《算法竞赛入门经典（第2版）》代码 Chapter 3

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后面有些习题不想做了，留着以后做吧。觉得进度好慢啊。

讲解代码

3.1s1 逆序输出

// 3.1s1#include<stdio.h>#define MAXN 105int a[MAXN];int main(){int x, n = 0;while(scanf("%d", &x) == 1){a[++n] = x; }for(int i = n; i > 1; i--){printf("%d ", a[i]);}printf("%d\n", a[1]);return 0;}

3.1s2 开灯问题

// 3.1s2#include <stdio.h>#include <string.h>#define MAXN 1010int a[MAXN]; int main(){int n, k, first = 1;memset(a, 0, sizeof(a));scanf("%d%d", &n, &k);for(int i = 1; i <= k; i ++){for(int j = 1; j <= n; j++){if(j%i == 0) a[j] = !a[j];}}for(int i = 1; i <= n; i++){if(a[i]){if(first){first = 0;}else{printf(" ");}printf("%d", i);}}printf("\n");return 0;}

3.1s3 蛇形填数

// 3.1s3#include <stdio.h>#include <string.h>#define MAXN 20int a[MAXN][MAXN];int main(){int n, x, y, tot = 0;scanf("%d", &n);memset(a, 0, sizeof(a));tot = a[x=0][y=n-1] = 1;while(tot < n*n){while(x+1<n && !a[x+1][y]) a[++x][y] = ++tot;while(y-1>=0 && !a[x][y-1]) a[x][--y] = ++tot;while(x-1>=0 && !a[x-1][y]) a[--x][y] = ++tot;while(y+1<n && !a[x][y+1]) a[x][++y] = ++tot;}for(x = 0; x < n; x++){for(y = 0; y < n; y++){printf("%3d", a[x][y]);}printf("\n");}return 0;}

3.2s1 竖式问题

// 3.2s1#include <stdio.h>#include <string.h>int main(){int count = 0;char s[20], buf[99];scanf("%s", &s);for(int abc = 111; abc <= 999; abc++){for(int de = 11; de <= 99; de++){int x = abc*(de%10), y = abc*(de/10), z = abc*de;sprintf(buf, "%d%d%d%d%d", abc, de, x, y, z);int ok = 1;for(int i = 0; i < strlen(buf); i++){if(strchr(s, buf[i]) == NULL) ok = 0;}if(ok){printf("<%d>\n", ++count);printf("%5d\nX%4d\n-----\n%5d\n%4d \n-----\n%5d\n\n", abc, de, x, y, z);}}} printf("The number of solutions = %d\n", count);return 0;}

例题代码

3-1 TeX中的引号（TeX Quotes, UVa 272）

// 3-1#include <stdio.h>int main(){int c, q = 1;while((c = getchar()) != EOF){if(c == '"'){printf("%s", q ? "“" : "”");q = !q;}else{printf("%c", c);}}return 0;}

3-2 WERTYU（WERTYU, UVa 10082）

// 3-2#include <stdio.h>char s[] = "`1234567890-=QWERTYUIOP[]\\ASDFGHJKL;'ZXCVBNM,./";int main(){int i, c;while((c = getchar()) != EOF){for(i = 1; s[i] && s[i]!=c; i++) {} if(s[i]) // 这点我不理解，但是可以推测出此条语句是在判断s[i]是否超出了字符串s的长度（即在不在字符串s中） {putchar(s[i-1]);}else{putchar(c);}}return 0;}

3-3 回文词（Palindromes, UVa 401）

// 3-3#include <stdio.h>#include <string.h>#include <ctype.h>const char* rev = "A   3  HIL JM O   2TUVWXY51SE Z  8 ";const char* msg[] = {"not a palindrom", "a regular palindrome", "a mirrored string", "a mirrored palindrome"};char r(char ch){if(isalpha(ch)){return rev[ch-'A'];}return rev[ch-'0'+25];}int main(){char s[30];while(scanf("%s", s) == 1){int len = strlen(s);int p = 1, m = 1;for(int i = 0; i < (len+1)/2; i++){if(s[i] != s[len-1-i]){p = 0; // 不是回文串 }if(r(s[i]) != s[len-1-i]){m = 0; // 不是镜像串 }}printf("%s -- is %s.\n\n", s, msg[m*2+p]); // 此处msg[]的设置挺巧妙，很简洁，值得借鉴 }return 0;}

