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451 lines
40 KiB
HTML
451 lines
40 KiB
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<meta http-equiv="Content-Type" content="text/html;charset=US-ASCII">
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<meta name="generator" content="ZealOS V0.05">
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<style type="text/css">
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body {background-color:#000000;}
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</style>
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</head>
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<body>
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<pre style="font-family:courier;font-size:10pt">
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<a name="l1"></a><span class=cF2>/*The magic pairs problem:</span><span class=cF0>
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<a name="l2"></a>
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<a name="l3"></a></span><span class=cF2>Let SumFact(n) be the sum of factors</span><span class=cF0>
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<a name="l4"></a></span><span class=cF2>of n.</span><span class=cF0>
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<a name="l5"></a>
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<a name="l6"></a></span><span class=cF2>Find all n1,n2 in a range such that</span><span class=cF0>
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<a name="l7"></a>
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<a name="l8"></a></span><span class=cF2>SumFact(n1)-n1-1 == n2</span><span class=cF0> </span><span class=cF2>and</span><span class=cF0>
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<a name="l9"></a></span><span class=cF2>SumFact(n2)-n2-1 == n1</span><span class=cF0>
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<a name="l10"></a>
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<a name="l11"></a></span><span class=cF2>-----------------------------------------------------</span><span class=cF0>
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<a name="l12"></a></span><span class=cF2>To find SumFact(k), start with prime factorization:</span><span class=cF0>
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<a name="l13"></a>
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<a name="l14"></a></span><span class=cF2>k=(p1^n1)(p2^n2) ... (pN^nN)</span><span class=cF0>
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<a name="l15"></a>
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<a name="l16"></a></span><span class=cF2>THEN,</span><span class=cF0>
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<a name="l17"></a>
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<a name="l18"></a></span><span class=cF2>SumFact(k)=(1+p1+p1^2...p1^n1)*(1+p2+p2^2...p2^n2)*</span><span class=cF0>
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<a name="l19"></a></span><span class=cF2>(1+pN+pN^2...pN^nN)</span><span class=cF0>
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<a name="l20"></a>
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<a name="l21"></a></span><span class=cF2>PROOF:</span><span class=cF0>
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<a name="l22"></a>
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<a name="l23"></a></span><span class=cF2>Do a couple examples -- it's obvious:</span><span class=cF0>
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<a name="l24"></a>
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<a name="l25"></a></span><span class=cF2>48=2^4*3</span><span class=cF0>
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<a name="l26"></a>
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<a name="l27"></a></span><span class=cF2>SumFact(48)=(1+2+4+8+16)*(1+3)=1+2+4+8+16+3+6+12+24+48</span><span class=cF0>
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<a name="l28"></a>
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<a name="l29"></a></span><span class=cF2>75=3*5^2</span><span class=cF0>
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<a name="l30"></a>
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<a name="l31"></a></span><span class=cF2>SumFact(75)=(1+3)*(1+5+25)</span><span class=cF0> </span><span class=cF2>=1+5+25+3+15+75</span><span class=cF0>
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<a name="l32"></a>
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<a name="l33"></a></span><span class=cF2>Corollary:</span><span class=cF0>
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<a name="l34"></a>
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<a name="l35"></a></span><span class=cF2>SumFact(k)=SumFact(p1^n1)*SumFact(p2^n2)*...*SumFact(pN^nN)</span><span class=cF0>
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<a name="l36"></a>
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<a name="l37"></a></span><span class=cF2>*/</span><span class=cF0>
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<a name="l38"></a>
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<a name="l39"></a></span><span class=cF2>//Primes are needed to sqrt(N). Therefore, we can use U32.</span><span class=cF0>
