Problem 15 - Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?

本文探讨了一个20x20网格中从左上角到右下角的不同路径数量问题,在不回头的情况下,通过组合数学原理计算可能的路径总数。文章提供了一种简单的方法来计算这一数值:利用排列组合公式 (m+n)!/(m!n!) 来求解。
 
题目:

Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 2020 grid?


	/**
	 * 
	 * 1. from 0,0 to m,n, it needs m+n steps.
	 * 
	 * 2. u need m steps to forward right.
	 * 
	 * 3. so, it's a simple permutation (m+n)!/(m!n!)
	 * 
	 * 4. It just like that u have 20 same red balls and 20 same blue balls.
	 * how many permutation there are.
	 * 
	 * @param m
	 * @param n
	 * @return
	 */
	public static long findRoutes(int m, int n) {
		BigDecimal bd = BigDecimal.ONE;
		for (int i = n + 1; i <= m + n; i++) {
			bd = bd.multiply(new BigDecimal(i));
		}

		for (int i = 1; i <= m; i++) {
			bd = bd.divide(new BigDecimal(i));
		}
		System.out.println("----" + bd);
		return bd.longValue();
	}

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Living in a **post–Spring Cloud Netflix** world means embracing the evolution of microservices architecture beyond the once-dominant stack of **Eureka, Ribbon, Hystrix, and Zuul**, which have all entered maintenance mode or been deprecated by Netflix and later removed from Spring Cloud. The good news? The ecosystem has matured. You're not losing functionality — you're gaining **more flexibility, cloud-native alignment, and better integration with modern platforms like Kubernetes**. Here’s how to thrive in this new era: --- ### 🔚 Why Did Spring Cloud Netflix End? | Component | Status | Reason | |---------|--------|--------| | **Eureka** | In maintenance (Netflix) | Self-preservation mode; no new features | | **Ribbon** | Deprecated | Client-side load balancing replaced by Spring Cloud LoadBalancer | | **Hystrix** | Deprecated | Circuit breaking evolved into Resilience4j and resilience patterns | | **Zuul 1/2** | Abandoned | Outdated model; replaced by Spring Cloud Gateway | > ⚠️ As of **Spring Cloud 2020.0.0 (Ilford)**, these components are **no longer included** in the default release train. --- ## ✅ How to Adapt: Key Replacements & Strategies ### 1. ❌ Replace Eureka with Service Discovery Alternatives #### 🔄 Option A: Use **Spring Cloud Kubernetes** - Automatically discovers services via Kubernetes DNS and APIs. - No need for a separate registry. ```yaml # application.yml spring: cloud: kubernetes: discovery: all-namespaces: false ``` ✅ Pros: Native to K8s, zero additional infrastructure ❌ Cons: Tied to Kubernetes only #### 🔄 Option B: Use **Hashicorp Consul** - Full-service mesh capabilities. - Health checks, KV store, UI. ```xml <dependency> <groupId>org.springframework.cloud</groupId> <artifactId>spring-cloud-starter-consul-discovery</artifactId> </dependency> ``` ✅ Pros: Multi-platform, rich feature set ❌ Cons: Requires running Consul agents/servers #### 🔄 Option C: Use **Nacos (by Alibaba)** - Dynamic service discovery, config management, and service metadata. - Popular in China and growing globally. ```xml <dependency> <groupId>com.alibaba.cloud</groupId> <artifactId>spring-cloud-starter-alibaba-nacos-discovery</artifactId> </dependency> ``` ✅ Pros: All-in-one solution (config + discovery) ❌ Cons: Less familiar outside Alibaba ecosystem --- ### 2. ❌ Replace Ribbon with Spring Cloud LoadBalancer Now the **default client-side load balancer**. #### Usage Example: ```java @RestController public class MyController { @LoadBalanced @Bean WebClient.Builder webClientBuilder() { return WebClient.builder(); } @Autowired WebClient.Builder webClientBuilder; @GetMapping("/call-service") public Mono<String> callService() { return webClientBuilder.build() .get().uri("http://my-microservice/api/data") .retrieve() .bodyToMono(String.class); } } ``` No configuration needed if using `spring-cloud-starter-loadbalancer`. ✅ Supports reactive (`WebClient`) and imperative (`RestTemplate`) styles ✅ Pluggable: Can integrate with service mesh or custom providers --- ### 3. ❌ Replace Hystrix with Resilience4j Modern, functional, lightweight