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    <p>This seems like a good candidate for dynamic programming:</p> <pre><code>//int[,] discountTable = new int[NumItems][NumCoupons+1] // bestDiscount[i][c] means the best discount if you can spend c coupons on items 0..i int[,] bestDiscount = new int[NumItems][NumCoupons+1]; // the best discount for a set of one item is just use the all of the coupons on it for (int c=1; c&lt;=MaxNumCoupons; c++) bestDiscount[0, c] = discountTable[0, c]; // the best discount for [i, c] is spending x coupons on items 0..i-1, and c-x coupons on item i for (int i=1; i&lt;NumItems; i++) for (int c=1; c&lt;=NumCoupons; c++) for (int x=0; x&lt;c; x++) bestDiscount[i, c] = Math.Max(bestDiscount[i, c], bestDiscount[i-1, x] + discountTable[i, c-x]); </code></pre> <p>At the end of this, the best discount will be the highest value of bestDiscount[NumItems][x]. To rebuild the tree, follow the graph backwards:</p> <p>edit to add algorithm:</p> <pre><code>//int couponsLeft; for (int i=NumItems-1; i&gt;=0; i++) { int bestSpend = 0; for (int c=1; c&lt;=couponsLeft; c++) if (bestDiscount[i, couponsLeft - c] &gt; bestDiscount[i, couponsLeft - bestSpend]) bestSpend = c; if (i == NumItems - 1) Console.WriteLine("Had {0} coupons left over", bestSpend); else Console.WriteLine("Spent {0} coupons on item {1}", bestSpend, i+1); couponsLeft -= bestSpend; } Console.WriteLine("Spent {0} coupons on item 0", couponsLeft); </code></pre> <p>Storing the graph in your data structure is also a good way, but that was the way I had thought of.</p>
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    1. POWhat is the algorithm to determine the best way to distribute these coupons?
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    1. POWhat is the algorithm to determine the best way to distribute these coupons?
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    1. COCan you expand on "To rebuild the tree, follow the graph backwards"? I like the look of your approach, but I'm having trouble figuring out how best to save the actual distribution of coupons for the best discount value.
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    2. COHmm. Also, shouldn't that last term be "discountTable[i, c-x]" ?
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    3. COI went with this approach, changing bestDiscount from a simple int to a class which holds the value and the coupon distribution used to get to it.
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