基础知识去看B站视频
说明:
1、分治与递归的区别
分治法是指一种算法(分而治之,逐步细化地处理);
递归是指一种实现(函数中调用自身)
分治法也可以不用递归实现,比如自己用一个堆栈去模拟。
总之前者是思路,后者是做法。
我们做家务,也可以用分治法,我们管理一个组织,也可以用分治法,但是这就和编程完全无关了。
2、分治算法的应用:
快速排序等
关于视频中的例题,我的代码:
#include <iostream> using namespace std; int solve(int coin[],int low,int high){ int sumLeft = 0,sumRight = 0,sumMid = 0; int ans;//这里写ans是为了递归的最终(最外层函数)返回 if(low + 1 == high){ //说明分治到了最后还剩两个数组的元素 if(coin[low] > coin[high]){ ans = high + 1; return ans; }else{ ans = low + 1; return ans; } }else if((high - low + 1) % 2 == 0){ //说明元素数是偶数,分成左面一半和右面一半 //int sumLeft = 0,sumRight = 0; for(int i = low;i <= low + (high - low) / 2;i++){ sumLeft = sumLeft + coin[i]; } for(int i = low + (high - low) / 2 + 1;i <= high;i++){ sumRight = sumRight + coin[i]; } if(sumLeft < sumRight){ ans = solve(coin,low,low + (high - low) / 2); return ans; }else if(sumLeft > sumRight){ ans = solve(coin,low + (high - low) / 2 + 1,high); return ans; }else{ } }else{ //说明元素个数为奇数 for(int i = low; i <= low + (high - low) / 2 - 1; i++){ sumLeft = sumLeft + coin[i]; } for(int i = low + (high - low) / 2 + 1; i <= high; i++){ sumRight = sumRight + coin[i]; } sumMid = coin[low + (high - low) / 2]; if(sumLeft < sumRight){ ans = solve(coin,low,low + (high - low) / 2 - 1); return ans; }else if(sumLeft > sumRight){ ans = solve(coin,low + (high - low) / 2 + 1,high); return ans; }else{ } if(sumRight + sumMid == sumLeft + sumMid){ ans = low + (high - low) / 2 + 1; return ans; } } return ans; } int main(){ int coinNum = 0; cout << "请输入硬币数" << endl; cin >> coinNum; int coin[coinNum]; cout << "请依次输入" << coinNum << "个硬币的每个硬币的重量:" << endl; for(int i = 0;i < coinNum;i++){ cin >> coin[i]; } cout << "不合格的那枚硬币是第" << solve(coin,0,coinNum - 1) << "枚硬币" << endl; }