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<a name="l40"></a></span><span class=cF1>class</span><span class=cF0> PowPrime
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<a name="l41"></a>{
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<a name="l42"></a> </span><span class=cF9>I64</span><span class=cF0> n;
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<a name="l43"></a> </span><span class=cF9>I64</span><span class=cF0> sumfact; </span><span class=cF2>//Sumfacts for powers of primes are needed beyond sqrt(N)</span><span class=cF0>
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<a name="l44"></a>};
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<a name="l45"></a>
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<a name="l46"></a></span><span class=cF1>class</span><span class=cF0> Prime
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<a name="l47"></a>{
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<a name="l48"></a> </span><span class=cF9>U32</span><span class=cF0> prime, pow_count;
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<a name="l49"></a> PowPrime *pp;
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<a name="l50"></a>};
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<a name="l51"></a>
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<a name="l52"></a></span><span class=cF9>I64</span><span class=cF0> *PrimesNew(</span><span class=cF9>I64</span><span class=cF0> N, </span><span class=cF9>I64</span><span class=cF0> *_sqrt_primes, </span><span class=cF9>I64</span><span class=cF0> *_cbrt_primes)
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<a name="l53"></a>{
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<a name="l54"></a> </span><span class=cF9>I64</span><span class=cF0> i, j, sqrt = </span><span class=cF5>Ceil</span><span class=cF0>(</span><span class=cF5>Sqrt</span><span class=cF7>(</span><span class=cF0>N</span><span class=cF7>)</span><span class=cF0>), cbrt = </span><span class=cF5>Ceil</span><span class=cF0>(N ` </span><span class=cF7>(</span><span class=cFE>1</span><span class=cF0> / </span><span class=cFE>3</span><span class=cF0>.</span><span class=cFE>0</span><span class=cF7>)</span><span class=cF0>),
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<a name="l55"></a> sqrt_sqrt = </span><span class=cF5>Ceil</span><span class=cF0>(</span><span class=cF5>Sqrt</span><span class=cF7>(</span><span class=cF0>sqrt</span><span class=cF7>)</span><span class=cF0>), sqrt_primes = </span><span class=cFE>0</span><span class=cF0>, cbrt_primes = </span><span class=cFE>0</span><span class=cF0>;
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<a name="l56"></a> </span><span class=cF1>U8</span><span class=cF0> *s = </span><span class=cF5>CAlloc</span><span class=cF0>(</span><span class=cF7>(</span><span class=cF0>sqrt + </span><span class=cFE>1</span><span class=cF0> + </span><span class=cFE>7</span><span class=cF7>)</span><span class=cF0> / </span><span class=cFE>8</span><span class=cF0>);
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<a name="l57"></a> Prime *primes, *p;
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<a name="l58"></a>
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<a name="l59"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>2</span><span class=cF0>; i <= sqrt_sqrt; i++)
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<a name="l60"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l61"></a> </span><span class=cF1>if</span><span class=cF0> (!</span><span class=cF5>Bt</span><span class=cF7>(</span><span class=cF0>s, i</span><span class=cF7>)</span><span class=cF0>)
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<a name="l62"></a> {
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<a name="l63"></a> j = i * </span><span class=cFE>2</span><span class=cF0>;
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<a name="l64"></a> </span><span class=cF1>while</span><span class=cF0> (j <= sqrt)
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<a name="l65"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l66"></a> </span><span class=cF5>Bts</span><span class=cF0>(s, j);
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<a name="l67"></a> j += i;
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<a name="l68"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l69"></a> }
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<a name="l70"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l71"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>2</span><span class=cF0>; i <= sqrt; i++)
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<a name="l72"></a> </span><span class=cF1>if</span><span class=cF0> (!</span><span class=cF5>Bt</span><span class=cF7>(</span><span class=cF0>s, i</span><span class=cF7>)</span><span class=cF0>)
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<a name="l73"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l74"></a> sqrt_primes++; </span><span class=cF2>//Count primes</span><span class=cF0>
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<a name="l75"></a> </span><span class=cF1>if</span><span class=cF0> (i <= cbrt)
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<a name="l76"></a> cbrt_primes++;
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<a name="l77"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l78"></a>
