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Why is this memoization faster with an array than with a map?

I was solving combination sum IV on leetcode (#377), which reads:
"Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target."
I solved it in Java using a top down recursive approach with a memoization array:
public int combinationSum4(int[] nums, int target){
int[] memo = new int[target+1];
for(int i = 1; i < target+1; i++) {
memo[i] = -1;
}
memo[0] = 1;
return topDownCalc(nums, target, memo);
}
public static int topDownCalc(int[] nums, int target, int[] memo) {
if (memo[target] >= 0) {
return memo[target];
}
int tot = 0;
for(int num : nums) {
if(target - num >= 0) {
tot += topDownCalc(nums, target - num, memo);
}
}
memo[target] = tot;
return tot;
}
Then I figured I was wasting time by initializing the entire memo array and could just use a Map instead (which would also save space / memory). So I rewrote the code as follows:
public int combinationSum4(int[] nums, int target) {
Map<Integer, Integer> memo = new HashMap<Integer, Integer>();
memo.put(0, 1);
return topDownMapCalc(nums, target, memo);
}
public static int topDownMapCalc(int[] nums, int target, Map<Integer, Integer> memo) {
if (memo.containsKey(target)) {
return memo.get(target);
}
int tot = 0;
for(int num : nums) {
if(target - num >= 0) {
tot += topDownMapCalc(nums, target - num, memo);
}
}
memo.put(target, tot);
return tot;
}
I am confused though, because after submitting the second version of my code Leetcode said it was slower and used more space than the first code. How does the HashMap use more space and run slower than an array whos values all had to be initialized and whos length is greater than the HashMaps size?

Then I figured I was wasting time by initializing the entire memo array
You could have stored 'answer + 1' instead, so that the default value (0) can now be a placeholder for 'not calculated yet', and save that initialization. Not that it is expensive. Let's dig into cache pages.
Cache pages
CPUs are complex beasts. They don't operate on memory directly; not anymore. They literally cannot do it; the chip's calculating parts are simply not hooked up. at all. Instead, the CPU has caches, which come in set sizes (for example, 64k - you can't have a single cache node hold more or less than precisely 64k, and that entire 64k is then considered to be a cached copy of some 64k segment of main memory). One such node is called a cache page.
The CPU can only operate on cache pages.
In java, int[] leads to a contiguous, straight sized chunk of memory representing the data. In other words, an int[] x = new int[1000] would declare a single chunk of memory of 1000*4 = 4000 bytes (because ints are 4 bytes, and you reserved room for 1000 of em). That fits inside a single page. So, when you write your loop to initialize the values to -1, that's asking the CPU to loop through a single cache page and write some data to it. CPUs have pipelines and other speedup factors; this costs maybe 250 cycles.
Contrast to the cost of fetching a cache page: The CPU will be twiddling its thumbs (which is good; it can cool down some, and on modern hardware, often the CPU is limited not by its raw speed capabilities, but by the ability of the system to wick away the thermal impact of having it run! - it can also spend time on other threads/processes) whilst it farms out the job of fetching some chunk of memory into a cache page to the memory controller. Nevertheless, that thumb twiddling takes on the order of magnitude of 500 cycles or more. It's nice the CPU gets to cool down or focus on other things during it, but it's still the case that writing 4000 contiguous bytes in a tight loop is faster than a single cache miss.
Thus, 'fill a 1000-large int array with -1s' is an extremely cheap operation.
Wrapper objects
maps operate on objects, not ints, which is why you had to write Integer and not int. an Integer, in memory at least, is a much, much larger load on memory. It's an entire object, containing an int field. Then, your variable (or your map) holds a pointer to it.
So, an int[] x = new int[1000] takes 4000 bytes, plus some change for the object headers (maybe add 12 bytes to it all), and 1 reference (depends on VM, but let's say 64 bit), for a grand total of 4020 bytes.
In contrast,
Integer[] x = new Integer[1000];
for (int i = 0; i < 1000; i++) x[i] = i;`
is much, much larger. It's 1000 pointers (can be as large as 8 bytes per pointer, or as small as 4. So, 4000 to 8000 bytes), to 1000 separate integer objects. Each integer object gets the object overhead (~12 bytes or more), + 1 integer field, generally word-aligned (so, 64-bits, even though it's only 32-bit, assuming a 64-bit VM running on 64-bit hardware, which is going to be the case on anything modern), for another 20000 bytes. A grand total of something closer to 30000 bytes.
That is about 8x more memory required.
Then consider that the 'key' in your memoized array is inherent (it's the index into the array) whereas in the map the key needs separate storage and it gets worse still: Each k/v pair in your map occupies at least 12+12+8+8+8+8 bytes (2 object overheads and 2 int fields for your key and value Integer objects, and 2 pointers for the map to point at these), 56 bytes. In contrast to your int[] which does it in 4.
That gives you a rate of 56/4 = 14.
If your map contains only 1 in 14 numbers, then the map should be about as large as your array, because the map can do a thing your array can't: The array is as large as it has to be from the get-go, the map only needs to store required nodes.
Still, one would assume for most 'interesting' inputs, the coverage factor of that map is going to be far north of 7.14%, thus resulting in the map being larger.
The map also has its objects smeared out over memory which risks them being in more than one cache page: Large memory load + fragmentation = an easy road to having the CPU wait for multiple cache page fetches vs. being able to do all the work in one go, never having to wait for cache misses.
Can it be faster?
Yeah, probably - but with map occupancy rates at 10% or higher, the concept of using a map to save space is dubious. If you want to try, you'd need a map specifically designed to hold ints and nothing else. These do exist, such as eclipse collections' IntIntMap.
But I bet in this case the simple array memoization strategy is just the winner, even if you use IntIntMap.

