Animation of Bubble Sort

Steven StreckerSteven Strecker

CS510 Computer AlgorithmsCS510 Computer Algorithms

Kalamazoo College

Introduction

void bubble(itemType a[], int N)void bubble(itemType a[], int N){{ int i, j;int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j);swap(a, j-1, j);}}

A N E X A M P L E

void bubbles(itemtype a[], int n) bubbles(a[], 9)void bubbles(itemtype a[], int n) bubbles(a[], 9){{ int i, j;int i, j; for (i = n; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = n; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2] if ((a[j-1] > a[j]) if (a[2-1] > a[2]

nono swap(a, j-1, j);swap(a, j-1, j);}}

A N E X A M P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[2]>a[3]) YESif ((a[j-1] > a[j]) if (a[2]>a[3]) YES swap(a, j-1, j);swap(a, j-1, j);}}

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[2]>a[3]) YESif ((a[j-1] > a[j]) if (a[2]>a[3]) YES swap(a, j-1, j); swap(a, 2, 3)swap(a, j-1, j); swap(a, 2, 3)}}

A E N X A M P L E

A E N X A M P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[3]>a[4]) NOif ((a[j-1] > a[j]) if (a[3]>a[4]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A E N X A M P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[4]>a[5]) YESif ((a[j-1] > a[j]) if (a[4]>a[5]) YES swap(a, j-1, j);swap(a, j-1, j);}}

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[4]>a[5]) YESif ((a[j-1] > a[j]) if (a[4]>a[5]) YES swap(a, j-1, j); swap(a, 4, 5); swap(a, j-1, j); swap(a, 4, 5);

}}

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A E N A X M P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[5]>a[6]) YESif ((a[j-1] > a[j]) if (a[5]>a[6]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E N A M X P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[5]>a[6]) YESif ((a[j-1] > a[j]) if (a[5]>a[6]) YES swap(a, j-1, j); swap(a, 5, 6); swap(a, j-1, j); swap(a, 5, 6);

}}

A E N A M X P L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[6]>a[7]) YESif ((a[j-1] > a[j]) if (a[6]>a[7]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E N A M P X L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[6]>a[7]) YESif ((a[j-1] > a[j]) if (a[6]>a[7]) YES swap(a, j-1, j); swap(a, 6, 7); swap(a, j-1, j); swap(a, 6, 7);

}}

A E N A M P X L E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[7]>a[8]) YESif ((a[j-1] > a[j]) if (a[7]>a[8]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E N A M P L X E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[7]>a[8]) YESif ((a[j-1] > a[j]) if (a[7]>a[8]) YES swap(a, j-1, j); swap(a, 7, 8); swap(a, j-1, j); swap(a, 7, 8);

}}

A E N A M P L X E

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[8]>a[9]) YESif ((a[j-1] > a[j]) if (a[8]>a[9]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E N A M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j;int i, j; for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--)for (i = N; i >= 1; i--) for ( i = 9; i >= 1; i--) for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++)for (j = 2; j <= i; j++) for (j = 2; j <= 9; j++) if ((a[j-1] > a[j]) if (a[8]>a[9]) YESif ((a[j-1] > a[j]) if (a[8]>a[9]) YES swap(a, j-1, j); swap(a, 8, 9); swap(a, j-1, j); swap(a, 8, 9);

}}

A E N A M P L E X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j);swap(a, j-1, j);}}

A E N A M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A E N A M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) NOif ((a[j-1] > a[j]) if (a[3-1] > a[3]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A E N A M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) YESif ((a[j-1] > a[j]) if (a[4-1] > a[4]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E A N M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) YESif ((a[j-1] > a[j]) if (a[4-1] > a[4]) YES swap(a, j-1, j); swap(a, 3, 4) swap(a, j-1, j); swap(a, 3, 4) }}

A E A N M P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E A M N P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j); swap(a, 4, 5) swap(a, j-1, j); swap(a, 4, 5) }}

A E A M N P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[6-1] > a[6]) NOif ((a[j-1] > a[j]) if (a[6-1] > a[6]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A E A M N P L E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[7-1] > a[7]) YESif ((a[j-1] > a[j]) if (a[7-1] > a[7]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E A M N L P E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[7-1] > a[7]) YESif ((a[j-1] > a[j]) if (a[7-1] > a[7]) YES swap(a, j-1, j); swap(a, 6, 7)swap(a, j-1, j); swap(a, 6, 7)}}

A E A M N L P E X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[8-1] > a[8]) YESif ((a[j-1] > a[j]) if (a[8-1] > a[8]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A E A M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=8; j++)for (j = 2; j <= i; j++) for (j = 2; j<=8; j++) if ((a[j-1] > a[j]) if (a[8-1] > a[8]) YESif ((a[j-1] > a[j]) if (a[8-1] > a[8]) YES swap(a, j-1, j); swap(a, 7, 8)swap(a, j-1, j); swap(a, 7, 8)}}

