10334 solved

10334.cpp

@@ -0,0 +1,317 @@
+/*	bignum.c
+	Implementation of large integer arithmetic: addition, subtraction,
+		multiplication, and division.
+
+	begun: February 7, 2002
+	by: Steven Skiena
+*/
+
+/*
+Copyright 2003 by Steven S. Skiena; all rights reserved. 
+
+Permission is granted for use in non-commerical applications
+provided this copyright notice remains intact and unchanged.
+
+This program appears in my book:
+
+"Programming Challenges: The Programming Contest Training Manual"
+by Steven Skiena and Miguel Revilla, Springer-Verlag, New York 2003.
+
+See our website www.programming-challenges.com for additional information.
+
+This book can be ordered from Amazon.com at
+
+http://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo/
+
+*/
+
+
+#include <stdio.h>
+#include <iostream>
+#include <cstdlib>
+using namespace std;
+
+#define	MAXDIGITS	10000		/* maximum length bignum */ 
+
+#define PLUS		1		/* positive sign bit */
+#define MINUS		-1		/* negative sign bit */
+
+typedef struct {
+        char digits[MAXDIGITS];         /* represent the number */
+	int signbit;			/* 1 if positive, -1 if negative */ 
+        int lastdigit;			/* index of high-order digit */
+} bignum;
+
+
+void print_bignum(bignum*);
+void string_to_bignum(string, bignum*);
+void int_to_bignum(int, bignum*);
+void initialize_bignum(bignum*);
+int max(int, int);
+void add_bignum(bignum*, bignum*, bignum*);
+void subtract_bignum(bignum*, bignum*, bignum*);
+int compare_bignum(bignum*, bignum*);
+void zero_justify(bignum*);
+void digit_shift(bignum*, int);
+void multiply_bignum(bignum*, bignum*, bignum*);
+void divide_bignum(bignum*, bignum*, bignum*);
+
+
+void print_bignum(bignum *n)
+{
+	int i;
+
+	if (n->signbit == MINUS) printf("- ");
+	for (i=n->lastdigit; i>=0; i--)
+		printf("%c",'0'+ n->digits[i]);
+
+	printf("\n");
+}
+
+void string_to_bignum (string s, bignum* n) {
+	n->signbit = PLUS; // TODO: currently no negative numbers
+
+	for (int i = 0; i < MAXDIGITS; i++) n->digits[i] = (char) 0;
+
+	n->lastdigit = -1;
+
+	for (int i = s.size() - 1; i >= 0; i--) {
+		n->lastdigit++;
+		n->digits[n->lastdigit] = s[i] - 48;
+	}
+
+	if (s == "0") n->lastdigit = 0;
+}
+
+void int_to_bignum(int s, bignum *n)
+{
+	int i;				/* counter */
+	int t;				/* int to work with */
+
+	if (s >= 0) n->signbit = PLUS;
+	else n->signbit = MINUS;
+
+	for (i=0; i<MAXDIGITS; i++) n->digits[i] = (char) 0;
+
+	n->lastdigit = -1;
+
+	t = abs(s);
+
+	while (t > 0) {
+		n->lastdigit ++;
+		n->digits[ n->lastdigit ] = (t % 10);
+		t = t / 10;
+	}
+
+	if (s == 0) n->lastdigit = 0;
+}
+
+void initialize_bignum(bignum *n)
+{
+	int_to_bignum(0,n);
+}
+
+
+int max(int a, int b)
+{
+	if (a > b) return(a); else return(b);
+}
+
+/*	c = a +-/* b;	*/
+
+void add_bignum(bignum *a, bignum *b, bignum *c)
+{
+	int carry;			/* carry digit */
+	int i;				/* counter */
+
+	initialize_bignum(c);
+
+	if (a->signbit == b->signbit) c->signbit = a->signbit;
+	else {
+		if (a->signbit == MINUS) {
+			a->signbit = PLUS;
+			subtract_bignum(b,a,c);
+			a->signbit = MINUS;
+		} else {
+                        b->signbit = PLUS;
+                        subtract_bignum(a,b,c);
+                        b->signbit = MINUS;
+		}
+		return;
+	}
+
+	c->lastdigit = max(a->lastdigit,b->lastdigit)+1;
+	carry = 0;
+
+	for (i=0; i<=(c->lastdigit); i++) {
+		c->digits[i] = (char) (carry+a->digits[i]+b->digits[i]) % 10;
+		carry = (carry + a->digits[i] + b->digits[i]) / 10;
+	}
+
+	zero_justify(c);
