アルゴリズムとデータ構造 補足資料 13-2 「 2 分探索木への節点の追加」...
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アルゴリズムとデータ構造補足資料 13-2
「 2 分探索木への節点の追加」
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
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
search(7, NULL) : 呼出 1
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 7 t NULL
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
search(7, NULL) : 呼出 1
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 7 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
search(7, NULL) : 呼出 1
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 7 t
71
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
search(7, NULL) : 呼出 1
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 7 t
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
search(7, NULL) : 呼出 1
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 7 t
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root NULL
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 7 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
search(2, NULL) : 呼出 3
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t NULL
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
search(2, NULL) : 呼出 3
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
search(2, NULL) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
21
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
search(2, NULL) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
search(2, NULL) : 呼出 3
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
search(2, root) : 呼出 2
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 2 t
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 2 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2 が入るのは、7 の左部分木
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
search(9, NULL) : 呼出 5
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t NULL
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
search(9, NULL) : 呼出 5
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
search(9, NULL) : 呼出 5
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
91
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
search(9, NULL) : 呼出 5
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
search(9, NULL) : 呼出 5
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
7
NULL
1
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
9
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9 が入るのは、7 の右部分木
9
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
1
search(9, root) : 呼出 4
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 9 t
9
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木search(1, NULL) : 呼出 8
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t NULL
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木search(1, NULL) : 呼出 8
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
11
search(1, NULL) : 呼出 8
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
1
NULL
NULL
1
search(1, NULL) : 呼出 8
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
1
NULL
NULL
1
search(1, NULL) : 呼出 8
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、2 の左部分木
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
search(1, t->left) : 呼出 7
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1 が入るのは、7 の左部分木
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
search(1, root) : 呼出 6
if ( t == NULL ) { t = (struct tree *)malloc(sizeof(struct tree)); t->key = x; t->count = 1; t->left = NULL; t->right = NULL;}else if ( x < t->key ) t->left = search( x, t->left );else if ( x > t->key ) t->right = search( x, t->right );else (t->count)++;
return (t);
x 1 t
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 1 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 6 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 6 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
6 が入るのは、7 の左部分木
1
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 6 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
2
NULL
19
NULL
NULL
1
6 が入るのは、2 の右部分木
1
NULL
NULL
1
6 が入るのは、7 の左部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 6 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
1
6 が入るのは、2 の右部分木
1
NULL
NULL
1
6 が入るのは、7 の左部分木
6
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
1
1
NULL
NULL
16
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
1
1
NULL
NULL
16
NULL
NULL
1
9 が入るのは、7 の右部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 9 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
2
1
NULL
NULL
16
NULL
NULL
1
9 が入るのは、7 の右部分木
9 があったのでcount++
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 8 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
2
1
NULL
NULL
16
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 8 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
2
1
NULL
NULL
16
NULL
NULL
1
8 が入るのは、7 の右部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 8 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
NULL
2
1
NULL
NULL
16
NULL
NULL
1
8 が入るのは、7 の右部分木
8 が入るのは、9 の左部分木
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 8 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
2
1
NULL
NULL
16
NULL
NULL
1
8 が入るのは、7 の右部分木
8 が入るのは、9 の左部分木
8
NULL
NULL
1
探索木 (search tree)
main()
root = NULL;while( ( y=get_data() )!= EOD ) root = search( y, root )
…
y 8 root
int a[] = { 7, 2, 9, 1, 6, 9, 8, …}
71
21
9
NULL
2
1
NULL
NULL
16
NULL
NULL
18
NULL
NULL
1