A E A M N L E P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A E A M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A E A M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) YESif ((a[j-1] > a[j]) if (a[3-1] > a[3]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) YESif ((a[j-1] > a[j]) if (a[3-1] > a[3]) YES swap(a, j-1, j); swap(a, 2, 3) swap(a, j-1, j); swap(a, 2, 3) }}

A A E M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) NOif ((a[j-1] > a[j]) if (a[4-1] > a[4]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) NOif ((a[j-1] > a[j]) if (a[5-1] > a[5]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E M N L E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[6-1] > a[6]) YESif ((a[j-1] > a[j]) if (a[6-1] > a[6]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E M L N E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[6-1] > a[6]) YESif ((a[j-1] > a[j]) if (a[6-1] > a[6]) YES swap(a, j-1, j); swap(a, 5, 6);swap(a, j-1, j); swap(a, 5, 6);}}

A A E M L N E P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[7-1] > a[7]) YESif ((a[j-1] > a[j]) if (a[7-1] > a[7]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E M L E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=7; j++)for (j = 2; j <= i; j++) for (j = 2; j<=7; j++) if ((a[j-1] > a[j]) if (a[7-1] > a[7]) YESif ((a[j-1] > a[j]) if (a[7-1] > a[7]) YES swap(a, j-1, j); swap(a, 6, 7);swap(a, j-1, j); swap(a, 6, 7);}}

A A E M L E N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E M L E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E M L E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) NOif ((a[j-1] > a[j]) if (a[3-1] > a[3]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E M L E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) NOif ((a[j-1] > a[j]) if (a[4-1] > a[4]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E M L E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E L M E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j); swap(a, 4, 5)swap(a, j-1, j); swap(a, 4, 5)}}

A A E L M E N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[6-1] > a[6]) YESif ((a[j-1] > a[j]) if (a[6-1] > a[6]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E L E M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=6; j++)for (j = 2; j <= i; j++) for (j = 2; j<=6; j++) if ((a[j-1] > a[j]) if (a[6-1] > a[6]) YESif ((a[j-1] > a[j]) if (a[6-1] > a[6]) YES swap(a, j-1, j); swap(a, 5, 6)swap(a, j-1, j); swap(a, 5, 6)}}

A A E L E M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E L E M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=5; j++)for (j = 2; j <= i; j++) for (j = 2; j<=5; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E L E M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=5; j++)for (j = 2; j <= i; j++) for (j = 2; j<=5; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) NOif ((a[j-1] > a[j]) if (a[3-1] > a[3]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E L E M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=5; j++)for (j = 2; j <= i; j++) for (j = 2; j<=5; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) NOif ((a[j-1] > a[j]) if (a[4-1] > a[4]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E L E M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=5; j++)for (j = 2; j <= i; j++) for (j = 2; j<=5; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j);swap(a, j-1, j);}}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=5; j++)for (j = 2; j <= i; j++) for (j = 2; j<=5; j++) if ((a[j-1] > a[j]) if (a[5-1] > a[5]) YESif ((a[j-1] > a[j]) if (a[5-1] > a[5]) YES swap(a, j-1, j); swap(a, 4, 5)swap(a, j-1, j); swap(a, 4, 5)}}

A A E E L M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=4; j++)for (j = 2; j <= i; j++) for (j = 2; j<=4; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=4; j++)for (j = 2; j <= i; j++) for (j = 2; j<=4; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) NOif ((a[j-1] > a[j]) if (a[3-1] > a[3]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=4; j++)for (j = 2; j <= i; j++) for (j = 2; j<=4; j++) if ((a[j-1] > a[j]) if (a[4-1] > a[4]) NOif ((a[j-1] > a[j]) if (a[4-1] > a[4]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=3; j++)for (j = 2; j <= i; j++) for (j = 2; j<=3; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=3; j++)for (j = 2; j <= i; j++) for (j = 2; j<=3; j++) if ((a[j-1] > a[j]) if (a[3-1] > a[3]) NOif ((a[j-1] > a[j]) if (a[3-1] > a[3]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N) bubbles(a[], 9)void bubbles(itemType a[], int N) bubbles(a[], 9){{ int i, j; int i, j; for (i = N; i >= 1; i--) for (i = 9; i>=1; i--)for (i = N; i >= 1; i--) for (i = 9; i>=1; i--) for (j = 2; j <= i; j++) for (j = 2; j<=2; j++)for (j = 2; j <= i; j++) for (j = 2; j<=2; j++) if ((a[j-1] > a[j]) if (a[2-1] > a[2]) NOif ((a[j-1] > a[j]) if (a[2-1] > a[2]) NO swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

A A E E L M N P X

void bubbles(itemType a[], int N)void bubbles(itemType a[], int N){{ int i, j; int i, j; for (i = N; i >= 1; i--)for (i = N; i >= 1; i--) for (j = 2; j <= i; j++)for (j = 2; j <= i; j++) if ((a[j-1] > a[j])if ((a[j-1] > a[j]) swap(a, j-1, j); swap(a, j-1, j); }}

THE END