16" height="16" fill="currentColor" display="inline-block" overflow="visible" style="vertical-align:text-bottom"><path d="M8 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3ZM1.5 9a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Zm13 0a1.5 1.5 0 1 0 0-3 1.5 1.5 0 0 0 0 3Z"></path></svg></button><span class="prc-TooltipV2-Tooltip-cYMVY" data-direction="s" aria-hidden="true" id=":Rv5bd5db:">Issue body actions</span></div></div></div></div></div><div class="IssueBodyViewer-module__IssueBody--MXyFt"><div data-testid="markdown-body" data-team-hovercards-enabled="true" class="markdown-body" data-turbolinks="false"><div class="Box-sc-g0xbh4-0 markdown-body NewMarkdownViewer-module__safe-html-box--cRsz0"><p dir="auto">Given an array of integers <code class="notranslate">arr</code>, you are initially positioned at the first index of the array.</p> <p dir="auto">In one step you can jump from index <code class="notranslate">i</code> to index:</p> <ul dir="auto"> <li><code class="notranslate">i + 1</code> where: <code class="notranslate">i + 1 &lt; arr.length</code>.</li> <li><code class="notranslate">i - 1</code> where: <code class="notranslate">i - 1 &gt;= 0</code>.</li> <li><code class="notranslate">j</code> where: <code class="notranslate">arr[i] == arr[j]</code> and <code class="notranslate">i != j</code>.</li> </ul> <p dir="auto">Return <em>the minimum number of steps</em> to reach the <strong>last index</strong> of the array.</p> <p dir="auto">Notice that you can not jump outside of the array at any time.</p> <p dir="auto"><strong>Example 1:</strong></p> <p dir="auto"><strong>Input:</strong> arr = [100,-23,-23,404,100,23,23,23,3,404]<br> <strong>Output:</strong> 3<br> <strong>Explanation:</strong> You need three jumps from index 0 --&gt; 4 --&gt; 3 --&gt; 9. Note that index 9 is the last index of the array.</p> <p dir="auto"><strong>Example 2:</strong></p> <p dir="auto"><strong>Input:</strong> arr = [7]<br> <strong>Output:</strong> 0<br> <strong>Explanation:</strong> Start index is the last index. You do not need to jump.</p> <p dir="auto"><strong>Example 3:</strong></p> <p dir="auto"><strong>Input:</strong> arr = [7,6,9,6,9,6,9,7]<br> <strong>Output:</strong> 1<br> <strong>Explanation:</strong> You can jump directly from index 0 to index 7 which is last index of the array.</p> <p dir="auto"><strong>Constraints:</strong></p> <ul dir="auto"> <li><code class="notranslate">1 &lt;= arr.length &lt;= 5 * 104</code></li> <li><code class="notranslate">-108 &lt;= arr[i] &lt;= 108</code></li> </ul> <p dir="auto">这道题是跳跃游戏 Jump Game 系列的第四道题,这个系列目前至少已经有八道题了,每道题都有些许不同,基本都是跳跃的方式不同,这道题说是每次可以跳到左右相邻的两个位置,以及所有和当前位置上的数字相同的位置。这道题独特的地方就是这个可以跳到和当前位置上数字相同的任意位置,相当于开了一个虫洞,可以连接任意两个点,这也是本题的难点所在。这里求的是到达数组末尾位置的最少跳跃步数,如果把每个位置都当作一个结点,能到达的下一个位置当作与之相连的结点,则左右两个位置,以及相同数字的位置都是相邻的结点,这样看的话数组就变成了一个无向图,则最小步数就是起始结点和目标结点间的最短距离了。</p> <p dir="auto">想通了这种转换,就可以通过图的遍历来求最短距离了,这里使用广度优先遍历 BFS 是比较合适的。由于需要遍历每个结点的所有相邻结点,就需要快速知道相同数字的位置都有哪些,这里使用一个 HashMap 来建立每个数字跟所有出现该数字位置的集合之间的映射,只需要遍历一遍原数组,就可以建立好这个 HashMap。之后就是 BFS 的实现了,使用队列 queue 来辅助遍历,队列里放数组坐标,初始化把位置0放进去。BFS 遍历需要避免重复,即需要知道哪些结点已经访问过了,博主最开始想的是用一个布尔型的 visited 数组来记录每个位置是否访问过,但是这种方法最终超时了 Time Limit Exceed,这里需要利用之前建立的 HashMap 来优化一下 BFS。使用一个 while 循环开始 BFS 遍历,因为要求最短距离,这里用一个 for 循环进行层序遍历,一次要处理完每一层的结点。</p> <p dir="auto">在 for 循环中,取出队首结点,然后判断是否是末尾位置,是的话就返回结果 res。否则就要将其所有相邻的结点加入队列,先来找左右相邻的结点,左结点存在的条件是当前坐标位置大于0,同时没有被访问过,如何确定没有被访问过呢,就看该位置上的数字是否在 HashMap 中存在(因为最开始时建立了数组中所有数字的映射),存在的话就将左位置排入队列。同理,对右结点进行相同的操作。接下来就是处理相同数字位置了,根据之前建立 HashMap 找到所有相同数字的位置,并进行遍历,将不是当前位置的所有位置排入队列。最后在 HashMap 中将当前数字移除,因为当前数字已经访问完了,这样 HashMap 帮助我们进行去重复操作了。