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<a name="l79"></a> p = primes = </span><span class=cF5>CAlloc</span><span class=cF0>(sqrt_primes * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF0>Prime</span><span class=cF7>)</span><span class=cF0>);
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<a name="l80"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>2</span><span class=cF0>; i <= sqrt; i++)
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<a name="l81"></a> </span><span class=cF1>if</span><span class=cF0> (!</span><span class=cF5>Bt</span><span class=cF7>(</span><span class=cF0>s, i</span><span class=cF7>)</span><span class=cF0>)
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<a name="l82"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l83"></a> p->prime = i;
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<a name="l84"></a> p++;
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<a name="l85"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l86"></a> </span><span class=cF5>Free</span><span class=cF0>(s);
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<a name="l87"></a>
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<a name="l88"></a> *_sqrt_primes = sqrt_primes;
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<a name="l89"></a> *_cbrt_primes = cbrt_primes;
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<a name="l90"></a>
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<a name="l91"></a> </span><span class=cF1>return</span><span class=cF0> primes;
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<a name="l92"></a>}
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<a name="l93"></a>
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<a name="l94"></a>PowPrime *PowPrimesNew(</span><span class=cF9>I64</span><span class=cF0> N, </span><span class=cF9>I64</span><span class=cF0> sqrt_primes, Prime *primes, </span><span class=cF9>I64</span><span class=cF0> *_num_powprimes)
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<a name="l95"></a>{
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<a name="l96"></a> </span><span class=cF9>I64</span><span class=cF0> i, j, k, sf, num_powprimes = </span><span class=cFE>0</span><span class=cF0>;
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<a name="l97"></a> Prime *p;
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<a name="l98"></a> PowPrime *powprimes, *pp;
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<a name="l99"></a>
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<a name="l100"></a> p = primes;
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<a name="l101"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < sqrt_primes; i++)
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<a name="l102"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l103"></a> num_powprimes += </span><span class=cF5>Floor</span><span class=cF0>(</span><span class=cF5>Ln</span><span class=cF7>(</span><span class=cF0>N</span><span class=cF7>)</span><span class=cF0> / </span><span class=cF5>Ln</span><span class=cF7>(</span><span class=cF0>p->prime</span><span class=cF7>)</span><span class=cF0>);
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<a name="l104"></a> p++;
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<a name="l105"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l106"></a>
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<a name="l107"></a> p = primes;
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<a name="l108"></a> pp = powprimes = </span><span class=cF5>MAlloc</span><span class=cF0>(num_powprimes * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF0>PowPrime</span><span class=cF7>)</span><span class=cF0>);
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<a name="l109"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < sqrt_primes; i++)
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<a name="l110"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l111"></a> p->pp = pp;
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<a name="l112"></a> j = p->prime;
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<a name="l113"></a> k = </span><span class=cFE>1</span><span class=cF0>;
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<a name="l114"></a> sf = </span><span class=cFE>1</span><span class=cF0>;
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<a name="l115"></a> </span><span class=cF1>while</span><span class=cF0> (j < N)
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<a name="l116"></a> {
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<a name="l117"></a> sf += j;
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<a name="l118"></a> pp->n = j;
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<a name="l119"></a> pp->sumfact = sf;
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<a name="l120"></a> j *= p->prime;
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<a name="l121"></a> pp++;
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<a name="l122"></a> p->pow_count++;
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<a name="l123"></a> }
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<a name="l124"></a> p++;
