基于java下的表达式求导代码（含表达式求导和表达式化简）

这个代码是错误示范，只实现了功能但是结构和逻辑有点乱，还存在一些代码复用未做检查，由于时间有限比较仓促，本代码支持常数函数、指数函数和三角函数以及其复合下的表达式求导

例如5* sin(x) **4* sin(x)+4*x--2,可函数嵌套也可实现函数求导四则运算。

本程序基本功能都已经实现，需要注释的请在下方评论，我看到会进行更新。

import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;public class Qiudao {public String miQiu(String base, int zhi){// 求导int newzhi = zhi - 1;int xi = zhi;String derivative;if(newzhi == 1)derivative = xi + "*" + base;else derivative = xi + "*" + base + "**" + newzhi;// 返回求导结果return derivative;}public String SanjQiu(String san, String jidi){if (san.equals("sin")) {return "cos("+jidi+")";}// 如果表达式为余弦函数，则求导为负的正弦函数else {return "-sin("+jidi+")";}}public String chenQiu(String op1, String op2, String dfdx1, String dfdx2){// 将两个导数按照乘法法则组合起来String xi1 = chen(op1, dfdx2);String xi2 = chen(op2, dfdx1);String result = complexPlus(xi1, xi2);if(result.split("[+]").length!= 1){return "("+result+")";}else return result;}public String plusQiu(String c){String[] factors = c.split("\\+");// 分别求出两个简单函数的导数String dfdx1 = complexQiu(factors[0]);String dfdx2 = complexQiu(factors[1]);// 将两个导数按照乘法法则组合起来String result = Plus(dfdx1, dfdx2);return result;}public ArrayList<String> plusSplit(String s){ArrayList<String> result = new ArrayList<>();s = s.replaceAll("\\s", "");String[] parts = s.split("(?<=[+-]|\\s)|(?<=\\*|\\s)|(?<=[()]|\\s)|(<=[()])");ArrayList<String> format = new ArrayList<>();for (int i = 0; i < parts.length; i++) {if(parts[i].length() >1&&(parts[i].endsWith("*")||parts[i].endsWith("+")||parts[i].endsWith("-")||parts[i].endsWith("(")||parts[i].endsWith(")"))){format.add(parts[i].substring(0, parts[i].length() - 1));format.add(""+parts[i].charAt(parts[i].length()-1));}else if(parts[i].equals("*")&&format.get(format.size()-1).equals("*")){format.set(format.size()-1, "**");}else{format.add(parts[i]);}}String index = "";if(format.get(0).equals("(")) {format.remove(0);format.remove(format.size()-1);}for(int i = 0;i<format.size();i++){if(format.get(i).equals("+")) {result.add(index);index = "";}else{index += format.get(i);}}result.add(index);return result;}public ArrayList<String> MultiSplit(String s){ArrayList<String> result = new ArrayList<>();s = s.replaceAll("\\s", "");String[] parts = s.split("(?<=[+-]|\\s)|(?<=\\*|\\s)|(?<=[()]|\\s)|(<=[()])");ArrayList<String> format = new ArrayList<>();for (int i = 0; i < parts.length; i++) {if(parts[i].length() >1&&(parts[i].endsWith("*")||parts[i].endsWith("+")||parts[i].endsWith("-")||parts[i].endsWith("(")||parts[i].endsWith(")"))){format.add(parts[i].substring(0, parts[i].length() - 1));format.add(""+parts[i].charAt(parts[i].length()-1));}else if(parts[i].equals("*")&&format.get(format.size()-1).equals("*")){format.set(format.size()-1, "**");}else{format.add(parts[i]);}}String index = "";for(int i = 0;i<format.size();i++){if(format.get(i).equals("*")&&!format.get(i+1).equals("*")) {result.add(index);index = "";}else{index += format.get(i);}}result.add(index);return result;}public String chen(String a, String b){if(a.equals("0")||b.equals("0"))return "0";else if(a.equals("1")) return b;else if(b.equals("1")) return a;else if(a.equals("-1"))return "-"+b;else if(b.equals("-1"))return "-"+a;else if(b.charAt(0) == '-'&&a.charAt(0)!= '-') return "-"+a+"*"+b.substring(1, b.length());else if(b.charAt(0) == '-'&&a.charAt(0)== '-') return a+"*"+b.substring(1, b.length());else if(b.charAt(0) == '('){String result = "";ArrayList<String> splits = plusSplit(b.substring(1, b.length()-1));for(int i = 0; i< splits.size();i++){result += a + "*" +splits.get(i)+"+";}return result.substring(0, result.length()-1);}else if(a.charAt(0) == '('){String result = "";ArrayList<String> splits = plusSplit(a.substring(1, a.length()-1));for(int i = 0; i< splits.size();i++){result += b + "*" +splits.get(i)+"+";}return result.substring(0, result.length()-1);}else if(a.charAt(0) == '(' && b.charAt(0) == '('){String