for 循环结束后,结果 res 自增1即可,参见代码如下:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="class Solution { public: int minJumps(vector&lt;int&gt;&amp; arr) { int res = 0, n = arr.size(); unordered_map&lt;int, vector&lt;int&gt;&gt; m; queue&lt;int&gt; q{{0}}; for (int i = 0; i &lt; n; ++i) { m[arr[i]].push_back(i); } while (!q.empty()) { for (int i = q.size(); i &gt; 0; --i) { int t = q.front(); q.pop(); if (t == n - 1) return res; if (t &gt; 0 &amp;&amp; m.count(arr[t - 1])) { q.push(t - 1); } if (t &lt; n - 1 &amp;&amp; m.count(arr[t + 1])) { q.push(t + 1); } if (m.count(arr[t])) { for (int idx : m[arr[t]]) { if (idx != t) { q.push(idx); } } } m.erase(arr[t]); } ++res; } return res; } };"><pre class="notranslate"><code class="notranslate">class Solution { public: int minJumps(vector&lt;int&gt;&amp; arr) { int res = 0, n = arr.size(); unordered_map&lt;int, vector&lt;int&gt;&gt; m; queue&lt;int&gt; q{{0}}; for (int i = 0; i &lt; n; ++i) { m[arr[i]].push_back(i); } while (!q.empty()) { for (int i = q.size(); i &gt; 0; --i) { int t = q.front(); q.pop(); if (t == n - 1) return res; if (t &gt; 0 &amp;&amp; m.count(arr[t - 1])) { q.push(t - 1); } if (t &lt; n - 1 &amp;&amp; m.count(arr[t + 1])) { q.push(t + 1); } if (m.count(arr[t])) { for (int idx : m[arr[t]]) { if (idx != t) { q.push(idx); } } } m.erase(arr[t]); } ++res; } return res; } }; </code></pre></div> <p dir="auto">Github 同步地址:</p> <p dir="auto"><a class="issue-link js-issue-link" data-error-text="Failed to load title" data-id="450396712" data-permission-text="Title is private" data-url="https://github.com/grandyang/leetcode/issues/1345" data-hovercard-type="issue" data-hovercard-url="/grandyang/leetcode/issues/1345/hovercard" href="https://github.com/grandyang/leetcode/issues/1345">#1345</a></p> <p dir="auto">类似题目:</p> <p dir="auto"><a href="http://www.cnblogs.com/grandyang/p/4371526.html" rel="nofollow">Jump Game</a></p> <p dir="auto"><a href="http://www.cnblogs.com/grandyang/p/4373533.html" rel="nofollow">Jump Game II</a></p> <p dir="auto"><a href="https://www.cnblogs.com/grandyang/p/16367963.html" rel="nofollow">Jump Game III</a></p> <p dir="auto"><a href="https://www.cnblogs.com/grandyang/p/17317999.html" rel="nofollow">Jump Game V</a></p> <p dir="auto">Jump Game VI</p> <p dir="auto">Jump Game VII</p> <p dir="auto">Jump Game VIII</p> <p dir="auto">参考资料:</p> <p dir="auto"><a 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3.996v2.5a.75.75 0 0 1-1.5 0v-2.5a.75.75 0 0 1 1.5 0ZM9 11a1 1 0 1 1-2 0 1 1 0 0 1 2 0Z"></path> </svg> <button type="button" class="flash-close js-ajax-error-dismiss" aria-label="Dismiss error"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> You can’t perform that action at this time. </div> <template id="site-details-dialog"> <details class="details-reset details-overlay details-overlay-dark lh-default color-fg-default hx_rsm" open> <summary role="button" aria-label="Close dialog"></summary> <details-dialog class="Box Box--overlay d-flex flex-column anim-fade-in fast hx_rsm-dialog hx_rsm-modal"> <button class="Box-btn-octicon m-0 btn-octicon position-absolute right-0 top-0" type="button" aria-label="Close dialog" data-close-dialog> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> <div class="octocat-spinner my-6 js-details-dialog-spinner"></div> </details-dialog> </details> </template> <div class="Popover js-hovercard-content position-absolute" style="display: none; outline: none;"> <div class="Popover-message Popover-message--bottom-left Popover-message--large Box color-shadow-large" style="width:360px;"> </div> </div> <template id="snippet-clipboard-copy-button"> <div class="zeroclipboard-container position-absolute right-0 top-0"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn js-clipboard-copy m-2 p-0" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>

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