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<a name="l125"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l126"></a> *_num_powprimes = num_powprimes;
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<a name="l127"></a>
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<a name="l128"></a> </span><span class=cF1>return</span><span class=cF0> powprimes;
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<a name="l129"></a>}
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<a name="l130"></a>
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<a name="l131"></a></span><span class=cF9>I64</span><span class=cF0> SumFact(</span><span class=cF9>I64</span><span class=cF0> n, </span><span class=cF9>I64</span><span class=cF0> sqrt_primes, Prime *p)
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<a name="l132"></a>{
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<a name="l133"></a> </span><span class=cF9>I64</span><span class=cF0> i, k, sf = </span><span class=cFE>1</span><span class=cF0>;
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<a name="l134"></a> PowPrime *pp;
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<a name="l135"></a>
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<a name="l136"></a> </span><span class=cF1>if</span><span class=cF0> (n < </span><span class=cFE>2</span><span class=cF0>)
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<a name="l137"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cFE>1</span><span class=cF0>;
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<a name="l138"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < sqrt_primes; i++)
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<a name="l139"></a> </span><span class=cF7>{</span><span class=cF0>
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<a name="l140"></a> k = </span><span class=cFE>0</span><span class=cF0>;
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<a name="l141"></a> </span><span class=cF1>while</span><span class=cF0> (!</span><span class=cF7>(</span><span class=cF0>n % p->prime</span><span class=cF7>)</span><span class=cF0>)
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<a name="l142"></a> {
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<a name="l143"></a> n /= p->prime;
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<a name="l144"></a> k++;
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<a name="l145"></a> }
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<a name="l146"></a> </span><span class=cF1>if</span><span class=cF0> (k)
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<a name="l147"></a> {
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<a name="l148"></a> pp = p->pp + (k - </span><span class=cFE>1</span><span class=cF0>);
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<a name="l149"></a> sf *= pp->sumfact;
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<a name="l150"></a> </span><span class=cF1>if</span><span class=cF0> (n == </span><span class=cFE>1</span><span class=cF0>)
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<a name="l151"></a> </span><span class=cF1>return</span><span class=cF0> sf;
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<a name="l152"></a> }
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<a name="l153"></a> p++;
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<a name="l154"></a> </span><span class=cF7>}</span><span class=cF0>
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<a name="l155"></a>
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<a name="l156"></a> </span><span class=cF1>return</span><span class=cF0> sf * (</span><span class=cFE>1</span><span class=cF0> + n); </span><span class=cF2>//Prime</span><span class=cF0>
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<a name="l157"></a>}
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<a name="l158"></a>
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<a name="l159"></a></span><span class=cF1>Bool</span><span class=cF0> TestSumFact(</span><span class=cF9>I64</span><span class=cF0> n, </span><span class=cF9>I64</span><span class=cF0> target_sf, </span><span class=cF9>I64</span><span class=cF0> sqrt_primes, </span><span class=cF9>I64</span><span class=cF0> cbrt_primes, Prime *p)
|
||
|
|
<a name="l160"></a>{
|
||
|
|
<a name="l161"></a> </span><span class=cF9>I64</span><span class=cF0> i = </span><span class=cFE>0</span><span class=cF0>, k, b, x1, x2;
|
||
|
|
<a name="l162"></a> PowPrime *pp;
|
||
|
|
<a name="l163"></a> </span><span class=cF1>F64</span><span class=cF0> disc;
|
||
|
|
<a name="l164"></a>
|
||
|
|
<a name="l165"></a> </span><span class=cF1>if</span><span class=cF0> (n < </span><span class=cFE>2</span><span class=cF0>)
|
||
|
|
<a name="l166"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l167"></a> </span><span class=cF1>while</span><span class=cF0> (i++ < cbrt_primes)
|
||
|
|
<a name="l168"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l169"></a> k = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l170"></a> </span><span class=cF1>while</span><span class=cF0> (!</span><span class=cF7>(</span><span class=cF0>n % p->prime</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l171"></a> {
|
||
|
|
<a name="l172"></a> n /= p->prime;
|
||
|
|
<a name="l173"></a> k++;
|
||
|
|
