增量包算法，時間複雜度3n

時間 2019-11-08

標籤增量算法時間複雜度 3n 简体版

原文原文鏈接

研究了編輯距離、lcd等字符比較的算法，發現它們的時間複雜度和空間複雜度都在n*m，太複雜了。腦海想了下人是怎麼比較字符的，聯想出動態規劃公式，以後就有了這個字符掃描比較法。html

設字符s1長度爲n,字符s2長度爲m，算法

當s1[n1]!==s2[n2], 掃描s2求出d1,l1,掃描s1求出d2,l2, 比較d一、d2，移動n一、n2,重複這個過程url

// 動態公式
// d1==0
// n1=n1+l1 l1>l2 或者 l1==l2 d1<d2
// n2=n2+d1+l1 l1>l2
//
// n1=n1+d2+l2 l1<l2 或者 l1==l2 d1>d2
// n2=n2+l2 l1<l2


//掃描法，複雜度爲 n+m
//生產增量包
function makeChunk(s1,s2) {
  var n=s1.length,m=s2.length;//長度
  var n1=0,n2=0;//掃描點
  const chunkArr=[]
//開始掃描
  while (n1<n&&n2<m){
    let nn1=n1;
    let nn2=n2;
    if(s1[nn1]===s2[nn2]){
      nn1++;
      nn2++;
      while (nn1<n&&nn2<m&&s1[nn1]===s2[nn2]){
        nn1++;
        nn2++;
      }
      chunkArr.push(['e',n1,nn1-n1,n2,nn2])
      n1=nn1;
      n2=nn2;
    }else if(n1+1<n&&n2+1<m&&s1[n1+1]===s2[n2+1]){
      chunkArr.push(['r',s2.substr(n2,1),n1,n2,1]);
      n1=n1+1;
      n2=n2+1;
    }else{
      //求n1,n2,d1,d2,l1,l2
      nn1=n1;
      nn2=n2+1;
      while (nn2<m&&s1[n1]!==s2[nn2]){
        nn2++;
      }
      let d1=nn2-n2;
      nn1=n1+1;
      nn2=n2;
      while (nn1<n&&s1[nn1]!==s2[n2]){
        nn1++;
      }
      let d2=nn1-n1;
      //結束
      if(d1<d2){
        chunkArr.push(['r',s2.substr(n2,1),n1,n2,1])
        // n1=n1+1;
        n2=n2+1;
      }else if(d1>d2){
        // chunkArr.push(['d',n1,1,s1.substr(n1,1)])
        n1=n1+1;
        // n2=n2+1;
      }else{
        chunkArr.push(['r',s2.substr(n2,1),n1,n2,1])
        n1=n1+1;
        n2=n2+1;
      }

    }
  }
  //壓縮指令
  for(let i=0;i<chunkArr.length;i++){
    const arr=chunkArr[i];
    if(arr[0]==='r'){
      chunkArr[i]=[arr[0],arr[1]]
    }
  }
  // if(n1<n){
  // chunkArr.push(['d',n1,n-n1,s1.substr(n1,n-n1)])
  // }
  if(n2<m){
    chunkArr.push(['a',s2.substr(n2,m-n2),n1,n2,m-n2])
  }
  return chunkArr;
}

//執行增量包
function execChunk(s1,chunk){
  var ns=''
  for(let i=0;i<chunk.length;i++){
    const arr=chunk[i];
    if(arr[0]==='e'){
      ns=ns+s1.substr(arr[1],arr[2])
    }else if(arr[0]==='r'){
      ns=ns+arr[1]
    }else if(arr[0]==='a'){
      ns=ns+arr[1]
    }
  }
  return ns
}


//定義兩個字符
var s1="\"191010\",UrlNode:d.b.UrlNode}},methods:{rpush:function(){w.a.push({path:Object(h.a)(\"wlh_intro\"),query:d.b.query})},forward1:function(){l.a.forward({data:{url:\"index.html\"}})},forward2:function(){l.a.forward({data:{url:\"login.html\",redirectURL:\"index.html\"}})},forward3:function(){l.a.forward({data:{url:",
  s2="\"1910011\",UrlNode:d.b.UrlNode}},methods:{rpush:function(){w.a.push({path:Object(h.a)(\"wlh_intro\"),query:d.b.query})},forward1:function(){l.a.forward({data:{url:\"index.html\"}})},forward2:function(){l.a.forward({data:{url:\"login.html\",redirectURL:\"index.html\"}})},forward3:function(){l.a.forward({data:{url:";
const chunk=makeChunk(s1,s2);
console.log(chunk)
const nstr=execChunk(s1,chunk)
console.log(nstr===s2)


console.log(nstr===s2)