circuit breaker and fault tolerance library. #### Add Dependency: ```xml <dependency> <groupId>org.springframework.cloud</groupId> <artifactId>spring-cloud-starter-circuitbreaker-resilience4j</artifactId> </dependency> ``` #### Configure Circuit Breaker: ```yaml resilience4j: circuitbreaker: instances: backendA: failureRateThreshold: 50 waitDurationInOpenState: 5000ms ringBufferSizeInHalfOpenState: 3 ``` #### Use It: ```java @CircuitBreaker(name = "backendA", fallbackMethod = "fallback") public String getData() { return webClient.get().uri("/api/data").retrieve().bodyToMono(String.class).block(); } public String fallback(Exception e) { return "Fallback response"; } ``` ✅ Lightweight, thread-isolated or semaphore-based ✅ Integrates well with Micrometer, Retry, Rate Limiter, Bulkhead --- ### 4. ❌ Replace Zuul with Spring Cloud Gateway The **official successor**: built on **Spring WebFlux (Reactor)**, fully non-blocking, high-performance API gateway. #### Features: - Route matching (path, host, headers) - Filters (pre/post) - Rate limiting - WebSocket support - Integration with OAuth2, Security, etc. #### Example Route Configuration: ```yaml spring: cloud: gateway: routes: - id: user-service uri: lb://user-service predicates: - Path=/users/** filters: - RewritePath=/users/(?<path>.*), /$\{path} ``` > `lb://` means use load balancing via Spring Cloud LoadBalancer. ✅ High throughput, low latency ✅ Reactive stack enables scalability ✅ Rich filter ecosystem --- ### 5. Embrace Platform-Native Patterns (Especially on Kubernetes) Instead of building your own resilience layer, consider leveraging: | Tool | Purpose | |------|--------| | **Istio / Linkerd** | Service mesh for mTLS, retries, timeouts, observability | | **Kubernetes Services & Ingress** | Built-in routing, health checks, rolling updates | | **Argo Rollouts / Flagger** | Progressive delivery (canary, blue/green) | | **Prometheus + Grafana + OpenTelemetry** | Observability without Hystrix Dashboard | > 💡 Think: *"Do I really need client-side logic?"* Often, the answer is **no** — let the platform handle it. --- ## 🧭 Mindset Shift: From Library-Centric to Platform-Centric | Old World (Netflix Stack) | New World (Cloud-Native) | |---------------------------|----------------------------| | Run everything inside JVM | Leverage sidecars and operators | | Build resilience in code | Defer to service mesh | | Manage discovery manually | Use K8s DNS/service abstraction | | Monolithic gateways | Edge + service mesh split | | Centralized tooling | GitOps, declarative configs | 👉 Focus shifts from **"what libraries do I add?"** to **"how is my platform configured?"** --- ## 🛠️ Migration Checklist | Step | Action | |------|--------| | 1 | Remove `spring-cloud-starter-netflix-*` dependencies | | 2 | Add `spring-cloud-starter-loadbalancer` | | 3 | Replace `RestTemplate` with `WebClient` (or keep but annotate with `@LoadBalanced`) | | 4 | Switch to `Resilience4j` or rely on service mesh for circuit breaking | | 5 | Replace Zuul with **Spring Cloud Gateway** | | 6 | Choose a discovery mechanism: K8s, Consul, Nacos | | 7 | Adopt externalized config: Config Server → **ConfigMap + Secret / Vault / Nacos** | | 8 | Implement observability: Micrometer + Prometheus + Tracing (Zipkin/Jaeger) | --- ## ✅ Summary: Thriving Post–Spring Cloud Netflix You don’t need Netflix OSS to build resilient, scalable microservices. Instead: > **Use Spring Cloud + Kubernetes + Modern Primitives = Better Outcome** 🔧 Tools you should now embrace: - ✅ **Spring Cloud Gateway** - ✅ **Spring Cloud LoadBalancer** - ✅ **Resilience4j** - ✅ **Spring Cloud Kubernetes / Consul / Nacos** - ✅ **Service Mesh (optional but powerful)** 🎯 Design principles: - Prefer **infrastructure-level resilience** over library-level where possible - Favor **GitOps, declarative config, and automation** - Build **polyglot systems** that aren't tied to Java-only solutions ---
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