<a name="l174"></a> }
|
||
|
|
<a name="l175"></a> </span><span class=cF1>if</span><span class=cF0> (k)
|
||
|
|
<a name="l176"></a> {
|
||
|
|
<a name="l177"></a> pp = p->pp + (k - </span><span class=cFE>1</span><span class=cF0>);
|
||
|
|
<a name="l178"></a> </span><span class=cF1>if</span><span class=cF0> (</span><span class=cF5>ModU64</span><span class=cF7>(</span><span class=cF0>&target_sf, pp->sumfact</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l179"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l180"></a> </span><span class=cF1>if</span><span class=cF0> (n == </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l181"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l182"></a> </span><span class=cF1>if</span><span class=cF0> (target_sf == </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l183"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>TRUE</span><span class=cF0>;
|
||
|
|
<a name="l184"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l185"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l186"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l187"></a> }
|
||
|
|
<a name="l188"></a> p++;
|
||
|
|
<a name="l189"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l190"></a></span><span class=cF2>/*</span><span class=cF0> </span><span class=cF2>At this point we have three possible cases to test</span><span class=cF0>
|
||
|
|
<a name="l191"></a></span><span class=cF2>1)n==p1 </span><span class=cF0> </span><span class=cF2>->sf==(1+p1)</span><span class=cF0> </span><span class=cF2>?</span><span class=cF0>
|
||
|
|
<a name="l192"></a></span><span class=cF2>2)n==p1*p1</span><span class=cF0> </span><span class=cF2>->sf==(1+p1+p1^2) </span><span class=cF0> </span><span class=cF2>?</span><span class=cF0>
|
||
|
|
<a name="l193"></a></span><span class=cF2>3)n==p1*p2</span><span class=cF0> </span><span class=cF2>->sf==(p1+1)*(p2+1) ?</span><span class=cF0>
|
||
|
|
<a name="l194"></a>
|
||
|
|
<a name="l195"></a></span><span class=cF2>*/</span><span class=cF0>
|
||
|
|
<a name="l196"></a> </span><span class=cF1>if</span><span class=cF0> (</span><span class=cFE>1</span><span class=cF0> + n == target_sf)
|
||
|
|
<a name="l197"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l198"></a> </span><span class=cF1>while</span><span class=cF0> (i++ < sqrt_primes)
|
||
|
|
<a name="l199"></a> {
|
||
|
|
<a name="l200"></a> k = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l201"></a> </span><span class=cF1>while</span><span class=cF0> (!</span><span class=cF7>(</span><span class=cF0>n % p->prime</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l202"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l203"></a> n /= p->prime;
|
||
|
|
<a name="l204"></a> k++;
|
||
|
|
<a name="l205"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l206"></a> </span><span class=cF1>if</span><span class=cF0> (k)
|
||
|
|
<a name="l207"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l208"></a> pp = p->pp + (k - </span><span class=cFE>1</span><span class=cF0>);
|
||
|
|
<a name="l209"></a> </span><span class=cF1>if</span><span class=cF0> (</span><span class=cF5>ModU64</span><span class=cF7>(</span><span class=cF0>&target_sf, pp->sumfact</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l210"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l211"></a> </span><span class=cF1>if</span><span class=cF0> (n == </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l212"></a> {
|
||
|
|
<a name="l213"></a> </span><span class=cF1>if</span><span class=cF0> (target_sf == </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l214"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>TRUE</span><span class=cF0>;
|
||
|
|
<a name="l215"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l216"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l217"></a> }
|
||
|
|
<a name="l218"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l219"></a> p++;
|
||
|
|
<a name="l220"></a> }
|
||
|
|
<a name="l221"></a> </span><span class=cF1>if</span><span class=cF0> (</span><span class=cFE>1</span><span class=cF0> + n == target_sf)
|
||
|
|
<a name="l222"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>TRUE</span><span class=cF0>;
|
||
|
|
<a name="l223"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l224"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l225"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l226"></a>
|
||
|
|
<a name="l227"></a> k =</span><span class=cF5>Sqrt</span><span class=cF0>(n);
|
||
|
|
<a name="l228"></a> </span><span class=cF1>if</span><span class=cF0> (k * k == n)
|
||
|
|
<a name="l229"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l230"></a> </span><span class=cF1>if</span><span class=cF0> (</span><span class=cFE>1</span><span class=cF0> + k + n == target_sf)
|
||
|
|
<a name="l231"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>TRUE</span><span class=cF0>;
|
||
|
|
<a name="l232"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l233"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l234"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l235"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l236"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l237"></a></span><span class=cF2>// n==p1*p2 -> sf==(p1+1)*(p2+1) ?</span><span class=cF0> </span><span class=cF2>where p1 != 1 && p2 != 1</span><span class=cF0>