<!DOCTYPE html><html lang="en"><head>  <meta charset="UTF-8">  <title>增量包算法</title></head><style>  .container{    width: 1000px;    margin: 0 auto;  }  .item{    margin-bottom: 20px;    vertical-align: middle;    float: none;    clear: both;  }  .item label{    width: 100px;    float: left;  }  .item textarea{    width: 60%;    min-height: 100px;  }</style><script>  //掃描法，複雜度爲 n+m  //生產增量包  function makeChunk(s1,s2) {    var n=s1.length,m=s2.length;//長度    var n1=0,n2=0;//掃描點    const chunkArr=[]//開始掃描    while (n1<n&&n2<m){      let nn1=n1;      let nn2=n2;      if(s1[nn1]===s2[nn2]){        nn1++;        nn2++;        while (nn1<n&&nn2<m&&s1[nn1]===s2[nn2]){          nn1++;          nn2++;        }        chunkArr.push(['e',n1,nn1-n1])        n1=nn1;        n2=nn2;      }else if(n1+1<n&&n2+1<m&&s1[n1+1]===s2[n2+1]){        chunkArr.push(['r',s2.substr(n2,1),n1,n2,1]);        n1=n1+1;        n2=n2+1;      }else{        //求d1,d2        nn1=n1;        nn2=n2+1;        while (nn2<m&&s1[n1]!==s2[nn2]){          nn2++;        }        let d1=nn2-n2;        nn1=n1+1;        nn2=n2;        while (nn1<n&&s1[nn1]!==s2[n2]){          nn1++;        }        let d2=nn1-n1;        //結束        if(d1<d2){          chunkArr.push(['a',s2.substr(n2,1)])          // n1=n1+1;          n2=n2+1;        }else if(d1>d2){          // chunkArr.push(['d',n1,1,s1.substr(n1,1)])          n1=n1+1;          // n2=n2+1;        }else{          chunkArr.push(['r',s2.substr(n2,1),n1,n2,1])          n1=n1+1;          n2=n2+1;        }      }    }    if(n2<m){      chunkArr.push(['a',s2.substr(n2,m-n2)])    }    //壓縮指令    const minChunk=[]    for(let i=0;i<chunkArr.length;i++){      let arr=chunkArr[i];      if(arr[0]==='e'&&arr[2]<String(arr[1]).length+8){        arr=['a',s1.substr(arr[1],arr[2])]      }      if(arr[0]==='r'){        arr=['a',arr[1]]      }      var lastArr=minChunk[minChunk.length-1];      if(arr[0]==='a'&&lastArr&&lastArr[0]==='a'){        lastArr[1]=lastArr[1]+arr[1];      }else{        minChunk.push(arr)      }    }    return minChunk;  }  //執行增量包  function execChunk(s1,chunk){    var ns=''    for(let i=0;i<chunk.length;i++){      const arr=chunk[i];      if(arr[0]==='e'){        ns=ns+s1.substr(arr[1],arr[2])      }else if(arr[0]==='a'){        ns=ns+arr[1]      }    }    return ns  }</script><script>  function s1makeChunk() {    var s1=document.getElementById('s1').value;    var s2=document.getElementById('s2').value;    var chunk=makeChunk(s1,s2)    var cstr=JSON.stringify(chunk)    document.getElementById('chunk').value=cstr    return cstr  }  function s1execChunk() {    var s1=document.getElementById('s1').value;    var s2=document.getElementById('s2').value;    var cstr=document.getElementById('chunk').value    if(!cstr){      cstr=s1makeChunk();    }    var chunk=JSON.parse(cstr)    var ns=execChunk(s1,chunk)    document.getElementById('result').innerText='結果爲'+(ns===s2);    document.getElementById('ns').value=ns;  }</script><body><div class="container">  <div class="item">    增量包算法:時間複雜度 2*n ~ 2*n階和 之間  </div>  <div class="item">    <label>輸入字符s1：</label> <textarea id="s1">ill:"071b136b",test:"acf98235",wlh_audit_ok:"0cfbdb93",wl</textarea>  </div>  <div class="item">    <label>輸入字符s2：</label> <textarea id='s2'>ill:"acf98235",test:"0cfbdb93",wlh_audit_ok:"0cfbdb93",wl</textarea>  </div>  <div class="item">    <label>s1-->s2：</label> <textarea id='chunk'></textarea><button onClick="s1makeChunk()">生產增量包：</button>  </div>  <div class="item">    <label>結果：</label> <textarea id="ns"></textarea><button onClick="s1execChunk()">執行增量包：</button>  </div>  <div id="result"></div></div></body></html>

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