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組合數學 POJ 1850 Code

2019-11-14 12:36:55
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Description

Transmitting and memorizing information is a task that requires different coding systems for the best use of the available space. A well known system is that one where a number is associated to a character sequence. It is considered that the Words are made only of small characters of the English alphabet a,b,c, …, z (26 characters). From all these words we consider only those whose letters are in lexigraphical order (each character is smaller than the next character).

The coding system works like this: ? The words are arranged in the increasing order of their length. ? The words with the same length are arranged in lexicographical order (the order from the dictionary). ? We codify these words by their numbering, starting with a, as follows: a - 1 b - 2 … z - 26 ab - 27 … az - 51 bc - 52 … vwxyz - 83681 …

Specify for a given word if it can be codified according to this coding system. For the affirmative case specify its code. Input

The only line contains a word. There are some constraints: ? The word is maximum 10 letters length ? The English alphabet has 26 characters. Output

The output will contain the code of the given word, or 0 if the word can not be codified. Sample Input

bf Sample Output

55

題目大意 符合題意的字符串要滿足位于后面字母比前面大的條件,輸入一個字符串,若不滿足該條件,輸出0,否則輸出按照排序系統該字符串之前有多少個字符串。

解題思路 符合答案的字符串包括兩種: 1、字符串長度小于輸入字符串長度。標記輸入字符串的長度為length,假設字符串為 i (i < length),則滿足條件的值為c[26][i],可以理解為該情況為從26個字母中選取 i 個,從小到大依次排列。 2、字符串長度等于輸入字符串長度。從左至右依次檢索,對于每一位 i 而言,該位字符的取值范圍應至少比前一位字符大一且小于當前字符,即 ch=[str[i-1]+1,str[i]);又因為該位字符之后剩余字符的取值范圍為 ‘z’-ch,剩余字符長度為 length-i-1,即滿足條件的值為 c[‘z’-ch][length-i-1]。

代碼實現

#include <iostream>#include<cstdio>#include<cstring>using namespace std;int c[27][27];void init(){ for(int i=0; i<=26; i++) { for(int j=0; j<=i; j++) { if(!j||i==j) c[i][j]=1; else c[i][j]=c[i-1][j]+c[i-1][j-1]; } }}int main(){ char str[11]; int sum=0; scanf("%s%*c",str); init(); int length=strlen(str); for(int i=0; i<length-2; i++) { if(str[i]>str[i+1]) {
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