result = "";ArrayList<String> split1 = plusSplit(a.substring(1, a.length()-1));ArrayList<String> split2 = plusSplit(b.substring(1, b.length()-1));for(int i = 0; i< split1.size();i++){for(int j = 0; j<split2.size();j++){result += split1.get(i) + "*" +split2.get(j);}result += "+";}return result.substring(0, result.length()-1);}return a + "*" + b;}public String Plus(String a, String b){if(a.equals("0")||a.equals("")) return b;else if(b.equals("0")||b.equals("")) return a;else if(a.matches("\\d+")&&b.matches("\\d+")){int c = Integer.parseInt(a)+Integer.parseInt(b);return Integer.toString(c);}else return a + "+" + b;}public String complexPlus(String a, String b){String result = "";int xi = 0;ArrayList<String> asplit = plusSplit(a);ArrayList<String> bsplit = plusSplit(b);ArrayList<String> res = new ArrayList<>();for(int i = 0; i < asplit.size();i++){if(asplit.get(i).matches("\\d+")){xi += Integer.parseInt(asplit.get(i));}else{res.add(asplit.get(i));}}for(int j = 0; j< bsplit.size(); j++){if(bsplit.get(j).matches("\\d+")){xi += Integer.parseInt(bsplit.get(j));}else{res.add(bsplit.get(j));}}result = Integer.toString(xi);for(int i = 0; i<res.size();i++){result = Plus(result, res.get(i));}return result;}public String jian(String a, String b){if(a.equals("0")) return "-"+b;else if(b.equals("0")) return a;else if(a.matches("\\d+")&&b.matches("\\d+")){int c = Integer.parseInt(a)-Integer.parseInt(b);return Integer.toString(c);}else return a + "-" + b;}public String complexQiu(String s) {if(s.charAt(0) == '(') s = s.substring(1, s.length()-1);Stack<String> biaoda = new Stack<>();Stack<String> operators = new Stack<>();s = s.replaceAll("\\s", "");String[] parts = s.split("(?<=[+-]|\\s)|(?<=\\*|\\s)|(?<=[()]|\\s)|(<=[()])");ArrayList<String> format = new ArrayList<>();for (int i = 0; i < parts.length; i++) {if(parts[i].length() >1&&(parts[i].endsWith("*")||parts[i].endsWith("+")||parts[i].endsWith("-")||parts[i].endsWith("(")||parts[i].endsWith(")"))){format.add(parts[i].substring(0, parts[i].length() - 1));format.add(""+parts[i].charAt(parts[i].length()-1));}else if(parts[i].equals("*")&&format.get(format.size()-1).equals("*")){format.set(format.size()-1, "**");}else{format.add(parts[i]);}}for (int i = 0; i < format.size(); i++) {if(i == 0 && ((format.get(i).equals("+")||format.get(i).equals("-"))&&format.get(i+1).matches("\\d+"))){biaoda.push("0");if(format.get(i).equals("+")) biaoda.push(format.get(i+1));else biaoda.push(format.get(i)+format.get(i+1));i++;}else if(format.get(i).matches("\\d+")){biaoda.push("0");biaoda.push(format.get(i));}else if((i < format.size() - 1&&format.get(i).equals("x")&&(!format.get(i+1).equals("**")))||i == format.size()-1){biaoda.push("1");biaoda.push(format.get(i));}else if(format.get(i).equals("(")){int cout = 1;String bos = "";i++;while(cout > 0){if(format.get(i).equals("("))cout++;if(format.get(i).equals(")"))cout--;bos += format.get(i);i++;}i--;biaoda.push(complexQiu(bos.substring(0, bos.length()-1)));biaoda.push(bos.substring(0, bos.length()-1));}else if(format.get(i).equals("sin")||format.get(i).equals("cos")){String jidi = format.get(i);String cpsqiu = "";String cps = "";i += 2;while(!format.get(i).equals(")")){cps += format.get(i);i++;}if(!cps.equals("x")){cpsqiu = complexQiu(cps);//求导函数 原函数biaoda.push(chen(SanjQiu(jidi, cps), cpsqiu));biaoda.push(jidi+"("+cps+")");}else{biaoda.push(SanjQiu(jidi, cps));biaoda.push(jidi+"("+cps+")");}}else if(format.get(i).equals("**")){String jidi = "";String zhi = "";String yuan = "";if(format.get(i-1).equals(")")){jidi = biaoda.pop();yuan = biaoda.pop();biaoda.push(chen(miQiu(jidi,Integer.parseInt(zhi)), yuan));biaoda.push(jidi+"**"+zhi);}else jidi = format.get(i - 1);zhi = format.get(i+1);i++;//求导函数+原函数biaoda.push(miQiu(jidi, Integer.parseInt(zhi)));biaoda.push(jidi+"**"+zhi);}else if(format.get(i).equals("*")){operators.push(format.get(i));}else