These things came to my mind first:
HashMap is what the name implies, a hash-based map. Sowhenever you put something into it or get something out of it, it has to hash the key, then find the target based on that hash.
put() operation isn't just a walk in the park, either - you can check here to get an idea what it does. Definitely more than array assignment.
in java it doesn't work with primitives, so for each value you have to convert ints to Integers and vice versa. (as noted by others, there are int-specialized map alternatives available, but not in standard lib)
aaand since you're not initializing it, it might need to resize internally several times during your run - default size for a hashmap is just 16 - which is definitely more expensive then one-shot initialization you did with array. here's what each resizing does.
it also works with Entry objects that it needs for each internal entry it's got, and all those objects also take some space, plenty more than just having an array of integers
So I wouldn't think a hashmap would save you neither space or time. Why would it?

Java - Large array advice on how to break it down [duplicate]

I'm trying to find a counterexample to the Pólya Conjecture which will be somewhere in the 900 millions. I'm using a very efficient algorithm that doesn't even require any factorization (similar to a Sieve of Eratosthenes, but with even more information. So, a large array of ints is required.
The program is efficient and correct, but requires an array up to the x i want to check for (it checks all numbers from (2, x)). So, if the counterexample is in the 900 millions, I need an array that will be just as large. Java won't allow me anything over about 20 million. Is there anything I can possibly do to get an array that large?

You may want to extend the max size of the JVM Heap. You can do that with a command line option.
I believe it is -Xmx3600m (3600 megabytes)

Java arrays are indexed by int, so an array can't get larger than 2^31 (there are no unsigned ints). So, the maximum size of an array is 2147483648, which consumes (for a plain int[]) 8589934592 bytes (= 8GB).
Thus, the int-index is usually not a limitation, since you would run out of memory anyway.
In your algorithm, you should use a List (or a Map) as your data structure instead, and choose an implementation of List (or Map) that can grow beyond 2^31. This can get tricky, since the "usual" implementation ArrayList (and HashMap) uses arrays internally. You will have to implement a custom data structure; e.g. by using a 2-level array (a list/array). When you are at it, you can also try to pack the bits more tightly.

Java will allow up to 2 billions array entries. It’s your machine (and your limited memory) that can not handle such a large amount.

