把所有的物品包装起来，但任一盒子都不能放置超过其容量的重物，使用尽量少的盒子

《数据结构与算法分析——c语言描述》 练习6.34 a b c  答案

毫无算法可言。不知道怎样用堆。。。最近事情真多，原来我想要的只是安安静静地写代码。

用了堆了。就是把盒子的容量放入堆中。

a

#include
#include
using namespace std;

#define MAXN 100


int w[MAXN];
int c;
int box[MAXN];

int main() {
	memset(box, 0, sizeof(box));
	scanf("%d", &c);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &w[i]);

	
	int boxCnt = 0;
	for (int i = 0; i < n; i++) {
		int j = 0;
		while ((c - box[j]) < w[i])
			j++;
		if (j > boxCnt)
			boxCnt = j;
		box[j] += w[i];
	}

	printf("%d", boxCnt+1);
}

b 堆版的，通过大堆来

leftheap.h

#ifndef _LeftHeap_H
#define _LeftHeap_H
typedef int ElementType;

struct TreeNode;
typedef struct TreeNode *PriorityQueue;

PriorityQueue initialize(void);
ElementType findMax(PriorityQueue h);
int isEmpty(PriorityQueue h);
PriorityQueue merge(PriorityQueue h1, PriorityQueue h2);
#define insert(X,H) (H=insert1((X),H))
PriorityQueue insert1(ElementType X, PriorityQueue h);
PriorityQueue deleteMax1(PriorityQueue h);
#define deleteMax(H) (H=deleteMax1(H))

#endif // !_BinHeap_H

leftheap.c

#include"leftheap.h"
#include"fatal.h"

struct TreeNode {
	ElementType element;
	PriorityQueue left;
	PriorityQueue right;
	int np1;
};

PriorityQueue initialize(void) {
	return NULL;
}

ElementType findMax(PriorityQueue h) {
	if (isEmpty(h))
		Error("EMPTY HEAP");
	return h->element;
}

int isEmpty(PriorityQueue h) {
	return h == NULL;
}


static PriorityQueue merge1(PriorityQueue h1, PriorityQueue h2) {
	if (h1->left == NULL) {
		h1->left = h2;
		return h1;
	}
	else {
		h1->right = merge(h1->right, h2);
		if (h1->right->np1 > h1->left->np1) {
			PriorityQueue temp;
			temp = h1->right;
			h1->right = h1->left;
			h1->left = temp;
		}
		h1->np1 = h1->right->np1 + 1;
		return h1;
	}
}

PriorityQueue merge(PriorityQueue h1, PriorityQueue h2) {
	if (h1 == NULL)
		return h2;
	else if (h2 == NULL)
		return h1;
	else {
		if (h1->element > h2->element)
			return merge1(h1, h2);
		else
			return merge1(h2, h1);
	}
}

PriorityQueue insert1(ElementType X, PriorityQueue h) {
	PriorityQueue newNode = malloc(sizeof(struct TreeNode));
	newNode->element = X;
	newNode->left = NULL;
	newNode->right = NULL;
	newNode->np1 = 0;
	return merge(newNode, h);
}

PriorityQueue deleteMax1(PriorityQueue h) {
	PriorityQueue temp1 = h->left;
	PriorityQueue temp2 = h->right;
	free(h);
	return merge(temp1, temp2);

}

main.c

#include
#include"leftheap.h"
#define MAXN 100


int w[MAXN];
int c;

int main() {
	scanf("%d", &c);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &w[i]);

	PriorityQueue h = initialize();

	int boxCnt = 0;
	for (int i = 0; i < n; i++) {
		int flag = 0;
		if (!isEmpty(h)) {
			int max = findMax(h);//最大盒子的容纳量
			if (max >= w[i]) {
				deleteMax(h);
				insert(max - w[i], h);
				flag = 1;
			}
		}
		if (!flag) {
			insert(c-w[i], h);
			boxCnt++;
		}
	}
	printf("%d", boxCnt );
}

b 数组版的

#include
#include
using namespace std;

#define MAXN 100


int w[MAXN];
int c;
int box[MAXN];

int main() {
	memset(box, 0, sizeof(box));
	scanf("%d", &c);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &w[i]);

	
	int boxCnt = 0;
	for (int i = 0; i < n; i++) {
		int j = 0;
		while (c - box[j] < w[i])
			j++;
		int maxPos = j;
		int max = c - box[j];
		for (int i = j+1; i <= boxCnt; i++) {
			if (c - box[i] > max) {
				maxPos = i;
				max = c - box[i];
			}
		}

		if (j > boxCnt)
			boxCnt = j;
		box[j] += w[i];
	}

	printf("%d", boxCnt+1);
}

c 堆版的

用的堆是小堆。

main.cpp

#include
#include"leftheap.h"
#define MAXN 100


int w[MAXN];
int c;

int main() {
	scanf("%d", &c);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &w[i]);

	PriorityQueue h = initialize();
	PriorityQueue h_temp = initialize();
	int boxCnt = 0;
	for (int i = 0; i < n; i++) {
		int flag = 0;
		if (!isEmpty(h)) {
			int min = findMin(h);//最大盒子的容纳量
			deleteMin(h);
			while (!isEmpty(h)&& min < w[i]) {
				insert(min, h_temp);
				min = findMin(h);
				deleteMin(h);
			}
			if (min >= w[i]) {
				insert(min - w[i], h);
				flag = 1;
			}
			h=merge(h, h_temp);
			h_temp = NULL;
		}
		if (!flag) {
			insert(c-w[i], h);
			boxCnt++;
		}
	}
	printf("%d", boxCnt );
}

c 数组版的

#include
#include
using namespace std;

#define MAXN 100


int w[MAXN];
int c;
int box[MAXN];

int main() {
	memset(box, 0, sizeof(box));
	scanf("%d", &c);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &w[i]);

	
	int boxCnt = 0;
	for (int i = 0; i < n; i++) {
		int j = 0;
		while (c - box[j] < w[i])
			j++;
		int minPos = j;
		int min = c - box[j];
		for (int i = j+1; i <= boxCnt; i++) {
			if (c - box[i]>=w[i] &&  c - box[i] < min) {
				minPos = i;
				min = c - box[i];
			}
		}

		if (j > boxCnt)
			boxCnt = j;
		box[j] += w[i];
	}

	printf("%d", boxCnt+1);
}