+}
+
+
+void subtract_bignum(bignum *a, bignum *b, bignum *c)
+{
+	int borrow;			/* has anything been borrowed? */
+	int v;				/* placeholder digit */
+	int i;				/* counter */
+
+	initialize_bignum(c);
+
+	if ((a->signbit == MINUS) || (b->signbit == MINUS)) {
+                b->signbit = -1 * b->signbit;
+                add_bignum(a,b,c);
+                b->signbit = -1 * b->signbit;
+		return;
+        }
+
+	if (compare_bignum(a,b) == PLUS) {
+		subtract_bignum(b,a,c);
+		c->signbit = MINUS;
+		return;
+	}
+
+        c->lastdigit = max(a->lastdigit,b->lastdigit);
+        borrow = 0;
+
+        for (i=0; i<=(c->lastdigit); i++) {
+		v = (a->digits[i] - borrow - b->digits[i]);
+		if (a->digits[i] > 0)
+			borrow = 0;
+		if (v < 0) {
+			v = v + 10;
+			borrow = 1;
+		}
+
+                c->digits[i] = (char) v % 10;
+        }
+
+	zero_justify(c);
+}
+
+int compare_bignum(bignum *a, bignum *b)
+{
+	int i;				/* counter */
+
+	if ((a->signbit == MINUS) && (b->signbit == PLUS)) return(PLUS);
+	if ((a->signbit == PLUS) && (b->signbit == MINUS)) return(MINUS);
+
+	if (b->lastdigit > a->lastdigit) return (PLUS * a->signbit);
+	if (a->lastdigit > b->lastdigit) return (MINUS * a->signbit);
+
+	for (i = a->lastdigit; i>=0; i--) {
+		if (a->digits[i] > b->digits[i]) return(MINUS * a->signbit);
+		if (b->digits[i] > a->digits[i]) return(PLUS * a->signbit);
+	}
+
+	return(0);
+}
+
+void zero_justify(bignum *n)
+{
+	while ((n->lastdigit > 0) && (n->digits[ n->lastdigit ] == 0))
+		n->lastdigit --;
+
+        if ((n->lastdigit == 0) && (n->digits[0] == 0))
+		n->signbit = PLUS;	/* hack to avoid -0 */
+}
+
+
+void digit_shift(bignum *n, int d)		/* multiply n by 10^d */
+{
+	int i;				/* counter */
+
+	if ((n->lastdigit == 0) && (n->digits[0] == 0)) return;
+
+	for (i=n->lastdigit; i>=0; i--)
+		n->digits[i+d] = n->digits[i];
+
+	for (i=0; i<d; i++) n->digits[i] = 0;
+
+	n->lastdigit = n->lastdigit + d;
+}
+
+
+
+void multiply_bignum(bignum *a, bignum *b, bignum *c)
+{
+	bignum row;			/* represent shifted row */
+	bignum tmp;			/* placeholder bignum */
+	int i,j;			/* counters */
+
+	initialize_bignum(c);
+
+	row = *a;
+
+	for (i=0; i<=b->lastdigit; i++) {
+		for (j=1; j<=b->digits[i]; j++) {
+			add_bignum(c,&row,&tmp);
+			*c = tmp;
+		}
+		digit_shift(&row,1);
+	}
+
+	c->signbit = a->signbit * b->signbit;
+
+	zero_justify(c);
+}
+
+
+void divide_bignum(bignum *a, bignum *b, bignum *c)
+{
+        bignum row;                     /* represent shifted row */
+        bignum tmp;                     /* placeholder bignum */
+	int asign, bsign;		/* temporary signs */
+        int i,j;                        /* counters */
+
+	initialize_bignum(c);
+
+	c->signbit = a->signbit * b->signbit;
+
+	asign = a->signbit;
+	bsign = b->signbit;
+
+	a->signbit = PLUS;
+        b->signbit = PLUS;
+
+	initialize_bignum(&row);
+	initialize_bignum(&tmp);
+
+	c->lastdigit = a->lastdigit;
+
+	for (i=a->lastdigit; i>=0; i--) {
+		digit_shift(&row,1);
+		row.digits[0] = a->digits[i];
+		c->digits[i] = 0;
+		while (compare_bignum(&row,b) != PLUS) {
+			c->digits[i] ++;
+			subtract_bignum(&row,b,&tmp);
+			row = tmp;
+		}
+	}
+
+	zero_justify(c);
+
+	a->signbit = asign;
+	b->signbit = bsign;
+}
+
+int main (void) {
+	int n;
+	bignum *f = new bignum[5001];
+
+	int_to_bignum (1, &f[0]);
+	int_to_bignum (2, &f[1]);
+
+	for (int i = 2; i < 1001; i++) {
+		add_bignum (&f[i-2], &f[i-1], &f[i]);
+	}
+
+	while (cin >> n) {
+		print_bignum(&f[n]);
+	}
+
+	delete f;
+}