900 million 32 bit ints with no further overhead - and there will always be more overhead - would require a little over 3.35 GiB. The only way to get that much memory is with a 64 bit JVM (on a machine with at least 8 GB of RAM) or use some disk backed cache.

If you don't need it all loaded in memory at once, you could segment it into files and store on disk.

What do you mean by "won't allow". You probably getting an OutOfMemoryError, so add more memory with the -Xmx command line option.

You could define your own class which stores the data in a 2d array which would be closer to sqrt(n) by sqrt(n). Then use an index function to determine the two indices of the array. This can be extended to more dimensions, as needed.
The main problem you will run into is running out of RAM. If you approach this limit, you'll need to rethink your algorithm or consider external storage (ie a file or database).

If your algorithm allows it:
Compute it in slices which fit into memory.
You will have to redo the computation for each slice, but it will often be fast enough.
Use an array of a smaller numeric type such as byte.

Depending on how you need to access the array, you might find a RandomAccessFile will allow you to use a file which is larger than will fit in memory. However, the performance you get is very dependant on your access behaviour.

I wrote a version of the Sieve of Eratosthenes for Project Euler which worked on chunks of the search space at a time. It processes the first 1M integers (for example), but keeps each prime number it finds in a table. After you've iterated over all the primes found so far, the array is re-initialised and the primes found already are used to mark the array before looking for the next one.
The table maps a prime to its 'offset' from the start of the array for the next processing iteration.
This is similar in concept (if not in implementation) to the way functional programming languages perform lazy evaluation of lists (although in larger steps). Allocating all the memory up-front isn't necessary, since you're only interested in the parts of the array that pass your test for primeness. Keeping the non-primes hanging around isn't useful to you.
This method also provides memoisation for later iterations over prime numbers. It's faster than scanning your sparse sieve data structure looking for the ones every time.

I second #sfossen's idea and #Aaron Digulla. I'd go for disk access. If your algorithm can take in a List interface rather than a plain array, you could write an adapter from the List to the memory mapped file.

Use Tokyo Cabinet, Berkeley DB, or any other disk-based key-value store. They're faster than any conventional database but allow you to use the disk instead of memory.

could you get by with 900 million bits? (maybe stored as a byte array).

You can try splitting it up into multiple arrays.
for(int x = 0; x <= 1000000; x++){
myFirstList.add(x);
}
for(int x = 1000001; x <= 2000000; x++){
mySecondList.add(x);
}
then iterate over them.
for(int x: myFirstList){
for(int y: myFirstList){
//Remove multiples
}
}
//repeat for second list

Use a memory mapped file (Java 5 NIO package) instead. Or move the sieve into a small C library and use Java JNI.

fastest way to map a large number of longs

I'm writing a java application that transforms numbers (long) into a small set of result objects. This mapping process is very critical to the app's performance as it is needed very often.
public static Object computeResult(long input) {
Object result;
// ... calculate
return result;
}
There are about 150,000,000 different key objects, and about 3,000 distinct values.
The transformation from the input number (long) to the output (immutable object) can be computed by my algorithm with a speed of 4,000,000 transformations per second. (using 4 threads)
I would like to cache the mapping of the 150M different possible inputs to make the translation even faster but i found some difficulties creating such a cache:
public class Cache {
private static long[] sortedInputs; // 150M length
private static Object[] results; // 150M length
public static Object lookupCachedResult(long input) {
int index = Arrays.binarySearch(sortedInputs, input);
return results[index];
}
}
i tried to create two arrays with a length of 150M. the first array holds all possible input longs, and it is sorted numerically. the second array holds a reference to one of the 3000 distinct, precalculated result objects at the index corresponding to the first array's input.
to get to the cached result, i do a binary search for the input number on the first array. the cached result is then looked up in the second array at the same index.
sadly, this cache method is not faster than computing the results. not even half, only about 1.5M lookups per second. (also using 4 threads)
Can anyone think of a faster way to cache results in such a scenario?
I doubt there is a database engine that is able to answer more than 4,000,000 queries per second on, let's say an average workstation.

