long long int countNumSet(int arr[], int lastInd, int numChoose, int remainder, int modNum, long long int memoTable[][MAX_CHOOSE_SIZE + 1][MAX_MOD]) { int r, nextR; if(numChoose == 0) { if(remainder == 0) return 1; return 0; } /* Base cases */ if(lastInd + 1 < numChoose) return 0; /* Cannot choose numChoose numbers */ if(memoTable[lastInd][numChoose][remainder] >= 0) return memoTable[lastInd][numChoose][remainder]; long long int numSet = 0; /* Not taking this element */ numSet += countNumSet(arr, lastInd - 1, numChoose, remainder, modNum, memoTable); /* Choose this element */ r = getRemainder(arr[lastInd], modNum); nextR = remainder - r; if(nextR < 0) nextR = modNum + nextR; numSet += countNumSet(arr, lastInd - 1, numChoose - 1, nextR, modNum, memoTable); memoTable[lastInd][numChoose][remainder] = numSet; return numSet; }
static int fcubes(BigInteger *pArgument) { int mod18, modulus, i, mod83, mask; int pow, exp; boolean converted = FALSE; CopyBigInt(&value, pArgument); // Compute argument mod 18. mod18 = getRemainder(pArgument, 18); if (mod18 == 4 || mod18 == 5 || mod18 == 13 || mod18 == 14) { return -1; // Applet does not work if the number is congruent to 4 or 5 (mod 9) } if (mod18 == 16) { // Change sign. converted = TRUE; BigIntNegate(&value, &value); } for (i = 0; i<(int)(sizeof(sums)/sizeof(sums[0])); i += 10) { modulus = sums[i]; if ((getRemainder(&value, modulus) + modulus)% modulus == sums[i + 1]) { break; } } if (i<(int)(sizeof(sums) / sizeof(sums[0]))) { subtractdivide(&value, sums[i + 1], modulus); // value <- (value-sums[i+1])/modulus multadd(&Base1, sums[i + 2], &value, sums[i + 3]); // Base1 <- sums[i+2]*value+sums[i+3] multadd(&Base2, sums[i + 4], &value, sums[i + 5]); // Base2 <- sums[i+4]*value+sums[i+5] multadd(&Base3, sums[i + 6], &value, sums[i + 7]); // Base3 <- sums[i+6]*value+sums[i+7] multadd(&Base4, sums[i + 8], &value, sums[i + 9]); // Base4 <- sums[i+8]*value+sums[i+9] } else if (getRemainder(&value, 54) == 2) { // If value == 2 (mod 54)... subtractdivide(&value, 2, 54); // value <- (value-2)/54 EvaluateQuadraticPoly(&Base1, &value, 29484, 2211, 43); EvaluateQuadraticPoly(&Base2, &value, -29484, -2157, -41); EvaluateQuadraticPoly(&Base3, &value, 9828, 485, 4); EvaluateQuadraticPoly(&Base4, &value, -9828, -971, -22); } else if (getRemainder(&value, 83 * 108) == 83*46) { // If value == 83*46 (mod 83*108)... subtractdivide(&value, 83*46, 83*108); // value <-(value - (83*46)) / (83*108) EvaluateQuadraticPoly(&Base1, &value, 29484, 25143, 5371); EvaluateQuadraticPoly(&Base2, &value, -29484, -25089, -5348); EvaluateQuadraticPoly(&Base3, &value, 9828, 8129, 1682); EvaluateQuadraticPoly(&Base4, &value, -9828, -8615, -1889); } else { // Perform Pell solution of Demjanenko's theorem // Using these values of P, Q, R and S, a and b will be // always one and zero (mod 6) respectively. // P <- -112488782561 = -(52*2^31+819632865) // Q <- -6578430178320 = -(3063*2^31+687764496) // R <- -1923517596 = -(0*2^31+1923517596) // S <- P // P1 <- 1 // Q1 <- 0 // R1 <- 0 // S1 <- 1 P.limbs[1].x = S.limbs[1].x = 52; P.limbs[0].x = S.limbs[0].x = 819632865; Q.limbs[1].x = 3063; Q.limbs[0].x = 687764496; R.limbs[1].x = 0; R.limbs[0].x = 1923517596; P.nbrLimbs = Q.nbrLimbs = R.nbrLimbs = S.nbrLimbs = 3; P.sign = Q.sign = R.sign = S.sign = SIGN_NEGATIVE; P1.limbs[0].x = S1.limbs[0].x = 1; Q1.limbs[0].x = R1.limbs[0].x = 0; P1.nbrLimbs = Q1.nbrLimbs = R1.nbrLimbs = S1.nbrLimbs = 1; P1.sign = Q1.sign = R1.sign = S1.sign = SIGN_POSITIVE; mod83 = getRemainder(&value, 83); pow = 71; exp = 0; while (pow != mod83) { exp++; pow = (pow * 50) % 83; } if (exp > 82 / 2) { exp = 82 - exp; Q.sign = R.sign = SIGN_POSITIVE; } // Now exp is in range 0-41. mask = 32; while (mask > 0) { // tmpP1 <- P1*P1 + Q1*R1 // tmpQ1 <- (P1+S1) * Q1 // tmpR1 <- (P1+S1) * R1 // tmpS1 <- S1*S1 + Q1*R1 // P1 <- tmpP1 // Q1 <- tmpQ1 // R1 <- tmpR1 // S1 <- tmpS1 (void)BigIntMultiply(&P1, &P1, &tmpP1); (void)BigIntMultiply(&Q1, &R1, &tmpQ1); (void)BigIntMultiply(&S1, &S1, &tmpS1); BigIntAdd(&P1, &S1, &tmpR1); BigIntAdd(&tmpP1, &tmpQ1, &P1); BigIntAdd(&tmpS1, &tmpQ1, &S1); (void)BigIntMultiply(&tmpR1, &Q1, &Q1); (void)BigIntMultiply(&tmpR1, &R1, &R1); if ((exp & mask) != 0) { // tmpP1 <- P*P1 + Q*R1 // tmpQ1 <- P*Q1 + Q*S1 // tmpR1 <- R*P1 + S*R1 // tmpS1 <- R*Q1 + S*S1 // P1 <- tmpP1 // Q1 <- tmpQ1 // R1 <- tmpR1 // S1 <- tmpS1 (void)BigIntMultiply(&P, &P1, &tmpP1); (void)BigIntMultiply(&Q, &R1, &tmpQ1); (void)BigIntMultiply(&R, &P1, &tmpR1); (void)BigIntMultiply(&S, &R1, &tmpS1); BigIntAdd(&tmpP1, &tmpQ1, &P1); BigIntAdd(&tmpR1, &tmpS1, &R1); (void)BigIntMultiply(&P, &Q1, &tmpP1); (void)BigIntMultiply(&Q, &S1, &tmpQ1); (void)BigIntMultiply(&R, &Q1, &tmpR1); (void)BigIntMultiply(&S, &S1, &tmpS1); BigIntAdd(&tmpP1, &tmpQ1, &Q1); BigIntAdd(&tmpR1, &tmpS1, &S1); } mask >>= 1; } addmult(&a, &P1, -3041, &Q1, -52); // a <- -3041*P1 - 52*Q1 addmult(&b, &R1, -3041, &S1, -52); // b <- -3041*R1 - 52*S1 addmult(&Base1, &a, 27, &b, -928); // Base1 <- 27*a - 928*b addmult(&Base2, &a, -9, &b, -602); // Base2 <- -9*a - 602*b addmult(&Base3, &a, 25, &b, -2937); // Base3 <- 25*a - 2937*b addmult(&Base4, &a, -19, &b, 2746); // Base4 <- -19*a - 2746*b // a <- (value - Base1^3 - Base2^3 - Base3^3 - Base4^3)/(18*83) getSumOfCubes(); // tmpP1 = Base1^3 + Base2^3 + Base3^3 + Base4^3 BigIntSubt(&value, &tmpP1, &a); subtractdivide(&a, 0, 18 * 83); // Divide a by 18*83. multint(&tmpP1, &a, 10); // Base1 <- Base1 + 10*a BigIntAdd(&tmpP1, &Base1, &Base1); multint(&tmpP1, &a, -19); // Base2 <- Base2 - 19*a BigIntAdd(&tmpP1, &Base2, &Base2); multint(&tmpP1, &a, -24); // Base3 <- Base3 - 24*a BigIntAdd(&tmpP1, &Base3, &Base3); multint(&tmpP1, &a, 27); // Base4 <- Base4 + 27*a BigIntAdd(&tmpP1, &Base4, &Base4); } if (converted != 0) { BigIntNegate(&Base1, &Base1); BigIntNegate(&Base2, &Base2); BigIntNegate(&Base3, &Base3); BigIntNegate(&Base4, &Base4); } // Sort cubes SortBigIntegers(&Base1, &Base2); SortBigIntegers(&Base1, &Base3); SortBigIntegers(&Base1, &Base4); SortBigIntegers(&Base2, &Base3); SortBigIntegers(&Base2, &Base4); SortBigIntegers(&Base3, &Base4); // Validate getSumOfCubes(); // tmpP1 = Base1^3 - Base2^3 - Base3^3 - Base4^3 BigIntSubt(&tmpP1, pArgument, &tmpQ1); if (tmpQ1.nbrLimbs != 1 || tmpQ1.limbs[0].x != 0) { return 1; // Result does not validate. } return 0; }