251211算法 搜索

问题 A: E001 数的划分

回溯

n里面拆i = 1...n/2 , n = i + ( n - i ) 第二层

n - i里面拆x = i... (n - i) / 2 , n - i = x + (n - i - x) 第三层

#include<iostream>
#include<string>
#include<algorithm>
using namespace std;
int cnt;//记录分法的全局变量
void backtracking(int depth,int start,int n,int k){
    //已经分出k份,增加一个分法
    if(depth == k){
        if(start <= n)cnt++;
        return;
    }
    //还没到，开始拆分
    for(int i = start;i <= n / 2;i++){ //for的动作代表不断拆不同的数
        depth++;//进入下一层拆分
        backtracking(depth,i,n - i,k);//开始拆更小的数n-i，从i开始拆
        depth--;//回溯到上一层，继续循环
    }
}
int main(){
    int n,k;
    while(scanf("%d%d",&n,&k) != EOF){
        cnt = 0;
        backtracking(1,1,n,k);//第一层，从1开始拆n
        printf("%d\n",cnt);
    }
}

动态规划

dp[i][j]含义：把数字i分成j份所得的划分总数。

dp数组初始化：dp[i][1] = 1; dp[0][j] = 0

递推公式：S[i][j]=s[i-1][j-1]+s[i-j][j]

推导：S[i][j]=s[i-j][1]+ s[i-j][2]+ s[i-j][3]+...+ s[i-j][j] 先分成j个1份，剩下的i-j分成1份+2份+...j份分法

S[i-1][j-1]=s[(i-1)-(j-1)][1]+ s[(i-1)-(j-1)][2]+...+s[(i-1)-(j-1)][j-1]

#include<iostream>
#include<string>
#include<algorithm>
using namespace std;
int dp[300][10] = {0};
int main(){
    int n,k;
    //初始化
    for(int i = 1;i <= 299;i++){
            dp[i][1] = 1;
        }
    while(scanf("%d%d",&n,&k) != EOF){

        for(int i = 1;i <= n;i++){
            for(int j = 2;j <= k;j++){
                if(i >= j)dp[i][j] = dp[i - 1][j - 1] + dp[i - j][j];
                else break;
            }
        }

        printf("%d\n",dp[n][k]);
    }

}

E002 闪避湖泊

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int dir[][2] = {
    {1,0},{-1,0},{0,-1},{0,1}
};

int graph[102][102] = {0};
int visit[102][102] = {0};
int maxsize = 0;
int mian = 0;
int n,m,k;

int bfs(int r,int c){
    if(r < 1 || r > n || c < 1 || c > m || visit[r][c]){
        return 0;
    }
    if(visit[r][c] || graph[r][c] == 0) return 0;

    visit[r][c] = 1;
    int ret = 1;
    for(int i = 0;i < 4;i++){

        ret += bfs(r + dir[i][0],c + dir[i][1]);
    }
    return ret;
}

int main(){

    while(scanf("%d%d%d",&n,&m,&k) != EOF){
        maxsize = 0;
        memset(graph,0,sizeof(graph));
        memset(visit,0,sizeof(visit));
        for(int i = 0;i < k;i++){
            int r,c;
            scanf("%d%d",&r,&c);
            graph[r][c] = 1;
        }
        for(int i = 1;i <= n;i++){
            for(int j = 1;j <= m;j++){
                if(graph[i][j] == 1 && visit[i][j] == 0){
                    maxsize = max(maxsize,bfs(i,j));
                }
            }
        }
        printf("%d\n",maxsize);

    }
}