|
||
|
|
<a name="l238"></a> </span><span class=cF2>// if p1==1 || p2==1, it is FALSE because we checked a single prime above.</span><span class=cF0>
|
||
|
|
<a name="l239"></a>
|
||
|
|
<a name="l240"></a> </span><span class=cF2>// sf==(p1+1)*(n/p1+1)</span><span class=cF0>
|
||
|
|
<a name="l241"></a> </span><span class=cF2>// sf==n+p1+n/p1+1</span><span class=cF0>
|
||
|
|
<a name="l242"></a> </span><span class=cF2>// sf*p1==n*p1+p1^2+n+p1</span><span class=cF0>
|
||
|
|
<a name="l243"></a> </span><span class=cF2>// p1^2+(n+1-sf)*p1+n=0</span><span class=cF0>
|
||
|
|
<a name="l244"></a> </span><span class=cF2>// x=(-b+/-sqrt(b^2-4ac))/2a</span><span class=cF0>
|
||
|
|
<a name="l245"></a> </span><span class=cF2>// a=1</span><span class=cF0>
|
||
|
|
<a name="l246"></a> </span><span class=cF2>// x=(-b+/-sqrt(b^2-4c))/2</span><span class=cF0>
|
||
|
|
<a name="l247"></a> </span><span class=cF2>// b=n+1-sf;c=n</span><span class=cF0>
|
||
|
|
<a name="l248"></a> b = n + </span><span class=cFE>1</span><span class=cF0> - target_sf;
|
||
|
|
<a name="l249"></a></span><span class=cF2>// x=(-b+/-sqrt(b^2-4n))/2</span><span class=cF0>
|
||
|
|
<a name="l250"></a> disc = b * b - </span><span class=cFE>4</span><span class=cF0> * n;
|
||
|
|
<a name="l251"></a> </span><span class=cF1>if</span><span class=cF0> (disc < </span><span class=cFE>0</span><span class=cF0>)
|
||
|
|
<a name="l252"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l253"></a> x1 = (-b - </span><span class=cF5>Sqrt</span><span class=cF7>(</span><span class=cF0>disc</span><span class=cF7>)</span><span class=cF0>) / </span><span class=cFE>2</span><span class=cF0>;
|
||
|
|
<a name="l254"></a> </span><span class=cF1>if</span><span class=cF0> (x1 <= </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l255"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l256"></a> x2 = n / x1;
|
||
|
|
<a name="l257"></a> </span><span class=cF1>if</span><span class=cF0> (x2 > </span><span class=cFE>1</span><span class=cF0> && x1 * x2 == n)
|
||
|
|
<a name="l258"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>TRUE</span><span class=cF0>;
|
||
|
|
<a name="l259"></a> </span><span class=cF1>else</span><span class=cF0>
|
||
|
|
<a name="l260"></a> </span><span class=cF1>return</span><span class=cF0> </span><span class=cF3>FALSE</span><span class=cF0>;
|
||
|
|
<a name="l261"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l262"></a>}
|
||
|
|
<a name="l263"></a>
|
||
|
|
<a name="l264"></a></span><span class=cF1>U0</span><span class=cF0> PutFactors(</span><span class=cF9>I64</span><span class=cF0> n) </span><span class=cF2>//For debugging</span><span class=cF0>
|
||
|
|
<a name="l265"></a>{
|
||
|
|
<a name="l266"></a> </span><span class=cF9>I64</span><span class=cF0> i, k, sqrt = </span><span class=cF5>Ceil</span><span class=cF0>(</span><span class=cF5>Sqrt</span><span class=cF7>(</span><span class=cF0>n</span><span class=cF7>)</span><span class=cF0>);
|
||
|
|
<a name="l267"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>2</span><span class=cF0>; i <= sqrt; i++)
|
||
|
|
<a name="l268"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l269"></a> k = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l270"></a> </span><span class=cF1>while</span><span class=cF0> (!</span><span class=cF7>(</span><span class=cF0>n % i</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l271"></a> {
|
||
|
|
<a name="l272"></a> k++;
|
||
|
|
<a name="l273"></a> n /= i;
|
||
|
|
<a name="l274"></a> }
|
||
|
|
<a name="l275"></a> </span><span class=cF1>if</span><span class=cF0> (k)
|
||
|
|
<a name="l276"></a> {
|
||
|
|
<a name="l277"></a> </span><span class=cF6>"%d"</span><span class=cF0>, i;
|
||
|
|
<a name="l278"></a> </span><span class=cF1>if</span><span class=cF0> (k > </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l279"></a> </span><span class=cF6>"^%d"</span><span class=cF0>, k;
|
||
|
|
<a name="l280"></a> </span><span class=cF6>''</span><span class=cF0> </span><span class=cF3>CH_SPACE</span><span class=cF0>;
|
||
|
|
<a name="l281"></a> }
|
||
|
|
<a name="l282"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l283"></a> </span><span class=cF1>if</span><span class=cF0> (n != </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l284"></a> </span><span class=cF6>"%d "</span><span class=cF0>, n;
|
||
|
|
<a name="l285"></a>}
|
||
|
|
<a name="l286"></a>
|
||
|
|
<a name="l287"></a></span><span class=cF1>class</span><span class=cF0> RangeJob
|
||
|
|
<a name="l288"></a>{
|
||
|
|
<a name="l289"></a> </span><span class=cF9>CDoc</span><span class=cF0> *doc;
|
||
|
|
<a name="l290"></a> </span><span class=cF9>I64</span><span class=cF0> num, lo, hi, N, sqrt_primes, cbrt_primes;
|
||
|
|
<a name="l291"></a> Prime *primes;
|
||
|
|
<a name="l292"></a> </span><span class=cF9>CJob</span><span class=cF0> *cmd;
|
||
|
|
<a name="l293"></a>
|
||
|
|
<a name="l294"></a>} rj[</span><span class=cFB>mp_count</span><span class=cF0>];
|
||
|
|
<a name="l295"></a>
|
||
|
|
<a name="l296"></a></span><span class=cF9>I64</span><span class=cF0> TestCoreSubRange(RangeJob *r)
|
||
|
|
<a name="l297"></a>{
|
||
|
|
<a name="l298"></a> </span><span class=cF9>I64</span><span class=cF0> i, j, m, n, n2, sf, res = </span><span class=cFE>0</span><span class=cF0>, range = r->hi - r->lo,
