Posted 2021-04-18 娣卞叆鍘熺悊

鐐瑰嚮馃憜钃濊壊鈥?nbsp;娣卞叆鍘熺悊鈥濓紝鍏虫敞骞垛€?/span>璁句负鏄熸爣鈥?/span>

鎶€鏈共璐э紝绗竴鏃堕棿鎺ㄩ€?/span> 

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濡備綍閲忓寲涓や釜瀛楃涓茬殑鐩镐技搴︼紵

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鏍规嵁鎵€鍖呭惈鐨勭紪杈戞搷浣滅绫荤殑涓嶅悓锛岀紪杈戣窛绂绘湁澶氱涓嶅悓鐨勮绠楁柟寮忥紝姣旇緝钁楀悕鐨勬湁鑾辨枃鏂潶璺濈锛圠evenshtein distance锛夊拰鏈€闀垮叕鍏卞瓙涓查暱搴?/span>锛圠ongest common substring length锛夈€傚叾涓紝鑾辨枃鏂潶璺濈鍏佽澧炲姞銆佸垹闄ゃ€佹浛鎹㈠瓧绗﹁繖涓変釜缂栬緫鎿嶄綔锛屾渶闀垮叕鍏卞瓙涓查暱搴﹀彧鍏佽澧炲姞銆佸垹闄ゅ瓧绗﹁繖涓や釜缂栬緫鎿嶄綔銆?/span>

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鍏充簬杩欎袱涓绠楁柟娉曪紝鎴戜妇涓緥瀛愮粰浣犺鏄庝竴涓嬨€傝繖閲岄潰锛屼袱涓瓧绗︿覆 mitcmu 鍜?mtacnu 鐨勮幈鏂囨柉鍧﹁窛绂绘槸 3锛屾渶闀垮叕鍏卞瓙涓查暱搴︽槸 4銆?/span>

浜嗚В浜嗙紪杈戣窛绂荤殑姒傚康涔嬪悗锛屾垜浠潵鐪嬶紝濡備綍蹇€熻绠椾袱涓瓧绗︿覆涔嬮棿鐨勭紪杈戣窛绂伙紵

濡備綍缂栫▼璁＄畻鑾辨枃鏂潶璺濈锛?/span>

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杩欎釜闂鏄眰鎶婁竴涓瓧绗︿覆鍙樻垚鍙︿竴涓瓧绗︿覆锛岄渶瑕佺殑鏈€灏戠紪杈戞鏁般€傛暣涓眰瑙ｈ繃绋嬶紝娑夊強澶氫釜鍐崇瓥闃舵锛屾垜浠渶瑕佷緷娆¤€冨療涓€涓瓧绗︿覆涓殑姣忎釜瀛楃锛岃窡鍙︿竴涓瓧绗︿覆涓殑瀛楃鏄惁鍖归厤锛屽尮閰嶇殑璇濆浣曞鐞嗭紝涓嶅尮閰嶇殑璇濆張濡備綍澶勭悊銆傛墍浠ワ紝杩欎釜闂绗﹀悎澶氶樁娈靛喅绛栨渶浼樿В妯″瀷銆?/span>

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鍥炴函鏄竴涓€掑綊澶勭悊鐨勮繃绋嬨€傚鏋?a[i]涓?b[j]鍖归厤锛屾垜浠€掑綊鑰冨療 a[i+1]鍜?b[j+1]銆傚鏋?a[i]涓?b[j]涓嶅尮閰嶏紝閭ｆ垜浠湁澶氱澶勭悊鏂瑰紡鍙€夛細

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鍙互灏?a[i]鏇挎崲鎴?b[j]锛屾垨鑰呭皢 b[j]鏇挎崲鎴?a[i]锛岀劧鍚庨€掑綊鑰冨療 a[i+1]鍜?b[j+1]銆?/span>