Hashing is the way to go here, but I would avoid using HashMap, as it only works with objects, i.e. must build a Long each time you insert a long, which can slow it down. Maybe this performance issue is not significant due to JIT, but I would recommend at least to try the following and measure performance against the HashMap-variant:
Save your longs in a long-array of some length n > 3000 and do the hashing by hand via a very simple hash-function (and thus efficient) like
index = key % n. Since you know your 3000 possible values before hand you can empirically find an array-length n such that this trivial hash-function won't cause collisions. So you circumvent rehashing etc. and have true O(1)-performance.
Secondly I would recommend you to look at Java-numerical libraries like
https://github.com/mikiobraun/jblas
https://github.com/fommil/matrix-toolkits-java
Both are backed by native Lapack and BLAS implementations that are usually highly optimized by very smart people. Maybe you can formulate your algorithm in terms of matrix/vector-algebra such that it computes the whole long-array at one time (or chunk-wise).

There are about 150,000,000 different key objects, and about 3,000 distinct values.
With the few values, you should ensure that they get re-used (unless they're pretty small objects). For this an Interner is perfect (though you can run your own).
i tried hashmap and treemap, both attempts ended in an outOfMemoryError.
There's a huge memory overhead for both of them. And there isn't much point is using a TreeMap as it uses a sort of binary search which you've already tried.
There are at least three implementations of a long-to-object-map available, google for "primitive collections". This should use slightly more memory than your two arrays. With hashing being usually O(1) (let's ignore the worst case as there's no reason for it to happen, is it?) and much better memory locality, it'll beat(*) your binary search by a factor of 20. You binary search needs log2(150e6), i.e., about 27 steps and hashing may need on the average maybe two. This depends on how tightly you pack the hash table; this is usually a parameter given when it gets created.
In case you run your own (which you most probably shouldn't), I'd suggest to use an array of size 1 << 28, i.e., 268435456 entries, so that you can use bitwise operations for indexing.
(*) Such predictions are hard, but I'm sure it's worth trying.

How to produce the cpu cache effect in C and java?

