アルゴリズムとデータ構造 補足資料 13-3 「 2 分探索木からの節点の削除」
DESCRIPTION
アルゴリズムとデータ構造 補足資料 13-3 「 2 分探索木からの節点の削除」. 横浜国立大学 理工 学部 数物・電子情報系学科 富井尚志. 探索木のオペレータ. 探索木 を探索する 探索木に節点を追加（挿入）する 探索木から節点を削除する 端点（葉： leaf ）の削除 一つの子孫しか持たない節点の削除 二つの子孫を持つ接点の削除. 探索木のオペレータ. 探索木 を探索する 探索木に節点を追加（挿入）する 探索木から節点を削除する 端点（葉： leaf ）の削除 一つの子孫しか持たない節点の削除 二つの子孫を持つ接点の削除. - PowerPoint PPT PresentationTRANSCRIPT
アルゴリズムとデータ構造補足資料 13-3
「 2 分探索木からの節点の削除」
横浜国立大学理工学部
数物・電子情報系学科富井尚志
探索木のオペレータ• 探索木を探索する
• 探索木に節点を追加（挿入）する
• 探索木から節点を削除する1. 端点（葉： leaf ）の削除2. 一つの子孫しか持たない節点の削除3. 二つの子孫を持つ接点の削除
探索木のオペレータ• 探索木を探索する
• 探索木に節点を追加（挿入）する
• 探索木から節点を削除する1. 端点（葉： leaf ）の削除2. 一つの子孫しか持たない節点の削除3. 二つの子孫を持つ接点の削除
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
delete(8, root)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t NULL q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t NULL q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t NULL q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t NULL q
delete(8, t->right) NULL
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
10NULL
NULL
9NULL
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right) NULL
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
10NULL
NULL
9NULL
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t q
delete(8, t->right)
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
10NULL
NULL
9NULL
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
10NULL
NULL
9NULL
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 8 t
delete(8, root) q
端点（葉： leaf ）の削除main()
… root = delete(8, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
10NULL
NULL
9NULL
7
※ メンバ count は省略
探索木のオペレータ• 探索木を探索する
• 探索木に節点を追加（挿入）する
• 探索木から節点を削除する1. 端点（葉： leaf ）の削除2. 一つの子孫しか持たない節点の削除3. 二つの子孫を持つ接点の削除
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
ゴールのイメージ
6 NULL
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, t->left)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 6 t q
delete(6, root)
一つの子孫しか持たない節点の削除main()
… root = delete(6, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
探索木のオペレータ• 探索木を探索する
• 探索木に節点を追加（挿入）する
• 探索木から節点を削除する1. 端点（葉： leaf ）の削除2. 一つの子孫しか持たない節点の削除3. 二つの子孫を持つ接点の削除
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
6 NULL
値を
コピ
ー
左部分木の最右要素で置き換える
ゴールのイメージ
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
7
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
値を
コピ
ー
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
値を
コピ
ー
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
6 NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
if ( t->right != NULL ) t->right = del( dstt, t->right );else{ dstt->key = t->key; dstt->count = t->count; q = t; t = t->left; free(q);} return (t);
dstt t
del(t, t->left) q
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略
if ( t == NULL ) printf(“ 見つかりませんでした \n”);else if ( x < t->key ) t->left = delete( x, t->left );else if ( x > t->key ) t->right = delete( x, t->right );else{ if( t->right == NULL ){ q = t; t = t->left; free(q); } else if( t->left == NULL ){ q = t; t = t->right; free(q); } else { t->left = del( t, t->left ); }} return (t);
x 7 t q
delete(7, root)
二つの子孫を持つ接点の削除main()
… root = delete(7, root);...
root
1NULL
NULL
4
3NULL
NULL
5NULL
NULL
2
8NULL
NULL
10NULL
NULL
9
6
※ メンバ count は省略