|
||
|
|
<a name="l299"></a> *sumfacts = </span><span class=cF5>MAlloc</span><span class=cF0>(range * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF9>I64</span><span class=cF7>)</span><span class=cF0>),
|
||
|
|
<a name="l300"></a> *residue = </span><span class=cF5>MAlloc</span><span class=cF0>(range * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF9>I64</span><span class=cF7>)</span><span class=cF0>);
|
||
|
|
<a name="l301"></a> </span><span class=cF9>U16</span><span class=cF0> *pow_count = </span><span class=cF5>MAlloc</span><span class=cF0>(range * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF9>U16</span><span class=cF7>)</span><span class=cF0>);
|
||
|
|
<a name="l302"></a> Prime *p = r->primes;
|
||
|
|
<a name="l303"></a> PowPrime *pp;
|
||
|
|
<a name="l304"></a>
|
||
|
|
<a name="l305"></a> </span><span class=cF5>MemSetI64</span><span class=cF0>(sumfacts, </span><span class=cFE>1</span><span class=cF0>, range);
|
||
|
|
<a name="l306"></a> </span><span class=cF1>for</span><span class=cF0> (n = r->lo; n < r->hi; n++)
|
||
|
|
<a name="l307"></a> residue[n - r->lo] = n;
|
||
|
|
<a name="l308"></a> </span><span class=cF1>for</span><span class=cF0> (j = </span><span class=cFE>0</span><span class=cF0>; j <r->sqrt_primes; j++)
|
||
|
|
<a name="l309"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l310"></a> </span><span class=cF5>MemSet</span><span class=cF0>(pow_count, </span><span class=cFE>0</span><span class=cF0>, range * </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF9>U16</span><span class=cF7>)</span><span class=cF0>);
|
||
|
|
<a name="l311"></a> m = </span><span class=cFE>1</span><span class=cF0>;
|
||
|
|
<a name="l312"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < p->pow_count; i++)
|
||
|
|
<a name="l313"></a> {
|
||
|
|
<a name="l314"></a> m *= p->prime;
|
||
|
|
<a name="l315"></a> n = m - r->lo % m;
|
||
|
|
<a name="l316"></a> </span><span class=cF1>while</span><span class=cF0> (n < range)
|
||
|
|
<a name="l317"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l318"></a> pow_count[n]++;
|
||
|
|
<a name="l319"></a> n += m;
|
||
|
|
<a name="l320"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l321"></a> }
|
||
|
|
<a name="l322"></a> </span><span class=cF1>for</span><span class=cF0> (n = </span><span class=cFE>0</span><span class=cF0>; n < range; n++)
|
||
|
|
<a name="l323"></a> </span><span class=cF1>if</span><span class=cF0> (i = pow_count[n])
|
||
|
|
<a name="l324"></a> {
|
||
|
|
<a name="l325"></a> pp = &p->pp[i - </span><span class=cFE>1</span><span class=cF0>];
|
||
|
|
<a name="l326"></a> sumfacts[n] *= pp->sumfact;
|
||
|
|
<a name="l327"></a> residue [n] /= pp->n;
|
||
|
|
<a name="l328"></a> }
|
||
|
|
<a name="l329"></a> p++;
|
||
|
|
<a name="l330"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l331"></a>
|
||
|
|
<a name="l332"></a> </span><span class=cF1>for</span><span class=cF0> (n = </span><span class=cFE>0</span><span class=cF0>; n < range; n++)
|
||
|
|
<a name="l333"></a> </span><span class=cF1>if</span><span class=cF0> (residue[n] != </span><span class=cFE>1</span><span class=cF0>)
|
||
|
|
<a name="l334"></a> sumfacts[n] *= </span><span class=cFE>1</span><span class=cF0> + residue[n];
|
||
|
|
<a name="l335"></a>
|
||
|
|
<a name="l336"></a> </span><span class=cF1>for</span><span class=cF0> (n = r->lo; n < r->hi; n++)
|
||
|
|
<a name="l337"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l338"></a> sf = sumfacts[n - r->lo];
|
||
|
|
<a name="l339"></a> n2 = sf - n - </span><span class=cFE>1</span><span class=cF0>;
|
||
|
|
<a name="l340"></a> </span><span class=cF1>if</span><span class=cF0> (n < n2 < r->N)
|
||
|
|
<a name="l341"></a> {
|
||
|
|
<a name="l342"></a> </span><span class=cF1>if</span><span class=cF0> (r->lo <= n2<r->hi && sumfacts[n2 - r->lo] - n2 - </span><span class=cFE>1</span><span class=cF0> == n ||
|
||
|
|
<a name="l343"></a> TestSumFact</span><span class=cF7>(</span><span class=cF0>n2, sf, r->sqrt_primes, r->cbrt_primes, r->primes</span><span class=cF7>)</span><span class=cF0>)
|
||
|
|
<a name="l344"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l345"></a> </span><span class=cF5>DocPrint</span><span class=cF0>(r->doc, </span><span class=cF6>"%u:%u\n"</span><span class=cF0>, n, sf - n - </span><span class=cFE>1</span><span class=cF0>);
|
||
|
|
<a name="l346"></a> res++;
|
||
|
|
<a name="l347"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l348"></a> }
|
||
|
|
<a name="l349"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l350"></a> </span><span class=cF5>Free</span><span class=cF0>(pow_count);
|
||
|
|
<a name="l351"></a> </span><span class=cF5>Free</span><span class=cF0>(residue);
|
||
|
|
<a name="l352"></a> </span><span class=cF5>Free</span><span class=cF0>(sumfacts);
|
||
|
|
<a name="l353"></a>
|
||
|
|
<a name="l354"></a> </span><span class=cF1>return</span><span class=cF0> res;
|
||
|
|
<a name="l355"></a>}
|
||
|
|
<a name="l356"></a>
|
||
|
|
<a name="l357"></a>#</span><span class=cF1>define</span><span class=cF0> CORE_SUB_RANGE </span><span class=cFE>0x1000</span><span class=cF0>
|
||
|
|
<a name="l358"></a>
|
||
|
|
<a name="l359"></a></span><span class=cF9>I64</span><span class=cF0> TestCoreRange(RangeJob *r)
|
||
|
|
<a name="l360"></a>{
|
||
|
|