if(i<format.size()-1&&(format.get(i).equals("+")||format.get(i).equals("-"))){while(!operators.isEmpty() && operators.peek().equals("*")){operators.pop();String op1 = biaoda.pop();String Qop1 = biaoda.pop();String op2 = biaoda.pop();String Qop2 = biaoda.pop();//求导函数biaoda.push(chenQiu(op1, op2, Qop1, Qop2));//原函数biaoda.push(chen(op2, op1));}if((format.get(i).equals("-")&&format.get(i+1).equals("+"))||(format.get(i).equals("+")&&format.get(i+1).equals("-"))) {operators.push("-");i++;if(biaoda.isEmpty()){String op = operators.pop();if(op.equals("-")) format.set(i+1, op+format.get(i+1));}}else if((format.get(i).equals("-")&&format.get(i+1).equals("-"))||(format.get(i).equals("+")&&format.get(i+1).equals("+"))) {operators.push("+");i++;if(biaoda.isEmpty()){String op = operators.pop();if(op.equals("-")) format.set(i+1, op+format.get(i+1));}}else operators.push(format.get(i));}}while (!operators.isEmpty()) {String operator = operators.pop();if(operator.equals("*")){String op1 = biaoda.pop();String Qop1 = biaoda.pop();String op2 = biaoda.pop();String Qop2 = biaoda.pop();//求导函数biaoda.push(chenQiu(op1, op2, Qop1, Qop2));//原函数biaoda.push(chen(op2, op1));}else{String yop1 = biaoda.pop();String op1 = biaoda.pop();String yop2 = biaoda.pop();String op2 = biaoda.pop();if(operator.equals("+")){biaoda.push(complexPlus(op1,op2));biaoda.push(complexPlus(yop1,yop2));}else{biaoda.push(jian(op1,op2));biaoda.push(jian(yop1,yop2));}}}biaoda.pop();return  biaoda.pop();}public String Simplify(String s){String result = "";ArrayList<String> resdis = new ArrayList<>();ArrayList<String> plusdis = plusSplit(s);HashMap<String, String> alls = new HashMap<>();for(int i = 0; i<plusdis.size();i++){ArrayList<String> multdis = MultiSplit(plusdis.get(i));HashMap<String, Integer> multSim = new HashMap<>();int xi = 1;if(multdis.get(0).charAt(0) == '-') {xi = -1;multdis.set(0, multdis.get(0).substring(1,multdis.get(0).length()));}for(int j = 0; j < multdis.size();j++){if(multdis.get(j).matches("\\d+")){xi *= Integer.parseInt(multdis.get(j));}else if(multdis.get(j).matches("x")){if(multSim.containsKey("x"))multSim.put("x", multSim.get("x")+1);else multSim.put("x", 1);}else if(multdis.get(j).matches("(.*)\\*\\*\\d+")){String base = multdis.get(j).split("\\*\\*")[0];int zhi = Integer.parseInt(multdis.get(j).split("\\*\\*")[1]);if(multSim.containsKey(base))multSim.put(base, multSim.get(base)+zhi);else multSim.put(base, zhi);}else if(multdis.get(j).matches("sin\\(.*\\)")||multdis.get(j).matches("cos\\(.*\\)")){if(multSim.containsKey(multdis.get(j)))multSim.put(multdis.get(j), multSim.get(multdis.get(j))+1);else multSim.put(multdis.get(j), 1);}}resdis.add(Integer.toString(xi));String index = "";String all = Integer.toString(xi);for(String key:multSim.keySet()){index = "";if(multSim.get(key) == 1)index += key;else index+=key+"**"+Integer.toString(multSim.get(key));resdis.add(index);if(alls.containsKey(index)) alls.put(index, complexPlus(alls.get(index), all));else alls.put(index, all);all = chen(all, index);}resdis.add("+");}
//        System.out.println(alls);String index = "1";for(int i = 0; i<resdis.size();i++){
//            System.out.println(resdis.get(i));if(resdis.get(i).equals("+")){result = complexPlus(result, index);index = "1";}else{if(alls.containsKey(resdis.get(i))&&!alls.get(resdis.get(i)).equals(index)&&!alls.get(resdis.get(i)).equals("no")){index = "("+alls.get(resdis.get(i))+")"+"*"+resdis.get(i);alls.put(resdis.get(i), "no");}else if(alls.containsKey(resdis.get(i))&&alls.get(resdis.get(i)).equals("no")){index = "0";}else{index = chen(index, resdis.get(i));}}}return result;}public static void main(String[] args) {Qiudao q = new Qiudao();String yuan = q.complexQiu("5* x**4* sin(x)");System.out.println(yuan);String s = q.Simplify(yuan);System.out.println(s);}}

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