In Ulrich Drepper's paper What every programmer should know about memory, the 3rd part: CPU Caches, he shows a graph that shows the relationship between "working set" size and the cpu cycle consuming per operation (in this case, sequential reading). And there are two jumps in the graph which indicate the size of L1 cache and L2 cache. I wrote my own program to reproduce the effect in c. It just simply read a int[] array sequentially from head to tail, and I've tried different size of the array(from 1KB to 1MB). I plot the data into a graph and there is no jump, the graph is a straight line.
My questions are:
Is there something wrong with my method? What is the right way to produce the cpu cache effect(to see the jumps).
I was thinking, if it is sequential read, then it should operate like this:
When read the first element, it's a cache miss, and within the cache line size(64K), there will be hits. With the help of the prefetching, the latency of reading the next cache line will be hidden. It will contiguously read data into the L1 cache, even when the working set size is over the L1 cache size, it will evict the least recently used ones, and continue prefetch. So most of the cache misses will be hidden, the time consumed by fetch data from L2 will be hidden behind the reading activity, meaning they are operating at the same time. the assosiativity (8 way in my case) will hide the latency of reading data from L2. So, phenomenon of my program should be right, am I missing something?
Is it possible to get the same effect in java?
By the way, I am doing this in linux.
Edit 1
Thanks for Stephen C's suggestion, here are some additional Information:
This is my code:
int *arrayInt;
void initInt(long len) {
int i;
arrayInt = (int *)malloc(len * sizeof(int));
memset(arrayInt, 0, len * sizeof(int));
}
long sreadInt(long len) {
int sum = 0;
struct timespec tsStart, tsEnd;
initInt(len);
clock_gettime(CLOCK_REALTIME, &tsStart);
for(i = 0; i < len; i++) {
sum += arrayInt[i];
}
clock_gettime(CLOCK_REALTIME, &tsEnd);
free(arrayInt);
return (tsEnd.tv_nsec - tsStart.tv_nsec) / len;
}
In main() function, I've tried from 1KB to 100MB of the array size, still the same, average time consuming per element is 2 nanoseconds. I think the time is the access time of L1d.
My cache size:
L1d == 32k
L2 == 256k
L3 == 6144k
EDIT 2
I've changed my code to use a linked list.
// element type
struct l {
struct l *n;
long int pad[NPAD]; // the NPAD could be changed, in my case I set it to 1
};
struct l *array;
long globalSum;
// for init the array
void init(long len) {
long i, j;
struct l *ptr;
array = (struct l*)malloc(sizeof(struct l));
ptr = array;
for(j = 0; j < NPAD; j++) {
ptr->pad[j] = j;
}
ptr->n = NULL;
for(i = 1; i < len; i++) {
ptr->n = (struct l*)malloc(sizeof(struct l));
ptr = ptr->n;
for(j = 0; j < NPAD; j++) {
ptr->pad[j] = i + j;
}
ptr->n = NULL;
}
}
// for free the array when operation is done
void release() {
struct l *ptr = array;
struct l *tmp = NULL;
while(ptr) {
tmp = ptr;
ptr = ptr->n;
free(tmp);
}
}
double sread(long len) {
int i;
long sum = 0;
struct l *ptr;
struct timespec tsStart, tsEnd;
init(len);
ptr = array;
clock_gettime(CLOCK_REALTIME, &tsStart);
while(ptr) {
for(i = 0; i < NPAD; i++) {
sum += ptr->pad[i];
}
ptr = ptr->n;
}
clock_gettime(CLOCK_REALTIME, &tsEnd);
release();
globalSum += sum;
return (double)(tsEnd.tv_nsec - tsStart.tv_nsec) / (double)len;
}
At last, I will printf out the globalSum in order to avoid the compiler optimization. As you can see, it is still a sequential read, I've even tried up to 500MB of the array size, the average time per element is approximately 4 nanoseconds (maybe because it has to access the data 'pad' and the pointer 'n', two accesses), the same as 1KB of the array size. So, I think it is because the cache optimization like prefetch hide the latency very well, am I right? I will try a random access, and put the result on later.
EDIT 3
I've tried a random access to the linked list, this is the result:
the first red line is my L1 cache size, the second is L2. So we can see a little jump there. And some times the latency still be hidden well.

This answer isn't an answer, but more of a set of notes.
First, the CPU tends to operate on cache lines, not on individual bytes/words/dwords. This means that if you sequentially read/write an array of integers then the first access to a cache line may cause a cache miss but subsequent accesses to different integers in that same cache line won't. For 64-byte cache lines and 4-byte integers this means that you'd only get a cache miss once for every 16 accesses; which will dilute the results.
Second, the CPU has a "hardware pre-fetcher." If it detects that cache lines are being read sequentially, the hardware pre-fetcher will automatically pre-fetch cache lines it predicts will be needed next (in an attempt to fetch them into cache before they're needed).
Third, the CPU does other things (like "out of order execution") to hide fetch costs. The time difference (between cache hit and cache miss) that you can measure is the time that the CPU couldn't hide and not the total cost of the fetch.
These 3 things combined mean that; for sequentially reading an array of integers, it's likely that the CPU pre-fetches the next cache line while you're doing 16 reads from the previous cache line; and any cache miss costs won't be noticeable and may be entirely hidden. To prevent this; you'd want to "randomly" access each cache line once, to maximise the performance difference measured between "working set fits in cache/s" and "working set doesn't fit in cache/s."
Finally, there are other factors that may influence measurements. For example, for an OS that uses paging (e.g. Linux and almost all other modern OSs) there's a whole layer of caching above all this (TLBs/Translation Look-aside Buffers), and TLB misses once the working set gets beyond a certain size; which should be visible as a fourth "step" in the graph. There's also interference from the kernel (IRQs, page faults, task switches, multiple CPUs, etc); which might be visible as random static/error in the graph (unless tests are repeated often and outliers discarded). There are also artifacts of the cache design (cache associativity) that can reduce the effectiveness of the cache in ways that depend on the physical address/es allocated by the kernel; which might be seen as the "steps" in the graph shifting to different places.