鎴戜滑灏嗕笂闈㈢殑鍥炴函绠楁硶鐨勫鐞嗘€濊矾锛岀炕璇戞垚浠ｇ爜锛屽氨鏄笅闈㈣繖涓牱瀛愶細

private char[] a = "mitcmu".toCharArray();private char[] b = "mtacnu".toCharArray();private int n = 6;private int m = 6;private int minDist = Integer.MAX_VALUE; // 瀛樺偍缁撴灉// 璋冪敤鏂瑰紡 lwstBT(0, 0, 0);public lwstBT(int i, int j, int edist) { if (i == n || j == m) { if (i < n) edist += (n-i); if (j < m) edist += (m - j); if (edist < minDist) minDist = edist; return; } if (a[i] == b[j]) { // 涓や釜瀛楃鍖归厤 lwstBT(i+1, j+1, edist); } else { // 涓や釜瀛楃涓嶅尮閰?/span> lwstBT(i + 1, j, edist + 1); // 鍒犻櫎a[i]鎴栬€卋[j]鍓嶆坊鍔犱竴涓瓧绗?/span> lwstBT(i, j + 1, edist + 1); // 鍒犻櫎b[j]鎴栬€卆[i]鍓嶆坊鍔犱竴涓瓧绗?/span> lwstBT(i + 1, j + 1, edist + 1); // 灏哸[i]鍜宐[j]鏇挎崲涓虹浉鍚屽瓧绗?/span> }}

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鍦ㄩ€掑綊鏍戜腑锛屾瘡涓妭鐐逛唬琛ㄤ竴涓姸鎬侊紝鐘舵€佸寘鍚笁涓彉閲?(i, j, edist)锛屽叾涓紝edist 琛ㄧず澶勭悊鍒?a[i]鍜?b[j]鏃讹紝宸茬粡鎵ц鐨勭紪杈戞搷浣滅殑娆℃暟銆?/span>

鍦ㄩ€掑綊鏍戜腑锛?i, j) 涓や釜鍙橀噺閲嶅鐨勮妭鐐瑰緢澶氾紝姣斿 (3, 2) 鍜?(2, 3)銆傚浜?(i, j) 鐩稿悓鐨勮妭鐐癸紝鎴戜滑鍙渶瑕佷繚鐣?edist 鏈€灏忕殑锛岀户缁€掑綊澶勭悊灏卞彲浠ヤ簡锛屽墿涓嬬殑鑺傜偣閮藉彲浠ヨ垗寮冦€傛墍浠ワ紝鐘舵€佸氨浠?(i, j, edist) 鍙樻垚浜?(i, j, min_edist)锛屽叾涓?min_edist 琛ㄧず澶勭悊鍒?a[i]鍜?b[j]锛屽凡缁忔墽琛岀殑鏈€灏戠紪杈戞鏁般€?/span>

鐪嬪埌杩欓噷锛屼綘鏈夋病鏈夎寰楋紝杩欎釜闂璺熶笂涓よ妭璁茬殑鍔ㄦ€佽鍒掍緥瀛愰潪甯哥浉浼硷紵涓嶈繃锛岃繖涓棶棰樼殑鐘舵€佽浆绉绘柟寮忥紝瑕佹瘮涔嬪墠涓よ妭璇句腑璁插埌鐨勪緥瀛愰兘瑕佸鏉傚緢澶氥€備笂涓€鑺傛垜浠鐨勭煩闃垫渶鐭矾寰勯棶棰樹腑锛屽埌杈剧姸鎬?(i, j) 鍙兘閫氳繃 (i-1, j) 鎴?(i, j-1) 涓や釜鐘舵€佽浆绉昏繃鏉ワ紝鑰屼粖澶╄繖涓棶棰橈紝鐘舵€?(i, j) 鍙兘浠?(i-1, j)锛?i, j-1)锛?i-1, j-1) 涓変釜鐘舵€佷腑鐨勪换鎰忎竴涓浆绉昏繃鏉ャ€?/span>

鍩轰簬鍒氬垰鐨勫垎鏋愶紝鎴戜滑鍙互灏濊瘯鐫€灏嗘妸鐘舵€佽浆绉荤殑杩囩▼锛岀敤鍏紡鍐欏嚭鏉ャ€傝繖灏辨槸鎴戜滑鍓嶉潰璁茬殑鐘舵€佽浆绉绘柟绋嬨€?/span>

濡傛灉锛歛[i]!=b[j]锛岄偅涔堬細min_edist(i, j)灏辩瓑浜庯細

min(min_edist(i-1,j)+1, min_edist(i,j-1)+1, min_edist(i-1,j-1)+1)

濡傛灉锛歛[i]==b[j]锛岄偅涔堬細min_edist(i, j)灏辩瓑浜庯細

min(min_edist(i-1,j)+1, min_edist(i,j-1)+1锛宮in_edist(i-1,j-1))