3-4 猜数字游戏的提示（Master-Mind Hints, UVa 340）

// 3-4// 直接统计可得A，为了求B，对于每个数字（1~9），统计二者出现的次数c1和c2，则min(c1,c2)，就是该数字对B的贡献。最后要减去A的部分。 // 上面这句话不太好理解，好好想一想。 #include <stdio.h>#define MAXN 1010int main(){int n, a[MAXN], b[MAXN];int round = 0;while(scanf("%d", &n) == 1 && n){printf("Game %d:\n", ++round);for(int i = 0; i < n; i++){scanf("%d", &a[i]);}for(;;){int A = 0, B = 0;for(int i = 0; i < n; i++){scanf("%d", &b[i]);if(a[i] == b[i]){A++;}}if(b[0] == 0){break;}for(int d = 1; d <= 9; d++){int c1 = 0, c2 = 0;for(int i = 0; i < n; i++){if(a[i] == d) c1++;if(b[i] == d) c2++;}if(c1 < c2){B += c1;}else{B += c2;}}printf("    (%d, %d)\n", A, B-A);}} return 0;}

3-5 生成元（Digit Generator, ACM/ICPC Seoul 2005, UVa 1583）

#include <stdio.h>#include <string.h>#define MAXN 10005int ans[MAXN];int main(){int T, n;memset(ans, 0, sizeof(ans));for(int m = 1; m < MAXN ; m++){int x = m, y = m;while(x > 0){y += x%10;x /= 10; }if(ans[y] == 0 || m < ans[y]) // ans[i]是i的最小生成元 {ans[y] = m; }}scanf("%d", &T);while(T--) // T应该代表输入数据共有T组 {scanf("%d", &n);printf("%d\n", ans[n]); }return 0;}

3-6 环状序列（Circular Sequence, ACM/ICPC Seoul 2004, UVa 1584）

#include <stdio.h>#include <string.h>#define MAXN 105int less(const char* s, int p, int q){int n = strlen(s);for(int i = 0; i < n; i++){//if(s[(p+i)%n] < s[(q+i)%n])//return 1;// 上面的代码是不正确的，为什么？不解 if(s[(p+i)%n] != s[(q+i)%n])return s[(p+i)%n] < s[(q+i)%n];}return 0;}int main(){int T;char s[MAXN];scanf("%d", &T);while(T--){scanf("%s", s);int ans = 0;int n = strlen(s);for(int i = 1; i < n; i++){if(less(s, i, ans)) ans = i;}for(int i = 0; i < n; i++){putchar(s[(i+ans)%n]);}putchar('\n');}return 0;}

习题代码

t3-1 得分（Score, ACM/ICPC Seoul 2005, UVa 1585）

// t3-1#include <stdio.h>int main(){char a;int score = 0, nu = 0;while((a = getchar()) != '\n'){if(a == 'O'){score += ++nu;}else{nu = 0;}}printf("%d\n", score);return 0;}

t3-2 分子量（Molar Mass, ACM/ICPC Seoul 2007, UVa 1586）

// t3-2#include <stdio.h>#include <ctype.h>#define C 12.01#define H 1.008#define O 16.00#define N 14.01int main(){int n;char c;double sum = 0, mas;while((c = getchar()) && c != '\n'){if(isalpha(c)){if(c == 'C') mas = C;if(c == 'H') mas = H;if(c == 'O') mas = O;if(c == 'N') mas = N;n = 1;sum += mas;}else{n = c-'1';sum += mas*n;}}printf("%3fg/mol\n", sum);return 0;}

t3-3 数数字（Digit Counting, ACM/ICPC Danang 2007, UVa 1225）

// t3-3#include <stdio.h>#include <string.h>int main(){int num[10];char c;memset(num, 0, sizeof(num));while((c = getchar()) && c != '\n'){num[c-'0']++;}for(int i = 0; i < 9; i++){printf("%d ", num[i]);}printf("%d\n", num[9]);return 0;}

t3-4 周期串（Periodic Strings, UVa 455）

// t3-4 参考了别人的代码#include <stdio.h>#include <string.h>#define MAXN 105int main(){char s[MAXN];scanf("%s", s);int len = strlen(s);for(int i = 1; i < len; i++){int ok = 1;if(len%i == 0){for(int j = 1; j < len; j++){if(s[j] != s[j%i]){ok = 0;break;}}if(ok){printf("%d\n", i);break;}}}return 0;}