Is there something wrong with my method?
Possibly, but without seeing your actual code that cannot be answered.
Your description of what your code is doing does not say whether you are reading the array once or many times.
The array may not be big enough ... depending on your hardware. (Don't some modern chips have a 3rd level cache of a few megabytes?)
In the Java case in particular you have to do lots of things the right way to implement a meaningful micro-benchmark.
In the C case:
You might try adjusting the C compiler's optimization switches.
Since your code is accessing the array serially, the compiler might be able to order the instructions so that the CPU can keep up, or the CPU might be optimistically prefetching or doing wide fetches. You could try reading the array elements in a less predictable order.
It is even possible that the compiler has entirely optimized the loop away because result of the loop calculation is not used for anything.
(According to this Q&A - How much time does it take to fetch one word from memory?, a fetch from L2 cache is ~7 nanoseconds and a fetch from main memory is ~100 nanoseconds. But you are getting ~2 nanoseconds. Something clever has to be going on here to make it run as fast as you are observing.)

With gcc-4.7 and compilation with gcc -std=c99 -O2 -S -D_GNU_SOURCE -fverbose-asm tcache.c you can see that the compiler is optimizing enough to remove the for loop (because sum is not used).
I had to improve your source code; some #include-s are missing, and i is not declared in the second function, so your example don't even compile as it is.
Make sum a global variable, or pass it somehow to the caller (perhaps with a global int globalsum; and putting globalsum=sum; after the loop).
And I am not sure you are right to clear the array with a memset. I could imagine a clever-enough compiler understanding that you are summing all zeros.
At last your code has extremely regular behavior with good locality: once in a while, a cache miss happens, the entire cache line is loaded and data is good enough for many iterations. Some clever optimizations (e.g. -O3 or better) might generate the good prefetch instructions. This is optimal for caches, because for a 32 words L1 cache line the cache miss happens every 32 loops so is well amortized.
Making a linked list of data will make cache behavior be worse. Conversely, in some real programs carefully adding a __builtin_prefetch at few well chosen places may improve performance by more than 10% (but adding too many of them will decrease performance).
In real life, the processor is spending the majority of the time to wait for some cache (and it is difficult to measure that; this waiting is CPU time, not idle time). Remember that during an L3 cache miss, the time needed to load data from your RAM module is the time needed to execute hundreds of machine instructions!

I can't say for certain about 1 and 2, but it would be more challenging to successfully run such a test in Java. In particular, I might be concerned that managed language features like automatic garbage collection might happen during the middle of your testing and throw off your results.

As you can see from graph 3.26 the Intel Core 2 shows hardly any jumps while reading (red line at the top of the graph). It is writing/copying where the jumps are clearly visible. Better to do a write test.

Java large datastructure for storing a matrix

I need to store a 2d matrix containing zip codes and the distance in km between each one of them. My client has an application that calculates the distances which are then stored in an Excel file. Currently, there are 952 places. So the matrix would have 952x952 = 906304 entries.
I tried to map this into a HashMap[Integer, Float]. The Integer is the hash code of the two Strings for two places, e.g. "A" and "B". The float value is the distance in km between them.
While filling in the data I run into OutOfMemoryExceptions after 205k entries. Do you have a tip how I can store this in a clever way? I even don't know if it's clever to have the whole bunch in memory. My options are SQL and MS Access...
The problem is that I need to access the data very quickly and possibly very often which is why I chose the HashMap because it runs in O(1) for the look up.
Thansk for your replies and suggestions!
Marco

A 2d array would be more memory efficient.
You can use a small hashmap to map the 952 places into a number between 0 and 951 .
Then, just do:
float[][] distances= new float[952][952];
To look things up, just use two hash lookups to convert the two places into two integers, and use them as indexes into the 2d array.
By doing it this way, you avoid the boxing of floats, and also the memory overhead of the large hashmap.
However, 906304 really isn't that many entries, you may just need to increase the Xmx maximum heap size

I would have thought that you could calculate the distances on the fly. Presumably someone has already done this, so you simply need to find out what algorithm they used, and the input data; e.g. longitude/latitude of the notional centres of each ZIP code.
EDIT: There are two commonly used algorithms for finding the (approximate) geodesic distance between two points given by longitude/latitude pairs.
The Vicenty formula is based on an ellipsoid approximation. It is more accurate, but more complicated to implement.
The Haversine formula is based on a spherical approximation. It is less accurate (0.3%), but simpler to implement.

