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#include <stdio.h> |
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#include "utils.h" |
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#include <stdlib.h> |
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/*
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n! means n × (n − 1) × ... × 3 × 2 × 1 |
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For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, |
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and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. |
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Find the sum of the digits in the number 100! |
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https://projecteuler.net/problem=20
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*/ |
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int digitCount(int numb) { |
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int digitCount=1; |
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while (numb>=10) { |
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numb/=10; |
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digitCount++; |
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} |
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return digitCount; |
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} |
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char*numberToString(int numb) { |
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char*num=malloc(digitCount(numb)); |
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int counter=digitCount(numb)-1; |
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while (numb!=0) { |
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num[counter--]=(numb%10)+'0'; |
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numb/=10; |
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} |
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return num; |
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} |
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int main(int argc,char**argv) { |
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struct String factorialSum = {1,"1"}; |
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int counter=2; |
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while (counter<=100) { |
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factorialSum=mult(factorialSum,(struct String){digitCount(counter),numberToString(counter)}); |
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printf("%s\n",factorialSum.str); |
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counter++; |
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} |
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printf("%s",factorialSum.str); |
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int digitSum=0; |
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for (int i=0;i<factorialSum.length;i++) { |
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digitSum+=factorialSum.str[i]-'0'; |
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} |
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printf("\nThe sum of the digits are %d",digitSum); |
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return 0; |
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} |
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#include "utils.h" |
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#include <stdio.h> |
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#include <stdlib.h> |
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struct String mult(struct String numb1, struct String numb2) { |
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struct String n1 = numb1; |
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struct String n2 = numb2; |
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byte carryover = 0; |
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if (numb2.length>numb1.length) { |
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n1=numb2; |
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n2=numb1; |
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} |
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int addends[n2.length][n1.length+1]; |
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for (int i=0;i<n2.length;i++) { |
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for (int j=0;j<n1.length+1;j++) { |
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addends[i][j]=0; |
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} |
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} |
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for (int i=n2.length-1;i>=0;i--) { |
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carryover=0; |
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for (int j=n1.length-1;j>=0;j--) { |
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int mult = (n1.str[j]-'0')*(n2.str[i]-'0')+((carryover!=0)?carryover:0); |
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//printf(" %d/%d\n",mult,carryover);
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carryover=0; |
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if (mult>=10) { |
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carryover=mult/10; |
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mult=mult%10; |
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} |
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addends[(n2.length-1)-i][j+1]=mult; |
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} |
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if (carryover>0) { |
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addends[(n2.length-1)-i][0]=carryover; |
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} |
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} |
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//printIntDoubleArr(n2.length,n1.length+1,addends);
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struct String sum = {1,"0"}; |
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for (int i=0;i<n2.length;i++) { |
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char val[n1.length+1+i]; |
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for (int j=0;j<n1.length+1+i;j++) { |
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val[j]='0'; |
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} |
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for (int j=0;j<n1.length+1;j++) { |
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val[j]=addends[i][j]+'0'; |
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} |
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sum=add((struct String){n1.length+1+i,val},sum); |
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//printf("%s\n",sum.str);
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} |
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if (sum.str[0]=='0') { |
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char*newStr=malloc(sum.length-1); |
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for (int i=1;i<sum.length;i++) { |
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newStr[i-1]=sum.str[i]; |
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} |
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free(sum.str); |
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sum=(struct String){sum.length-1,newStr}; |
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} |
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//printf("%s",sum.str);
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return sum; |
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} |
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struct String add(struct String numb1, struct String numb2){ |
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//printf("%s %s\n",numb1.str,numb2.str);
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byte carryover=0; |
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int digitCount=0; |
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char*str = malloc(0); |
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if (numb1.length>=numb2.length) { |
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for (int offset=0;offset<numb1.length;offset++) { |
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str = realloc(str,++digitCount); |
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//printf("Digit count is now %d\n",digitCount);
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if (numb2.length>offset) { |
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//printf("%c %c\n",numb1.str[numb1.length-offset-1],numb2.str[numb2.length-offset-1]);
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int sum=((numb1.str[numb1.length-offset-1]-'0')+(numb2.str[numb2.length-offset-1]-'0'))+((carryover>0)?carryover--:0); |
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if (sum>=10) { |
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carryover=1; |
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sum-=10; |
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} |
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str[offset]=sum+'0'; |
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} else { |
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str[offset]=numb1.str[numb1.length-offset-1]+((carryover>0)?carryover--:0); |
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} |
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} |
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} else { |
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for (int offset=0;offset<numb2.length;offset++) { |
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str = realloc(str,++digitCount); |
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//printf("Digit count is now %d\n",digitCount);
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if (numb1.length>offset) { |
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//printf("%c %c\n",numb1.str[numb1.length-offset-1],numb2.str[numb2.length-offset-1]);
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int sum=((numb1.str[numb1.length-offset-1]-'0')+(numb2.str[numb2.length-offset-1]-'0'))+((carryover>0)?carryover--:0); |
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if (sum>=10) { |
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carryover=1; |
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sum-=10; |
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} |
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str[offset]=sum+'0'; |
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} else { |
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str[offset]=numb2.str[numb2.length-offset-1]+((carryover>0)?carryover--:0); |
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} |
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} |
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} |
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if (carryover>0) { |
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str = realloc(str,++digitCount); |
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str[digitCount-1]='1'; |
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} |
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for (int i=0;i<digitCount/2;i++) { |
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char c = str[i]; |
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char c2 = str[digitCount-i-1]; |
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str[digitCount-i-1]=c; |
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str[i]=c2; |
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} |
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struct String newStr = {digitCount,str}; |
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return newStr; |
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} |
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void printLongDoubleArr(int a,int b,long doubleArr[a][b]) { |
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for (int i=0;i<a;i++) { |
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for (int j=0;j<b;j++) { |
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printf("%ld\t",doubleArr[i][j]); |
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} |
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printf("\n"); |
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} |
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} |
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void printIntDoubleArr(int a,int b,int doubleArr[a][b]) { |
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for (int i=0;i<a;i++) { |
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for (int j=0;j<b;j++) { |
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printf("%d\t",doubleArr[i][j]); |
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} |
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printf("\n"); |
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} |
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} |
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@ -0,0 +1,12 @@ |
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#define true 1 |
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#define false 0 |
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#define boolean char |
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#define byte char |
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struct String{ |
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int length; |
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char*str; |
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}; |
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struct String add(struct String numb1, struct String numb2); |
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struct String mult(struct String numb1, struct String numb2); |
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void printLongDoubleArr(int a,int b,long doubleArr[a][b]); |
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void printIntDoubleArr(int a,int b,int doubleArr[a][b]); |
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