C++——USACO Section 1.5 题解

Number Triangles

Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

          7        3   8      8   1   0    2   7   4   4  4   5   2   6   5

In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.

PROGRAM NAME: numtri

INPUT FORMAT

The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.

SAMPLE INPUT (file numtri.in)

573 88 1 02 7 4 44 5 2 6 5

OUTPUT FORMAT

A single line containing the largest sum using the traversal specified.

SAMPLE OUTPUT (file numtri.out)

30

#include<cstdio>int f[1001][1001],ans;inline int readint(){    int i=0;    char ch;    for(ch=getchar();ch<'0'||ch>'9';ch=getchar());    for(;ch>='0' && ch<='9';ch=getchar())        i=(i<<3)+(i<<1)+ch-'0';    return i;}int max(int a,int b){return a>b?a:b;}int main(){int n;n=readint();for(int i=1;i<=n;++i)for(int j=1;j<=i;++j)f[i][j]=readint();for(int i=1;i<=n;++i)for(int j=1;j<=i;++j)f[i][j]+=max(f[i-1][j-1],f[i-1][j]);for(int i=1;i<=n;++i) ans=max(ans,f[n][i]);int num=0;char c[12];do{c[++num]=(ans%10)+48;ans/=10;}while(ans);    while(num) putchar(c[num--]);    return 0;}

Prime Palindromes

The number 151 is a prime palindrome because it is both a prime number and a palindrome (it is the same number when read forward as backward). Write a program that finds all prime palindromes in the range of two supplied numbers a and b (5 <= a < b <= 100,000,000); both a and b are considered to be within the range .

PROGRAM NAME: pprime

INPUT FORMAT

Line 1:Two integers, a and b

SAMPLE INPUT (file pprime.in)

5 500

OUTPUT FORMAT

The list of palindromic primes in numerical order, one per line.

SAMPLE OUTPUT (file pprime.out)

5711101131151181191313353373383

#include <stdio.h>#include <string.h>#include <assert.h>#include <stdlib.h>FILE *fout;long a, b;intisprime(long n){    long i;    if(n == 2)return 1;    if(n%2 == 0)return 0;    for(i=3; i*i <= n; i+=2)if(n%i == 0)    return 0;    return 1;}voidgen(int i, int isodd){    char buf[30];    char *p, *q;    long n;    sprintf(buf, "%d", i);    p = buf+strlen(buf);    q = p - isodd;    while(q > buf)*p++ = *--q;    *p = '\0';    n = atol(buf);    if(a <= n && n <= b && isprime(n))fprintf(fout, "%ld\n", n);}voidgenoddeven(int lo, int hi){    int i;    for(i=lo; i<=hi; i++)        gen(i, 1);    for(i=lo; i<=hi; i++)        gen(i, 0);}voidgenerate(void){    genoddeven(1, 9);    genoddeven(10, 99);    genoddeven(100, 999);    genoddeven(1000, 9999);}voidmain(void){    FILE *fin;    fin = fopen("pprime.in", "r");    fout = fopen("pprime.out", "w");    assert(fin != NULL && fout != NULL);    fscanf(fin, "%ld %ld", &a, &b);    generate();    exit (0);}

Superprime Rib

Butchering Farmer John's cows always yields the best prime rib. You can tell prime ribs by looking at the digits lovingly stamped across them, one by one, by FJ and the USDA. Farmer John ensures that a purchaser of his prime ribs gets really prime ribs because when sliced from the right, the numbers on the ribs continue to stay prime right down to the last rib, e.g.:

     7  3  3  1

The set of ribs denoted by 7331 is prime; the three ribs 733 are prime; the two ribs 73 are prime, and, of course, the last rib, 7, is prime. The number 7331 is called a superprime of length 4.

Write a program that accepts a number N 1 <=N<=8 of ribs and prints all the superprimes of that length.

The number 1 (by itself) is not a prime number.

PROGRAM NAME: sprime

INPUT FORMAT

A single line with the number N.

SAMPLE INPUT (file sprime.in)

4

OUTPUT FORMAT

The superprime ribs of length N, printed in ascending order one per line.

SAMPLE OUTPUT (file sprime.out)

2333233923932399293931193137373337393793379759397193733173337393

#include <stdio.h>#include <stdlib.h>#include <string.h>#include <assert.h>FILE *fout;intisprime(int n){int i;if(n == 2)return 1;if(n%2 == 0)return 0;for(i=3; i*i <= n; i+=2)if(n%i == 0)return 0;return 1;}/* print all sprimes possible by adding ndigit digits to the number n */voidsprime(int n, int ndigit){if(ndigit == 0) {fprintf(fout, "%d\n", n);return;}n *= 10;if(isprime(n+1))sprime(n+1, ndigit-1);if(isprime(n+3))sprime(n+3, ndigit-1);if(isprime(n+7))sprime(n+7, ndigit-1);if(isprime(n+9))sprime(n+9, ndigit-1);}void main(void){int n;FILE *fin;fin = fopen("sprime.in", "r");assert(fin != NULL);fout = fopen("sprime.out", "w");assert(fout != NULL);fscanf(fin, "%d", &n);sprime(2, n-1);sprime(3, n-1);sprime(5, n-1);sprime(7, n-1);exit (0);}