<a name="l361"></a> </span><span class=cF9>I64</span><span class=cF0> i, n, res = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l362"></a> RangeJob rj;
|
||
|
|
<a name="l363"></a>
|
||
|
|
<a name="l364"></a> </span><span class=cF5>MemCopy</span><span class=cF0>(&rj, r, </span><span class=cF1>sizeof</span><span class=cF7>(</span><span class=cF0>RangeJob</span><span class=cF7>)</span><span class=cF0>);
|
||
|
|
<a name="l365"></a> </span><span class=cF1>for</span><span class=cF0> (i = r->lo; i < r->hi; i += CORE_SUB_RANGE)
|
||
|
|
<a name="l366"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l367"></a> rj.lo = i;
|
||
|
|
<a name="l368"></a> rj.hi = i + CORE_SUB_RANGE;
|
||
|
|
<a name="l369"></a> </span><span class=cF1>if</span><span class=cF0> (rj.hi > r->hi)
|
||
|
|
<a name="l370"></a> rj.hi = r->hi;
|
||
|
|
<a name="l371"></a> res += TestCoreSubRange(&rj);
|
||
|
|
<a name="l372"></a>
|
||
|
|
<a name="l373"></a> n = rj.hi - rj.lo;
|
||
|
|
<a name="l374"></a> </span><span class=cF1>lock</span><span class=cF0> {</span><span class=cFB>progress1</span><span class=cF0> += n;}
|
||
|
|
<a name="l375"></a>
|
||
|
|
<a name="l376"></a> </span><span class=cF5>Yield</span><span class=cF0>;
|
||
|
|
<a name="l377"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l378"></a>
|
||
|
|
<a name="l379"></a> </span><span class=cF1>return</span><span class=cF0> res;
|
||
|
|
<a name="l380"></a>}
|
||
|
|
<a name="l381"></a>
|
||
|
|
<a name="l382"></a></span><span class=cF9>I64</span><span class=cF0> MagicPairs(</span><span class=cF9>I64</span><span class=cF0> N)
|
||
|
|
<a name="l383"></a>{
|
||
|
|
<a name="l384"></a> </span><span class=cF1>F64</span><span class=cF0> t0 = </span><span class=cF5>tS</span><span class=cF0>;
|
||
|
|
<a name="l385"></a> </span><span class=cF9>I64</span><span class=cF0> res = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l386"></a> </span><span class=cF9>I64</span><span class=cF0> sqrt_primes, cbrt_primes, num_powprimes,
|
||
|
|
<a name="l387"></a> i, k, n = (N - </span><span class=cFE>1</span><span class=cF0>) / </span><span class=cFB>mp_count</span><span class=cF0> + </span><span class=cFE>1</span><span class=cF0>;
|
||
|
|
<a name="l388"></a> Prime *primes = PrimesNew(N, &sqrt_primes, &cbrt_primes);
|
||
|
|
<a name="l389"></a> PowPrime *powprimes = PowPrimesNew(N, sqrt_primes, primes, &num_powprimes);
|
||
|
|
<a name="l390"></a>
|
||
|
|
<a name="l391"></a> </span><span class=cF6>"N:%u SqrtPrimes:%u CbrtPrimes:%u PowersOfPrimes:%u\n"</span><span class=cF0>, N, sqrt_primes, cbrt_primes, num_powprimes;
|
||
|
|
<a name="l392"></a> </span><span class=cFB>progress1</span><span class=cF0> = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l393"></a> *</span><span class=cFB>progress1_desc</span><span class=cF0> = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l394"></a> </span><span class=cFB>progress1_max</span><span class=cF0> = N;
|
||
|
|
<a name="l395"></a> k = </span><span class=cFE>2</span><span class=cF0>;
|
||
|
|
<a name="l396"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < </span><span class=cFB>mp_count</span><span class=cF0>; i++)
|
||
|
|
<a name="l397"></a> </span><span class=cF7>{</span><span class=cF0>
|
||
|
|
<a name="l398"></a> rj[i].doc = </span><span class=cF5>DocPut</span><span class=cF0>;
|
||
|
|
<a name="l399"></a> rj[i].num = i;
|
||
|
|
<a name="l400"></a> rj[i].lo = k;
|
||
|
|
<a name="l401"></a> k += n;
|
||
|
|
<a name="l402"></a> </span><span class=cF1>if</span><span class=cF0> (k > N)
|
||
|
|
<a name="l403"></a> k = N;
|
||
|
|
<a name="l404"></a> rj[i].hi = k;
|
||
|
|
<a name="l405"></a> rj[i].N = N;
|
||
|
|
<a name="l406"></a> rj[i].sqrt_primes = sqrt_primes;
|
||
|
|
<a name="l407"></a> rj[i].cbrt_primes = cbrt_primes;
|
||
|
|
<a name="l408"></a> rj[i].primes = primes;
|
||
|
|
<a name="l409"></a> rj[i].cmd = </span><span class=cF5>JobQueue</span><span class=cF0>(&TestCoreRange, &rj[i], </span><span class=cFB>mp_count</span><span class=cF0> - </span><span class=cFE>1</span><span class=cF0> - i, </span><span class=cFE>0</span><span class=cF0>);
|
||
|
|
<a name="l410"></a> </span><span class=cF7>}</span><span class=cF0>
|
||
|
|
<a name="l411"></a> </span><span class=cF1>for</span><span class=cF0> (i = </span><span class=cFE>0</span><span class=cF0>; i < </span><span class=cFB>mp_count</span><span class=cF0>; i++)
|
||
|
|
<a name="l412"></a> res += </span><span class=cF5>JobResGet</span><span class=cF0>(rj[i].cmd);
|
||
|
|
<a name="l413"></a> </span><span class=cF5>Free</span><span class=cF0>(powprimes);
|
||
|
|
<a name="l414"></a> </span><span class=cF5>Free</span><span class=cF0>(primes);
|
||
|
|
<a name="l415"></a> </span><span class=cF6>"Found:%u Time:%9.4f\n"</span><span class=cF0>, res, </span><span class=cF5>tS</span><span class=cF0> - t0;
|
||
|
|
<a name="l416"></a> </span><span class=cFB>progress1</span><span class=cF0> = </span><span class=cFB>progress1_max</span><span class=cF0> = </span><span class=cFE>0</span><span class=cF0>;
|
||
|
|
<a name="l417"></a>
|
||
|
|
<a name="l418"></a> </span><span class=cF1>return</span><span class=cF0> res;
|
||
|
|
<a name="l419"></a>}
|
||
|
|
<a name="l420"></a>
|
||
|
|
<a name="l421"></a>MagicPairs(</span><span class=cFE>1000000</span><span class=cF0>);
|
||
|
|
</span></pre></body>
|
||
|
|
</html>
|