Can you simply boost the memory available to the JVM ?
java -Xmx512m ...
By default the maximum memory configuration is 64Mb. Some more tuning tips here. If you can do this then you can keep the data in-process and maximise the performance (i.e. you don't need to calculate on the fly).

I upvoted Chi's and Benjamin's answers, because they're telling you what you need to do, but while I'm here, I'd like to stress that using the hashcode of the two strings directly will get you into trouble. You're likely to run into the problem of hash collisions.
This would not be a problem if you were concatenating the two strings (being careful to use a delimiter which cannot appear in the place designators), and letting HashMap do its magic, but the method you suggested, using the hashcodes for the two strings as a key, that's going to get you into trouble.

You will simply need more memory. When starting your Java process, kick it off like so:
java -Xmx256M MyClass
The -Xmx defines the max heap size, so this says the process can use up to 256 MB of memory for the heap. If you still run out, keep bumping that number up until you hit the physical limit.

Lately I've managed similar requisites for my master thesis.
I ended with a Matrix class that uses a double[], not a double[][], in order to alleviate double deref costs (data[i] that is an array, then array[i][j] that is a double) while allowing the VM to allocate a big, contiguous chunk of memory:
public class Matrix {
private final double data[];
private final int rows;
private final int columns;
public Matrix(int rows, int columns, double[][] initializer) {
this.rows = rows;
this.columns = columns;
this.data = new double[rows * columns];
int k = 0;
for (int i = 0; i < initializer.length; i++) {
System.arraycopy(initializer[i], 0, data, k, initializer[i].length);
k += initializer[i].length;
}
}
public Matrix set(int i, int j, double value) {
data[j + i * columns] = value;
return this;
}
public double get(int i, int j) {
return data[j + i * columns];
}
}
this class should use less memory than an HashMap since it uses a primitive array (no boxing needed): it needs only 906304 * 8 ~ 8 Mb (for doubles) or 906304 * 4 ~ 4 Mb (for floats). My 2 cents.
NB
I've omitted some sanity checks for simplicity's sake

Stephen C. has a good point: if the distances are as-the-crow-flies, then you could probably save memory by doing some calculations on the fly. All you'd need is space for the longitude and latitude for 952 zip codes and then you could use the vicenty formula to do your calculation when you need to. This would make your memory usage O(n) in zipcodes.
Of course, that solution makes some assumptions that may turn out to be false in your particular case, i.e. that you have longitude and latitude data for your zipcodes and that you're concerned with as-the-crow-flies distances and not something more complicated like driving directions.
If those assumptions are true though, trading a few computes for a whole bunch of memory might help you scale in the future if you ever need to handle a bigger dataset.

The above suggestions regarding heap size will be helpful. However, I am not sure if you gave an accurate description of the size of your matrix.
Suppose you have 4 locations. Then you need to assess the distances between A->B, A->C, A->D, B->C, B->D, C->D. This suggests six entries in your HashMap (4 choose 2).
That would lead me to believe the actual optimal size of your HashMap is (952 choose 2)=452,676; NOT 952x952=906,304.
This is all assuming, of course, that you only store one-way relationships (i.e. from A->B, but not from B->A, since that is redundant), which I would recommend since you are already experiencing problems with memory space.
Edit: Should have said that the size of your matrix is not optimal, rather than saying the description was not accurate.

Create a new class with 2 slots for location names. Have it always put the alphabetically first name in the first slot. Give it a proper equals and hashcode method. Give it a compareTo (e.g. order alphabetically by names). Throw them all in an array. Sort it.
Also, hash1 = hash2 does not imply object1 = object2. Don't ever do this. It's a hack.