鍏朵腑锛宮in琛ㄧず姹備笁鏁颁腑鐨勬渶灏忓€笺€?nbsp;  

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public int lwstDP(char[] a, int n, char[] b, int m) { int[][] minDist = new int[n][m]; for (int j = 0; j < m; ++j) { // 鍒濆鍖栫0琛?a[0..0]涓巄[0..j]鐨勭紪杈戣窛绂?/span> if (a[0] == b[j]) minDist[0][j] = j; else if (j != 0) minDist[0][j] = minDist[0][j-1]+1; else minDist[0][j] = 1; } for (int i = 0; i < n; ++i) { // 鍒濆鍖栫0鍒?a[0..i]涓巄[0..0]鐨勭紪杈戣窛绂?/span> if (a[i] == b[0]) minDist[i][0] = i; else if (i != 0) minDist[i][0] = minDist[i-1][0]+1; else minDist[i][0] = 1; } for (int i = 1; i < n; ++i) { // 鎸夎濉〃 for (int j = 1; j < m; ++j) { if (a[i] == b[j]) minDist[i][j] = min( minDist[i-1][j]+1, minDist[i][j-1]+1, minDist[i-1][j-1]); else minDist[i][j] = min( minDist[i-1][j]+1, minDist[i][j-1]+1, minDist[i-1][j-1]+1); } } return minDist[n-1][m-1];}private int min(int x, int y, int z) { int minv = Integer.MAX_VALUE; if (x < minv) minv = x; if (y < minv) minv = y; if (z < minv) minv = z; return minv;}

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(i-1, j-1, max_lcs)锛屽叾涓?max_lcs 琛ㄧず a[0鈥-1]鍜?b[0鈥-1]鐨勬渶闀垮叕鍏卞瓙涓查暱搴︼紱

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濡傛灉锛歛[i]==b[j]锛岄偅涔堬細max_lcs(i, j)灏辩瓑浜庯細

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濡傛灉锛歛[i]!=b[j]锛岄偅涔堬細max_lcs(i, j)灏辩瓑浜庯細

max(max_lcs(i-1,j-1), max_lcs(i-1, j), max_lcs(i, j-1))锛?/span>

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public int lcs(char[] a, int n, char[] b, int m) { int[][] maxlcs = new int[n][m]; for (int j = 0; j < m; ++j) {//鍒濆鍖栫0琛岋細a[0..0]涓巄[0..j]鐨刴axlcs if (a[0] == b[j]) maxlcs[0][j] = 1; else if (j != 0) maxlcs[0][j] = maxlcs[0][j-1]; else maxlcs[0][j] = 0; } for (int i = 0; i < n; ++i) {//鍒濆鍖栫0鍒楋細a[0..i]涓巄[0..0]鐨刴axlcs if (a[i] == b[0]) maxlcs[i][0] = 1; else if (i != 0) maxlcs[i][0] = maxlcs[i-1][0]; else maxlcs[i][0] = 0; } for (int i = 1; i < n; ++i) { // 濉〃 for (int j = 1; j < m; ++j) { if (a[i] == b[j]) maxlcs[i][j] = max( maxlcs[i-1][j], maxlcs[i][j-1], maxlcs[i-1][j-1]+1); else maxlcs[i][j] = max( maxlcs[i-1][j], maxlcs[i][j-1], maxlcs[i-1][j-1]); } } return maxlcs[n-1][m-1];}private int max(int x, int y, int z) { int maxv = Integer.MIN_VALUE; if (x > maxv) maxv = x; if (y > maxv) maxv = y; if (z > maxv) maxv = z; return maxv;}

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鍐呭灏忕粨

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鍙寮勬噦浜嗚繖鍑犱釜闂锛屼竴鑸殑鍔ㄦ€佽鍒掗棶棰橈紝浣犲簲璇ラ兘鍙互搴斾粯銆傚浜庡姩鎬佽鍒掕繖涓煡璇嗙偣锛屼綘灏辩畻鏄叆闂ㄤ簡锛屽啀瀛︿範鏇村姞澶嶆潅鐨勫氨浼氱畝鍗曞緢澶氥€?/span>

  

-娣卞叆鍘熺悊-  

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