求不定方程x1+—xk=J的非负整数解
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#define K 3 #define J 5
void () { int a[K]={0}; bool TF; int i, j, t;
TF=false; t=0; i=0;
while(1) { if (i==0) { if (TF) { a[i]++; if (a[i]>J) break; }
t+=a[i]; i++; TF=false; continue; } else { if (TF) { a[i]++; if (a[i]>J-t) { a[i]=0; t-=a[i-1]; i--; TF=true; continue; } }
if (i==K-1) { if (t+a[i]==J) { for (j=0; j<K; j++) { printf("%d ", a[j]); } printf("n"); } TF=true; continue; }
t+=a[i]; i++; TF=false; continue; } } }
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变体一:
求不定方程x1+—xk=J的正整数解
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#define K 2 #define J 4
void () { int a[K]={0}; int i, j, t;
t=0; i=0;
while(1) { if (i==0) { a[i]++; if (a[i]>=J) break;
t+=a[i]; i++; continue; } else { a[i]++; if (a[i]>J-t) { a[i]=0; t-=a[i-1]; i--; continue; }
if (i==K-1) { if (t+a[i]==J) { for (j=0; j<K; j++) { printf("%d ", a[j]); } printf("n"); } continue; }
t+=a[i]; i++; continue; } } }
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变体二:求不定方程x1+—xk=J在约束条件0<=x1<=m1—-0<=xk<=mk下的非负整数解
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#define K 2 #define J 5
void () { int a[K]={0}; int m[K]={2, 3}; bool TF; int i, j, t;
TF=false; t=0; i=0;
while(1) { if (i==0) { if (TF) { a[i]++; if (a[i]>m[i] || a[i]>J) break; }
t+=a[i]; i++; TF=false; continue; } else { if (TF) { a[i]++; if (a[i]>J-t || a[i]>m[i]) { a[i]=0; t-=a[i-1]; i--; TF=true; continue; } }
if (i==K-1) { if (t+a[i]==J) { for (j=0; j<K; j++) { printf("%d ", a[j]); } printf("n"); } TF=true; continue; }
t+=a[i]; i++; TF=false; continue; } } }
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变体三:求不定方程x1+—xk=J在约束条件1<=x1<=m1—-1<=xk<=mk下的正整数解
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#define K 2 #define J 4
void () { int a[K]={0}; int m[K]={2, 3}; int i, j, t;
t=0; i=0;
while(1) { if (i==0) { a[i]++; if (a[i]>m[i] || a[i]>=J) break;
t+=a[i]; i++; continue; } else { a[i]++; if (a[i]>J-t || a[i]>m[i]) { a[i]=0; t-=a[i-1]; i--; continue; }
if (i==K-1) { if (t+a[i]==J) { for (j=0; j<K; j++) { printf("%d ", a[j]); } printf("n"); } continue; }
t+=a[i]; i++; continue; } } }
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